Can we train a 3D molecule generator using data from dense regions to generate samples in sparse regions? This challenge can be framed as an out-of-distribution (OOD) generation problem. While prior research on OOD generation predominantly targets property shifts, structural shifts, such as differences in molecular scaffolds or functional groups, represent an equally critical source of distributional shifts. This work introduces the Geometric OOD Diffusion Model (GODD), a novel diffusion-based framework that enables training on data-abundant molecular distributions while generalizing to data-scarce distributions under distributional structural shifts. Central to our approach is a designated equivariant asymmetric autoencoder to capture distributional structural priors. The asymmetric design allows the model to generalize to unseen structural variations by capturing distributional priors representing distinct distributions. The encoded structural-grained priors guide generation toward sparse regions without requiring explicit training on such data. Evaluated across standard benchmarks encompassing OOD structural shifts (e.g., scaffolds, rings), GODD achieves an improvement of 12.6% in success rate, defined based on molecular validity, uniqueness, and novelty. Furthermore, the framework demonstrates promising performance and generalization on canonical fragment-based drug design tasks, highlighting its utility in learning-based molecular discovery.

With the rise of 3D Gaussian Splatting (3DGS), a variety of digital watermarking techniques, embedding either 1D bitstreams or 2D images, are used for copyright protection. However, the robustness of these watermarking techniques against potential attacks remains underexplored. This paper introduces the first universal black-box attack framework, the Group-based Multi-objective Evolutionary Attack (GMEA), designed to challenge these watermarking systems. We formulate the attack as a large-scale multi-objective optimization problem, balancing watermark removal with visual quality. In a black-box setting, we introduce an indirect objective function that blinds the watermark detector by minimizing the standard deviation of features extracted by a convolutional network, thus rendering the feature maps uninformative. To manage the vast search space of 3DGS models, we employ a group-based optimization strategy to partition the model into multiple, independent sub-optimization problems. Experiments demonstrate that our framework effectively removes both 1D and 2D watermarks from mainstream 3DGS watermarking methods while maintaining high visual fidelity. This work reveals critical vulnerabilities in existing 3DGS copyright protection schemes and calls for the development of more robust watermarking systems.

Pretrained large language models (LLMs) are typically reused as indivisible artifacts, adapted, merged, or ensembled as a whole.In this study, we show that LLMs can instead be structurally recomposed as modular building blocks to create new architectures without access to original training data.We introduce architecturelevel reassembly as a new reuse paradigm, in which Transformer blocks from heterogeneous models are treated as reusable components.This idea is formalized through a twodimensional reassembly space that supports both vertical recombination across depth and horizontal composition within layers.To make this space tractable, we propose a chromosomebased architectural encoding and perform a bilevel multi-objective evolutionary optimization over vertical structure and horizontal composition.To resolve representation incompatibility across heterogeneous blocks, we introduce lightweight glue layers trained via data-free knowledge distillation, enabling valid information flow without modifying pretrained parameters.Our results demonstrate that architecturelevel reassembly unlocks a new dimension of flexibility in model reuse, pointing toward a modular and evolutionary view of LLM design.

Providing explainable molecular property predictions is critical for many scientific domains, such as drug discovery and material science. Though transformer-based language models have shown great potential in accurate molecular property prediction, they neither provide chemically meaningful explanations nor faithfully reveal the molecular structure-property relationships. In this work, we develop a framework for explainable molecular property prediction based on language models, dubbed as Lamole, which can provide chemical concepts-aligned explanations. We take a string-based molecular representation - Group SELFIES - as input tokens to pre-train and fine-tune our Lamole, as it provides chemically meaningful semantics. By disentangling the information flows of Lamole, we propose considering both self-attention weights and gradients for better quantification of each chemically meaningful substructure's impact on the model's output. To make the explanations more faithful to the structure-property relationship, we then carefully craft a marginal loss to explicitly optimize the explanations to align with the chemists' annotations. We bridge the manifold hypothesis with the elaborated marginal loss to prove that the loss can align the explanations with the tangent space of the data manifold, leading to concept-aligned explanations. Experimental results over eight datasets demonstrate Lamole can achieve comparable prediction accuracy and boost the explanation accuracy by up to 14.3%, being the state-of-the-art in explainable molecular property prediction. To further illustrate the actionable utility of the explanations derived from Lamole, we integrated the framework with an evolutionary algorithm. This integration established an interpretable optimization pipeline for molecular editing, demonstrating that Lamole functions beyond simple post-hoc analysis but serves as a practical guide for molecule discovery.

Neural Architecture Search (NAS) has emerged as a crucial method for automating the design of deep learning models. Despite its potential, NAS frequently requires substantial computational and hardware resources. To mitigate these challenges, transferable NAS (TNAS) has been introduced, leveraging prior NAS results to enhance performance on new tasks. However, existing methods largely focus on knowledge transfer within identical neural search spaces, overlooking the potential for cross-domain transferability. Motivated by this gap, we explore evolutionary TNAS across heterogeneous search spaces by learning common neural representations. In particular, we introduce a novel approach that encodes both operational and topological information of neural architectures into a unified sequence using a simple tokenizer. This sequence is then processed by a variational auto-encoder, with a Transformer-based encoder to capture rich neural representations and a decoder that reconstructs the original sequence. By utilizing these latent representations, we further establish an inter-domain mapping that acts as a bridge, enabling effective explicit solution transfer among diverse search spaces to enhance the evolutionary NAS process. To harness this capability, we develop an evolutionary sequential transfer optimization approach that transfers knowledge during population initialization, providing both flexibility and adaptability. To the best of our knowledge, this work serves as the first attempt in the literature exploring evolutionary TNAS across diverse spaces. Moreover, we demonstrate the utility of our method through comprehensive empirical studies using different architecture spaces, including NAS-Bench-101, NAS-Bench-201, and the DARTS search space. Our results show that the proposed method significantly enhances the adaptability and performance of NAS across varied domains.

Multi-objective optimization problems (MOPs) are ubiquitous in real-world applications, presenting a complex challenge of balancing multiple conflicting objectives. Traditional multi-objective evolutionary algorithms (MOEAs), though effective, often rely on domain-specific expertise for improved optimization performance, hindering adaptability to unseen MOPs. In recent years, the Large Language Models (LLMs) has revolutionized software engineering by enabling the autonomous generation and refinement of programs. Leveraging this breakthrough, we propose a new LLM-based framework that autonomously designs MOEAs for solving MOPs. The proposed framework includes a robust testing module to refine the generated MOEA through error-driven dialogue with LLMs, a dynamic selection strategy along with informative prompting-based crossover and mutation to fit textual optimization pipeline. Our approach facilitates the design of MOEA without the extensive demands for expert intervention, thereby speeding up the innovation of MOEA. Empirical studies across various MOP categories validate the robustness and superior performance of our proposed framework.

In this survey, we introduce Meta-Black-Box-Optimization (MetaBBO) as an emerging avenue within the Evolutionary Computation (EC) community, which incorporates Meta-learning approaches to assist automated algorithm design. Despite the success of MetaBBO, the current literature provides insufficient summaries of its key aspects and lacks practical guidance for implementation. To bridge this gap, we offer a comprehensive review of recent advances in MetaBBO, providing an in-depth examination of its key developments. We begin with a unified definition of the MetaBBO paradigm, followed by a systematic taxonomy of various algorithm design tasks, including algorithm selection, algorithm configuration, solution manipulation, and algorithm generation. Further, we conceptually summarize different learning methodologies behind current MetaBBO works, including reinforcement learning, supervised learning, neuroevolution, and in-context learning with Large Language Models. A comprehensive evaluation of the latest representative MetaBBO methods is then carried out, alongside an experimental analysis of their optimization performance, computational efficiency, and generalization ability. Based on the evaluation results, we meticulously identify a set of core designs that enhance the generalization and learning effectiveness of MetaBBO. Finally, we outline the vision for the field by providing insight into the latest trends and potential future directions. Relevant literature will be continuously collected and updated at https://github.com/MetaEvo/Awesome-MetaBBO.

Despite the popularity of graph neural networks, perturbed graph data is still a serious threat towards its inherent vulnerabilities. Adversarial examples can still easily manipulate the output of graph neural networks across various attack scenarios. Meanwhile, attacks on graph networks also appear to be crucial, as it can help model designers enhance the robustness of their models. In this study, we propose a sensitivity-oriented poisoning attack for self-supervised graph embedding models through bilevel optimization, which employs different optimization methods at each level. In addition, in order to improve attack effectiveness, we analyze graph structure to identify sensitive nodes and edges that guide attack directions, combining gradient-based and query-based methods to target both edge connections and node attributes. Besides, according to the defects of existing graph masked auto-encoders models, we design the feature sensitivity and feature variance to reduce the feature differentiability, which impairs the performance of the downstream model. Ablation studies validate our operator is effective on three citation datasets. And benchmark-based experiments support the effectiveness of our method on three different graph tasks. Specifically, our approach can achieve an average reduction of 3% in the accuracy of node classification compared to existing methods for attacking neural structures alone. For attacking both graph structures and attributes, our model has even achieved an average reduction of 4.5% for the node classification task, outperforming the existing methods.

Functional MRI (fMRI) and single-cell transcriptomics are pivotal in Alzheimer's disease (AD) research, each providing unique insights into neural function and molecular mechanisms. However, integrating these complementary modalities remains largely unexplored. Here, we introduce scBIT, a novel method for enhancing AD prediction by combining fMRI with single-nucleus RNA (snRNA). scBIT leverages snRNA as an auxiliary modality, significantly improving fMRI-based prediction models and providing comprehensive interpretability. It employs a sampling strategy to segment snRNA data into cell-type-specific gene networks and utilizes a self-explainable graph neural network to extract critical subgraphs. Additionally, we use demographic and genetic similarities to pair snRNA and fMRI data across individuals, enabling robust cross-modal learning. Extensive experiments validate scBIT's effectiveness in revealing intricate brain region-gene associations and enhancing diagnostic prediction accuracy. By advancing brain imaging transcriptomics to the single-cell level, scBIT sheds new light on biomarker discovery in AD research. Experimental results show that incorporating snRNA data into the scBIT model significantly boosts accuracy, improving binary classification by 3.39% and five-class classification by 26.59%. The codes were implemented in Python and have been released on GitHub (https://github.com/77YQ77/scBIT) and Zenodo (https://zenodo.org/records/11599030) with detailed instructions.

Transfer reinforcement learning (TRL) aims to boost the efficiency of reinforcement learning (RL) agents by leveraging knowledge from related tasks. Prior research primarily focuses on intradomain transfer, overlooking the complexities of transferring knowledge across tasks with differing state and action spaces. Recent efforts in cross-domain TRL aim to bridge this gap by establishing mappings between disparate source and target spaces, thereby enabling knowledge transfer across RL tasks with varied state and action configurations. However, existing studies often rely on strict prior assumptions about the relationships between state spaces, which limits their practical generality. In this article, we propose a novel approach to cross-domain TRL based on seeded graph matching, which enables alignment between source and target tasks regardless of differences in their state-action spaces. In particular, we model RL tasks as directed graphs, identify seed node pairs based on common RL properties, and devise a graph matching algorithm to align the source and target tasks by leveraging their structural characteristics. Building on this alignment, we introduce a policy-based transfer algorithm that improves the performance of the target RL task as its RL process progresses. Finally, we conduct comprehensive empirical studies on both discrete and continuous tasks with diverse state-action spaces. The experimental results validate the effectiveness of the proposed algorithm.

Multiphysics simulation aims to predict and understand interactions between multiple physical phenomena, aiding in comprehending natural processes and guiding engineering design. The system of Partial Differential Equations (PDEs) is crucial for representing these physical fields, and solving these PDEs is fundamental to such simulations. However, current methods primarily yield numerical outputs, limiting interpretability and generalizability. We introduce T-NNGP, a hybrid genetic programming algorithm that integrates traditional numerical methods with deep learning to derive approximate symbolic expressions for multiple unknown functions within a system of PDEs. T-NNGP initially obtains numerical solutions using traditional methods, then generates candidate symbolic expressions via deep reinforcement learning, and finally optimizes these expressions using genetic programming. Furthermore, a universal decoupling strategy guides the search direction and addresses coupling problems, thereby accelerating the search process. Experimental results on three types of PDEs demonstrate that our method can reliably obtain human-understandable symbolic expressions that fit both the PDEs and the numerical solutions from traditional methods. This work advances multiphysics simulation by enhancing our ability to derive approximate symbolic solutions for PDEs, thereby improving our understanding of complex physical phenomena.

Transferable neural architecture search (TNAS) has been introduced to design efficient neural architectures for multiple tasks, to enhance the practical applicability of NAS in real-world scenarios. In TNAS, architectural knowledge accumulated in previous search processes is reused to warm up the architecture search for new tasks. However, existing TNAS methods still search in an extensive search space, necessitating the evaluation of numerous architectures. To overcome this challenge, this work proposes a novel transfer paradigm, i.e., design principle transfer. In this work, the linguistic description of various structural components' effects on architectural performance is termed design principles. They are learned from established architectures and then can be reused to reduce the search space tasks by discarding unpromising architectures. Searching in the refined search space can boost both the search performance and efficiency for new NAS tasks. To this end, a large language model (LLM)-assisted design principle transfer (LAPT) framework is devised. In LAPT, LLM is applied to automatically reason the design principles from a set of given architectures, and then a principle adaptation method is applied to refine these principles progressively based on the search results. Experimental results demonstrate that LAPT can beat the state-of-the-art TNAS methods on most tasks and achieve comparable performance on the remainder.

Partial differential equations (PDEs) are fundamental in various scientific and engineering fields. Methods based on symbolic regression to solve PDEs have gained attention due to their inherent interpretability. However, existing symbolic regression methods rely solely on genetic programming (GP) during the search process, which presents opportunities for improvement in both precision and stability. We introduce a novel framework, itemd NetGP, which enhances symbolic regression for PDEs in three key aspects. First, NetGP employs prefix notation arrays to represent symbolic expressions, simplifying the evaluation process. Second, to improve the stability of the evolutionary process, deep reinforcement learning is integrated to generate new individuals. Additionally, a novel operator is proposed to avoid the generation of invalid expressions during crossover and mutation of array-based individuals. Empirical evaluations across five types of PDEs demonstrate that NetGP achieves outstanding accuracy and stability in solving these PDEs. The code can be found at https://github.com/grassdeerdeer/NetGP.

The design of new crystal materials is of significant scientific importance to society. In recent years, machine learning-based approaches have shown their potential in crystal material design. However, their effectiveness relies heavily on the availability of high-quality and extensive training data, which is difficult to collect in practice. To this end, this paper presents a novel physics-informed evolutionary transfer optimization framework that can design new crystal materials without the need for extensive data. Specifically, we first propose a novel physics-informed encoding for materials, enabling the use of multi-objective evolutionary optimization to simultaneously optimize multiple physical objectives, including the validity, properties, and energy of crystal materials. These physical objectives are critical to the effective design of crystal materials. Additionally, to mitigate the slow optimization speed of evolutionary computation, we propose a physics-informed evolutionary transfer optimization technique to enhance the design speed of optimized materials. We conducted comprehensive experiments to analyze the designed crystals from the perspectives of validity, density functional theory (DFT) validation, formation energy, and energy above hull. The experimental results validate the immense potential of the proposed physics-informed multi-objective evolutionary optimization framework in crystal material design.

Evolutionary transfer optimization (ETO) has been gaining popularity in research over the years due to its outstanding knowledge transfer ability to address various challenges in optimization. However, a pressing issue in this field is that the invention of new ETO algorithms has far outpaced the development of fundamental theories needed to clearly understand the key factors contributing to the success of these algorithms for effective generalization. In response to this challenge, this study aims to establish theoretical foundations for analogy-based ETO, specifically to support various algorithms that frequently reference a key concept known as similarity. First, we introduce analogical reasoning and link its subprocesses to three key issues in ETO. Then, we develop theories for analogy-based knowledge transfer, rooted in the principles that underlie the subprocesses. Afterwards, we present two theorems related to the performance gain of analogy-based knowledge transfer, namely unconditionally nonnegative performance gain and conditionally positive performance gain, to theoretically demonstrate the effectiveness of various analogy-based ETO methods. Last but not least, we offer a novel insight into analogy-based ETO that interprets its conditional superiority over traditional evolutionary optimization through the lens of the no free lunch theorem for optimization.

Temporal processing is vital for extracting meaningful information from time-varying signals. Recent advancements in Spiking Neural Networks (SNNs) have shown immense promise in efficiently processing these signals. However, progress in this field has been impeded by the lack of effective and standardized benchmarks, which complicates the consistent measurement of technological advancements and limits the practical applicability of SNNs. To bridge this gap, we introduce the Neuromorphic Sequential Arena (NSA), a comprehensive benchmark that offers an effective, versatile, and application-oriented evaluation framework for neuromorphic temporal processing. The NSA includes seven real-world temporal processing tasks from a diverse range of application scenarios, each capturing rich temporal dynamics across multiple timescales. Utilizing NSA, we conduct extensive comparisons of recently introduced spiking neuron models and neural architectures, presenting comprehensive baselines in terms of task performance, training speed, memory usage, and energy efficiency. Our findings emphasize an urgent need for efficient SNN designs that can consistently deliver high performance across tasks with varying temporal complexities while maintaining low computational costs. NSA enables systematic tracking of advancements in neuromorphic algorithm research and paves the way for developing effective and efficient neuromorphic temporal processing systems.

Neuroimaging analysis aims to reveal the information-processing mechanisms of the human brain in a noninvasive manner. In the past, graph neural networks (GNNs) have shown promise in capturing the non-Euclidean structure of brain networks. However, existing neuroimaging studies focused primarily on spatial functional connectivity, despite temporal dynamics in complex brain networks. To address this gap, we propose a spatio-temporal interactive graph representation framework (STIGR) for dynamic neuroimaging analysis that encompasses different aspects from classification and regression tasks to interpretation tasks. STIGR leverages a dynamic adaptive-neighbor graph convolution network to capture the interrelationships between spatial and temporal dynamics. To address the limited global scope in graph convolutions, a self-attention module based on Transformers is introduced to extract long-term dependencies. Contrastive learning is used to adaptively contrast similarities between adjacent scanning windows, modeling cross-temporal correlations in dynamic graphs. Extensive experiments on six public neuroimaging datasets demonstrate the competitive performance of STIGR across different platforms, achieving state-of-the-art results in classification and regression tasks. The proposed framework enables the detection of remarkable temporal association patterns between regions of interest based on sequential neuroimaging signals, offering medical professionals a versatile and interpretable tool for exploring task-specific neurological patterns. Our codes and models are available at https://github.com/77YQ77/STIGR/.

Evolutionary multitasking (EMT) is an emerging approach for solving multitask optimization problems (MTOPs) and has garnered considerable research interest. The implicit EMT is a significant research branch that utilizes evolution operators to enable knowledge transfer (KT) between tasks. However, current approaches in implicit EMT face challenges in adaptability, due to the limited use of different evolution operators with different parameter settings and insufficient utilization of evolutionary states for performing KT. This results in suboptimal exploitation of implicit KT's potential to tackle a variety of MTOPs. To overcome these limitations, we propose a novel learning-to-transfer (L2T) framework to automatically discover efficient KT policies for the MTOPs at hand. Our framework conceptualizes the KT process as a learning agent's sequence of strategic decisions within the EMT process. We propose an action formulation for deciding when and how to transfer, a state representation with informative features of evolution states, a reward formulation concerning convergence and transfer efficiency gain, and the environment for the agent to interact with MTOPs. We employ an actor-critic network structure for the agent and learn the policy via proximal policy optimization. This learned agent can be integrated with various evolutionary algorithms, enhancing their ability to address unseen MTOPs. Comprehensive empirical studies on both synthetic and real-world MTOPs, encompassing diverse intertask relationships, function classes, and task distributions are conducted to validate the proposed L2T framework. The results show a marked improvement in the adaptability and performance of implicit EMT when solving a wide spectrum of unseen MTOPs.

Despite the increasing interest in sequential transfer optimization (STO), a comprehensive benchmark suite for systematically comparing various STO algorithms remains underexplored. Existing test problems, which are often manually configured and lack scalability, can result in biased and nongeneralizable algorithm performance. In light of the above, we first introduce four concepts for characterizing STO problems (STOPs) in this study and present an important feature, namely similarity distribution, to quantitatively delineate the relationship between the optimal solutions of source and target tasks. Subsequently, we present general design guidelines for STOPs and introduce a problem generator that demonstrates strong scalability. Specifically, the similarity distribution of a problem can be easily customized through a novel inverse generation strategy, allowing for a continuous spectrum that captures the diverse similarity relationships present in real-world scenarios. Lastly, a benchmark suite comprising 12 STOPs, characterized by a range of customized similarity relationships, has been developed using the proposed generator and will serve as a platform for examining various STO algorithms. For instance, biased transferability representation, irregular mapping learning behaviors, and performance improvements unrelated to search experience are significant empirical findings that previous benchmarks failed to reveal, yet can be effectively identified through our test problems. The source code of the proposed problem generator is available at https://github.com/XmingHsueh/STOP-G.

Evolutionary sequential transfer optimization (ESTO), which aims to better optimize a target task using the knowledge extracted from a number of previously solved source tasks, has been gaining continually increasing research attention over the years. Particularly, solution-based ESTO (S-ESTO) that transfers task solutions has been receiving much popularity due to its ease of implementation and optimizer independency. However, the existing S-ESTO algorithms put much emphasis on utilizing source optimized solutions standing for global search experience without being aware of the potential of intermediate solutions that represent local optimization experience. Besides, most of them cannot take full advantage of the solution data from evolutionary search. In the light of the above, this study aims to develop a global and local search experience-based solution transfer technique to maximally release the potential of optimization experience hidden in the source tasks. First, a novel transferability metric named landscape encoding-based rank correlation (LERC) is developed. Then, we propose to divide the optimization experience into two classes: 1) global and 2) local search experience. Accordingly, by instantiating LERC into global and local versions, we develop two distinct transfer methods to exploit the global and local search experience, respectively. Finally, by combining the two transfer methods, we propose an S-ESTO algorithm that can transfer the global and local search experience simultaneously for maximum performance enhancement for the target task. Experiments conducted on a set of benchmark problems and a practical case study verify the efficacy of the proposed methods. The source code of our algorithm is available athttps://github.com/ccm831143/GL-LERC.

Inspired by natural evolutionary processes, Evolutionary Computation (EC) has established itself as a cornerstone of Artificial Intelligence. Recently, with the surge in data-intensive applications and large-scale complex systems, the demand for scalable EC solutions has grown significantly. However, most existing EC infrastructures fall short of catering to the heightened demands of large-scale problem solving. While the advent of some pioneering GPU-accelerated EC libraries is a step forward, they also grapple with some limitations, particularly in terms of flexibility and architectural robustness. In response, we introduce EvoX: a computing framework tailored for automated, distributed, and heterogeneous execution of EC algorithms. At the core of EvoX lies a unique programming model to streamline the development of parallelizable EC algorithms, complemented by a computation model specifically optimized for distributed GPU acceleration. Building upon this foundation, we have crafted an extensive library comprising a wide spectrum of 50+ EC algorithms for both single-and multi-objective optimization. Furthermore, the library offers comprehensive support for a diverse set of benchmark problems, ranging from dozens of numerical test functions to hundreds of reinforcement learning tasks. Through extensive experiments across a range of problem scenarios and hardware configurations, EvoX demonstrates robust system and model performances. EvoX is open-source and accessible at: https://github.com/EMI-Group/EvoX.

As a challenging research topic in evolutionary multitask optimization (EMTO), evolutionary many-task optimization (EMaTO) aims at solving more than three tasks simultaneously. The design of the EMaTO algorithm generally needs to consider two major open issues, which are how to obtain useful knowledge from similar source tasks and how to effectively transfer knowledge to the target task. In this paper, we discover that knowledge structure plays a significant role in dealing with these two issues and propose a novel knowledge structure preserving-based evolutionary algorithm (KSP-EA) to efficiently solve many-task optimization problems. KSP-EA aims to achieve two goals, which are firstly to obtain useful structure-preserved knowledge from similar source tasks and secondly to effectively transfer both direct and indirect knowledge to the target task. To achieve the first goal, we propose a local-structure-preserved knowledge acquisition strategy that projects the knowledge of similar source tasks into a unified subspace without loss of the knowledge structure, thus enhancing the quality of the obtained knowledge. To achieve the second goal, we propose a tree-based knowledge propagation strategy that constructs a knowledge propagating tree to connect all the tasks and propagates knowledge along the edges of this tree. This way, the target task can obtain both direct and indirect knowledge, improving the effectiveness of knowledge transfer. We conduct extensive experiments on CEC19 and WCCI22 many-task optimization test suites and a real-world application scenario to evaluate the performance of KSP-EA. The experimental results show that our KSP-EA generally outperforms state-of-the-art algorithms.

Evolutionary computation (EC) is a kind of meta-heuristic algorithm that takes inspiration from natural evolution and swarm intelligence behaviors. In the EC algorithm, there is a huge amount of data generated during the evolutionary process. These data reflect the evolutionary behavior and therefore mining and utilizing these data can obtain promising knowledge for improving the effectiveness and efficiency of EC algorithms to better solve optimization problems. Considering this and inspired by the ability of human beings that acquire knowledge from the historical successful experiences of their predecessors, this paper proposes a novel EC paradigm, named knowledge learning EC (KLEC). The KLEC aims to learn from historical successful experiences to obtain a knowledge library and to guide the evolutionary behaviors of individuals based on the knowledge library. The KLEC includes two main processes named “learning from experiences to obtain knowledge” and “utilizing knowledge to guide evolution”. First, KLEC maintains a knowledge library model and updates this model by learning the successful experiences collected in every generation. Second, KLEC not only adopts the evolutionary operation but also utilizes the knowledge library model to guide individuals for better evolution. The KLEC is a generic and effective framework, and we propose two algorithm instances of KLEC, which are knowledge learning-based differential evolution and knowledge learning-based particle swarm optimization. Also, we combine the knowledge learning framework with several state-of-the-art EC algorithms, showing that the performance of the state-of-the-art algorithms can be significantly enhanced by incorporating the knowledge learning framework.

Multiobjective multitasking evolutionary algorithms have shown promising performance for tackling a set of multiobjective optimization tasks simultaneously, as the optimization experience gained within one task can be transferred to accelerate the solving of others. However, most studies only select similar transfer tasks based on their designed metrics, which become less efficient when tackling a large number of optimization tasks, as their transferred knowledge may be insufficiently diversified. To alleviate this issue, this article proposes a multiobjective many-tasking evolutionary algorithm (MMaTEA) using Diversified Gaussian-based knowledge Transfer, named MMaTEA-DGT. In this algorithm, a diversified transfer selection strategy is presented to choose a number of similar and complementary source tasks for knowledge transfer. Then, based on the above diversified source tasks, a Gaussian-based transfer strategy is designed to transfer their various optimization knowledge. In this way, MMaTEA-DGT is more effective in transferring optimization knowledge to speed up the solving of many tasks. Experimental studies on both the benchmark suites and a real-world dynamic vaccine prioritization problem have indicated the superiority of MMaTEA-DGT over some recently proposed MMaTEAs.

The existing constrained multiobjective evolutionary algorithms (CMOEAs) still have great room for improvement in balancing populations convergence, diversity and feasibility on complex constrained multiobjective optimization problems (CMOPs). Besides, their effectiveness deteriorates dramatically when facing the CMOPs with scaling-up objective space or search space. We are thus motivated to design a learning-aided CMOEA with promising problem-solving ability and scalability for various CMOPs. In the proposed solver, two learning models are respectively trained online on constrained-ignored task and feasibility-first task, which are then used to learn the two improvement-based vectors for enhancing the search by differential evolution. In addition, the union population of parent and child solutions is divided into multiple subsets with a hierarchical clustering based on cosine similarity. A comprehensive indicator, considering objective-based performance and constraint violation degree of a solution, is developed to select the representative solution from each cluster. The effectiveness of the proposed optimizer is verified by solving the CMOPs with various irregular Pareto fronts, the number of objectives ranging from 2 to 15, and the dimensionality of search space scaling up to 1000.

In recent decades, various surrogate-assisted evolutionary algorithms (SAEAs) have been proposed to solve computationally expensive multiobjective optimization problems (EMOPs). Nevertheless, designing an SAEA to handle high-dimensional EMOPs and balance convergence, diversity, and computational complexity remains challenging. Here, we propose a two-phase SAEA (TP-SAEA), which follows the idea of convergence first and diversity second, for solving high-dimensional EMOPs. In Phase I, a surrogate-assisted problem reformulation method is proposed to fast-track the Pareto optimal set in association with some reference solutions. Specifically, the high-dimensional EMOP is reformulated into an expensive single-objective one with low-dimensional decision space. Then, the surrogate-assisted optimization is utilized to obtain well-converged solutions. In Phase II, the high-dimensional EMOP is decomposed into two subproblems to explore subregions of the decision space that can effectively promote the diversity of the solutions. The two subproblems are optimized independently via surrogate-assisted optimization, aiming to push the population towards different regions of the Pareto optimal front. Experiments are conducted on EMOPs with 100 to 500 decision variables compared with four state-of-the-art SAEAs. The proposed TP-SAEA obtains well-converged and diverse solutions with only 509 real function evaluations. Moreover, its superiority is examined in six real-world instances with up to 12,000 decision variables.

Robust multiobjective optimization problems (RMOPs) widely exist in real-world applications, which introduce a variety of uncertainty in optimization models. While some evolutionary algorithms have been developed to find optimal solutions robust to uncertainty, they are ineffective to handle RMOPs in high-dimensional decision spaces. Focusing on the large-scale RMOPs with sparse optimal solutions, this article proposes an evolutionary algorithm with novel strategies for the selection, generation, and evaluation of robust solutions. In order to handle the uncertainty in the optimization models, we first introduce an archive to separately consider optimality and robustness, which can achieve the selection of robust solutions effectively at a low cost. Based on the robust knowledge extracted from the archive, a guiding vector is adaptively updated to facilitate the generation of robust solutions in high-dimensional decision spaces. With the assistance of the guiding vector, a robustness indicator is suggested to assist in the evaluation of robust solutions without additional perturbations. Besides, we design a test suite to evaluate the performance of the proposed algorithm on the large-scale RMOPs. Our experimental results demonstrate that the proposed algorithm has significant advantages over the state-of-the-art evolutionary algorithms in terms of optimality and robustness, on both the proposed test suite and practical applications.

Evolutionary multitasking (EMT) is an emerging research direction within the evolutionary computation community, attempting to concurrently solve multiple optimization tasks by exploiting the underlying synergies between the tasks. Recently, numerous explicit transfer strategies have been developed for enhancing positive transfer among optimization tasks. Nevertheless, most of these methods conduct knowledge transfer by transferring the best solutions from a source task to the target task, while ignoring the proper use of information from the target task in solution selection. As a result, the transferred solutions could not well adapt to the target task, thus limiting the effectiveness of knowledge transfer across tasks. To address this issue, this paper proposes a solution selection method based on the lower confidence bound (LCB) for EMT, which is designed by leveraging task-specific information of both source and target tasks. With the proposed LCB metric, a number of high-quality solutions that could be more helpful for the target task can be selected and transferred to enhance positive transfer in EMT. To verify the effectiveness of the proposed approach, the solution selection method is embedded into several existing EMT algorithms and then evaluated on the single-objective multitasking benchmarks, the multiobjective multitasking benchmark, and a real-world application. The obtained results confirmed the generality and efficacy of the proposed solution selection approach.

Bilevel multiobjective optimization problem (BLMOP) can be seen as a special constrained multiobjective optimization problem (CMOP), where the optimality constraint of the lower-level (LL) problem cannot be easily and quickly checked, but must be verified by solving the LL problem. If there was a relatively simple alternative formulation for effectively identifying LL optimal solutions, the abovementioned special constraint could become as simple as the usual constraints and the nested optimization structure of BLMOP would be altered, which can greatly improve efficiency and effectively find LL optimal solutions with excellent upper-level (UL) performance. In this article, we improve the training mechanism for conditional generative adversarial network (cGAN) by introducing multiple generators to construct a reasonable reference distribution, so as to prevent the discriminator from performance degradation. With a discriminator identifying LL optimal solutions effectively, the nested optimization structure of BLMOP is altered by adding the objective that maximizing the discriminator output score into the UL objectives and removing the LL optimality constraint, realizing synchronous optimization of UL and LL vectors. The cooperation of generators and discriminator greatly reduces the computational overhead for solving BLMOPs. The proposed algorithm has achieved the best or competitive results in comparison with 6 state-of-the-art algorithms and a nested method on benchmark problems and a real-world problem, whose effectiveness has been demonstrated.

Surrogate-assisted evolutionary algorithms (SAEAs) have shown promising performance in tackling expensive multiobjective optimization problems (EMOPs). However, existing SAEAs solve EMOPs separately, which ignore their optimization experiences earned before. Inspired by multitasking optimization paradigm for multitasking multiobjective optimization problems (MTMOPs), this article designs the first SAEA for tackling expensive MTMOPs (EMTMOPs) with adaptive knowledge transfer. First, a competitive surrogate selection is proposed to improve the generalization ability of approximating various EMOP tasks, where two types of surrogate models are trained and then compete for use to replace real expensive evaluations. Then, an adaptive solution selection is designed, which identifies promising transfer solutions to accelerate the solving of target task and selects promising infill solutions for real expensive evaluations to refine the surrogate models. The performance of our algorithm is validated on three commonly used benchmark suites and some real-world EMTMOPs. The experiments validate our superiority over several state-of-the-art SAEAs on most test cases.

Large language models (LLMs) have not only revolutionized natural language processing but also extended their prowess to various domains, marking a significant stride toward artificial general intelligence. The interplay between LLMs and evolutionary algorithms (EAs), despite differing in objectives and methodologies, share a common pursuit of applicability in complex problems. Meanwhile, EA can provide an optimization framework for LLM’s further enhancement under closed box settings, empowering LLM with flexible global search capacities. On the other hand, the abundant domain knowledge inherent in LLMs could enable EA to conduct more intelligent searches. Furthermore, the text processing and generative capabilities of LLMs would aid in deploying EAs across a wide range of tasks. Based on these complementary advantages, this article provides a thorough review and a forward-looking roadmap, categorizing the reciprocal inspiration into two main avenues: 1) LLM-enhanced EA and 2) EA-enhanced LLM. Some integrated synergy methods are further introduced to exemplify the complementarity between LLMs and EAs in diverse scenarios, including code generation, software engineering, neural architecture search, and various generation tasks. As the first comprehensive review focused on the EA research in the era of LLMs, this article provides a foundational stepping stone for understanding the collaborative potential of LLMs and EAs. The identified challenges and future directions offer guidance for researchers and practitioners to unlock the full potential of this innovative collaboration in propelling advancements in optimization and artificial intelligence. We have created a GitHub repository to index the relevant papers:https://github.com/wuxingyu-ai/LLM4EC.

Expensive optimization problems (EOPs) have attracted increasing research attention over the decades due to their ubiquity in a variety of practical applications. Despite many sophisticated surrogate-assisted evolutionary algorithms (SAEAs) that have been developed for solving such problems, most of them lack the ability to transfer knowledge from previously-solved tasks and always start their search from scratch, making them troubled by the notorious cold-start issue. A few preliminary studies that integrate transfer learning into SAEAs still face some issues, such as defective similarity quantification that is prone to underestimate promising knowledge, surrogate-dependency that makes the transfer methods not coherent with the state-of-the-art in SAEAs, etc. In light of the above, a plug and play competitive knowledge transfer (CKT) method is proposed to boost various SAEAs in this article. Specifically, both the optimized solutions from the source tasks and the promising solutions acquired by the target surrogate are treated as task-solving knowledge, enabling them to compete with each other to elect the winner for expensive evaluation, thus boosting the search speed on the target task. Moreover, the lower bound of the convergence gain brought by the knowledge competition is mathematically analyzed, which is expected to strengthen the theoretical foundation of sequential transfer optimization. Experimental studies conducted on a series of benchmark problems and a practical application from the petroleum industry verify the efficacy of the proposed method. The source code of the CKT is available athttps://github.com/XmingHsueh/SAS-CKT.

In recent years, dynamic multiobjective evolutionary algorithms (DMOEAs) using the prediction strategy have shown promising performance for solving dynamic multiobjective optimization problems (DMOPs), as they can predict environmental changing trends in advance. However, most of them follow a regular change pattern and thus their performance is compromised when solving DMOPs with irregular change patterns (e.g., nonlinear correlations). To alleviate this challenge, this article proposes a DMOEA with a learnable prediction for tackling DMOPs. Specifically, a neural network is designed to effectively capture diverse change patterns of the environment. Based on the change patterns learned, a directional improvement prediction (DIP) is developed to guide the evolutionary search toward promising directions in the decision space. In this way, a superior initial population with good convergence and diversity is predicted by DIP, which can be more effective for solving various DMOPs. Comprehensive empirical studies show that the proposed DIP is effective and the proposed algorithm has some advantages over five competitive DMOEAs when solving three commonly used benchmarks and one real-world problem.

Drug discovery is an expensive and risky process. To combat the challenges in drug discovery, an increasing number of researchers and pharmaceutical companies recognize the benefits of utilizing computational techniques. Evolutionary computation (EC) offers promise as most drug discovery problems are essentially complex optimization problems beyond conventional optimization algorithms. EC methods have been widely applied to solve these complex optimization problems especially in lead com-pound generation and molecular virtual evaluation, substantially speeding up the process of drug discovery and development. This article presents a comprehensive survey of EC-based drug discovery methods. Particularly, a new taxonomy of the methods is provided and the advantages and limitations of the methods are reviewed. In addition, the potential future directions of EC-based drug discovery are discussed and the publicly available resources including databases and computational tools are compiled for the convenience of researchers seeking to pursue this field.

Neural architecture search (NAS) is widely used to automate the design of high-accuracy deep architectures, which are often vulnerable to adversarial attacks in practice due to the lack of adversarial robustness. Existing methods focus on the direct utilization of regularized optimization process to address this critical issue, which causes the lack of interpretability for the end users to learn how the robust architecture is constructed. In this paper, we introduce a robust enhanced plugin (REP) method for differentiable NAS to search for robust neural architectures. Different from existing peer methods, REP focuses on the robust search primitives in the search space of NAS methods, and naturally has the merit of contributing to understanding how the robust architectures are progressively constructed. Specifically, we first propose an effective sampling strategy to sample robust search primitives in the search space. In addition, we also propose a probabilistic enhancement method to guarantee natural accuracy and adversarial robustness simultaneously during the search process. We conduct experiments on both convolutional neural networks and graph neural networks with widely used benchmarks against state of the arts. The results reveal that REP can achieve superiority in terms of both the adversarial robustness to popular adversarial attacks and the natural accuracy of original data. REP is flexible and can be easily used by any existing differentiable NAS methods to enhance their robustness without much additional effort.

Speech enhancement (SE) is critical for improving speech intelligibility and quality in various audio devices. In recent years, deep learning-based methods have significantly improved SE performance, but they often come with a high computational cost, which is prohibitive for a large number of edge devices, such as headsets and hearing aids. This work proposes an ultralow-power SE system based on the brain-inspired spiking neural network (SNN) called Spiking-FullSubNet. Spiking-FullSubNet follows a full-band and subband fusioned approach to effectively capture both global and local spectral information. To enhance the efficiency of computationally expensive subband modeling, we introduce a frequency partitioning method inspired by the sensitivity profile of the human peripheral auditory system. Furthermore, we introduce a novel spiking neuron model that can dynamically control the input information integration and forgetting, enhancing the multiscale temporal processing capability of SNN, which is critical for speech denoising. Experiments conducted on the recent Intel Neuromorphic Deep Noise Suppression (N-DNS) Challenge dataset show that the Spiking-FullSubNet surpasses state-of-the-art (SOTA) methods by large margins in terms of both speech quality and energy efficiency metrics. Notably, our system won the championship of the Intel N-DNS Challenge (algorithmic track), opening up a myriad of opportunities for ultralow-power SE at the edge. Our source code and model checkpoints are publicly available at github.com/haoxiangsnr/spiking-fullsubnet.

Advancements in high-throughput technologies have yielded large-scale human gut microbiota profiles, sparking considerable interest in exploring the relationship between the gut microbiome and complex human diseases. Through extracting and integrating knowledge from complex microbiome data, existing machine learning (ML)-based studies have demonstrated their effectiveness in the precise identification of high-risk individuals. However, these approaches struggle to address the heterogeneity and sparsity of microbial features and explore the intrinsic relatedness among human diseases. In this work, we reframe human gut microbiome-based disease detection as a multilabel classification (MLC) problem and integrate a range of innovative techniques within the proposed MLC framework, aptly named GutMLC. Specifically, the entity semantic similarity as priori knowledge is incorporated into multilabel feature selection and loss functions by capturing the shared attributes and inherent associations among diseases and microbes. To tackle the issue of label imbalance, both within and between labels, we adapt the focal loss (FL) function for MLC using debiased inverse weighting. Extensive experiment results consistently demonstrate the competitive performance of GutMLC in comparison with commonly used MLC and single-label classification (SLC) algorithms. This work seeks to unlock the potential of gut microbiota as robust biomarkers for multiple disease prediction.

While graph neural networks (GNNs) have become the de facto standard for graph-based node classification, they impose a strong assumption on the availability of sufficient labeled samples. This assumption restricts the classification performance of prevailing GNNs on many real-world applications suffering from low-data regimes. Specifically, features extracted from scarce labeled nodes could not provide sufficient supervision for the unlabeled samples, leading to severe overfitting. We point out that leveraging subgraphs to capture long-range dependencies can augment the node representation, thus alleviating the low-data regime. To this end, we present a novel self-supervised learning (SSL) framework, called multiview subgraph neural networks (Muse), for handling the long-range dependencies. In particular, we propose an information theory-based identification mechanism to identify two types of subgraphs from the views of input space and latent space, respectively. The former is to capture the local structure of the graph, while the latter captures the long-range dependencies among nodes. By fusing these two views of subgraphs, the learned representations can preserve the topological properties of the graph at large, including the local structure and long-range dependencies, thus maximizing their expressiveness. Theoretically, we provide the generalization error bound to show the effectiveness of capturing complementary information from multiview subgraphs. Empirically, we show a proof-of-concept of Muse on canonical node classification problems on graph data.

Content-based medical image retrieval (CBMIR) enables physicians to make evidence-based diagnoses by retrieving similar medical images and recalling previous cases stored in databases. However, existing CBMIR models are prone to capturing superficial correlations due to confounding factors such as complex host organs and lesions, imaging discrepancies, artifacts, and inconsistent protocols. To address this issue, we propose a plug-and-play anti-confounding hashing (ACH) method, which uses debiased sample weighting and lesion counterfactual reasoning (LCR) to directly capture the natural direct effect (NDE) of lesions on query medical images without bias. The devised debiased weighting (DBW) loss adopts a backdoor adjustment to separate lesions from confounders. To effectively locate salient areas of lesions, we present a coarse-to-fine lesion positioning (C2F-LP) module by counterfactual reasoning. On two real-world radiological image datasets, ACH achieves 0.2%-9% improvement in mean average precision (mAP) over the six state-of-the-art methods, when using code lengths ranging from 8-bit to 32-bit. Its robustness to confounding factors is demonstrated through explainable visual analysis.

Cross-project defect prediction (CPDP) leverages machine learning (ML) techniques to proactively identify software defects, especially where project-specific data is scarce. However, existing CPDP approaches suffer from three critical limitations: ineffective exploration of high-dimensional parameter spaces, poor adaptability across diverse projects with heterogeneous data distributions, and inadequate handling of feature redundancy and distribution discrepancies between source and target projects. To address these challenges, we formulate CPDP as a multi-objective bilevel optimization (MBLO) method, dubbed MBL-CPDP. Our approach comprises two nested problems: the upper-level, a multi-objective combinatorial optimization problem, enhances robustness by optimizing ML pipelines that integrate feature selection, transfer learning, and classification techniques, while the lower-level problem fine-tunes their hyperparameters. Unlike traditional methods that employ fragmented optimization strategies or single-objective approaches that introduce bias, MBL-CPDP provides a holistic, end-to-end optimization framework. Additionally, we propose an ensemble learning method to better capture cross-project distribution differences and improve generalization across diverse datasets. An MBLO algorithm is then presented to effectively solve the formulated MBLO problem. To evaluate MBL-CPDP’s performance, we compare it with five automated ML tools and 50 CPDP techniques across 20 projects. Extensive empirical results show that MBL-CPDP outperforms the comparison methods, demonstrating its superior adaptability and comprehensive performance evaluation capability.

Traffic signal timing optimization (TSTO) is a significant problem in smart cities. Evolutionary computation (EC) algorithms have been widely studied to solve the TSTO problem. However, as existing EC-based algorithms usually use iterative-based evolution and simulation-based evaluation to optimize the timing plan for certain traffic situations, they still suffer from two difficulties, which are the time-consuming optimization process in certain traffic situations and the weak adaptation ability to unseen traffic situations. Therefore, this article proposes a novel learning for adaptation (LA) framework for real-time TSTO by changing the optimization process from evolution to adaptation. The LA learns a map model from the traffic volume input to the traffic signal timing. Then, the learned map model is expected to adapt to unseen traffic situations faster and better. The LA framework includes a data collection stage and a model learning (ML) stage. First, in the data collection stage, a multisource transfer-based particle swarm optimization (MTPSO) algorithm is proposed to avoid the under-optimizing issue. Second, in the ML stage, a multilevel smoothness regularization (MSR) method is proposed to deal with the over-fitting issue. The proposed LA framework with MTPSO and MSR is named as LMM method. This way, the TSTO process is changed from time-consuming evolution to time-efficient adaptation, which is significant in practical real-time applications. Comprehensive experiments with ten different synthetic and real-world road networks under different traffic volume distributions are carried out. The results show that the LMM method adapts better to unseen traffic volume inputs and can achieve real-time TSTO.

In recent years, machine learning algorithms, especially deep learning, have shown promising prospects in solving Partial Differential Equations (PDEs). However, as the dimension increases, the relationship and interaction between variables become more complex, and existing methods are difficult to provide fast and interpretable solutions for high-dimensional PDEs. To address this issue, we propose a genetic programming symbolic regression algorithm based on transfer learning and automatic differentiation to solve PDEs. This method uses genetic programming to search for a mathematically understandable expression and combines automatic differentiation to determine whether the search result satisfies the PDE and boundary conditions to be solved. To overcome the problem of slow solution speed caused by large search space, we propose a transfer learning mechanism that transfers the structure of one-dimensional PDE analytical solution to the form of high-dimensional PDE solution. We tested three representative types of PDEs, and the results showed that our proposed method can obtain reliable and human-understandable real solutions or algebraic equivalent solutions of PDEs, and the convergence speed is better than the compared methods. Code of this project is at https://github.com/grassdeerdeer/HD-TLGP.

A plethora of fair graph neural networks (GNNs) have been proposed to promote algorithmic fairness for high-stake real-life contexts. Meanwhile, explainability is generally proposed to help machine learning practitioners debug models by providing human-understandable explanations. However, seldom work on explainability is made to generate explanations for fairness diagnosis in GNNs. From the explainability perspective, this paper explores the problem of what subgraph patterns cause the biased behavior of GNNs, and what actions could practitioners take to rectify the bias? By answering the two questions, this paper aims to produce compact, diagnostic, and actionable explanations that are responsible for discriminatory behavior. Specifically, we formulate the problem of generating diagnostic and actionable explanations as a multi-objective combinatorial optimization problem. To solve the problem, a dedicated multi-objective evolutionary algorithm is presented to ensure GNNs' explainability and fairness in one go. In particular, an influenced nodes-based gradient approximation is developed to boost the computation efficiency of the evolutionary algorithm. We provide a theoretical analysis to illustrate the effectiveness of the proposed framework. Extensive experiments have been conducted to demonstrate the superiority of the proposed method in terms of classification performance, fairness, and interpretability.

The identification of sensory cues associated with potential opportunities and dangers is frequently complicated by unrelated events that separate useful cues by long delays. As a result, it remains a challenging task for state-of-the-art spiking neural networks (SNNs) to establish long-term temporal dependency between distant cues. To address this challenge, we propose a novel biologically inspired Two-Compartment Leaky Integrate-and-Fire spiking neuron model, dubbed TC-LIF. The proposed model incorporates carefully designed somatic and dendritic compartments that are tailored to facilitate learning long-term temporal dependencies. Furthermore, the theoretical analysis is provided to validate the effectiveness of TC-LIF in propagating error gradients over an extended temporal duration. Our experimental results, on a diverse range of temporal classification tasks, demonstrate superior temporal classification capability, rapid training convergence, and high energy efficiency of the proposed TC-LIF model. Therefore, this work opens up a myriad of opportunities for solving challenging temporal processing tasks on emerging neuromorphic computing systems. Our code is publicly available at https://github.com/ZhangShimin1/TC-LIF.

To enhance the generalization of multi-objective feature selection (MOFS) in classification, this paper proposes an evolutionary multitasking algorithm, diverging from previous approaches that exclusively target selected features. The algorithm integrates information from both selected and unselected features, introducing a novel objective to minimize the accuracy of unselected features. This objective, combined with the goal of minimizing classification errors for selected features, forms an auxiliary MOFS task. The paper presents a dual-population evolutionary multitasking framework that synergizes the main MOFS task with the auxiliary task. A knowledge transfer mechanism, based on accuracy preferences, seamlessly shares insights from the auxiliary to the main task, aiming to identify improved Pareto feature subsets. Empirical results demonstrate the superior performance of several state-of-the-art multi-objective algorithms within this framework, highlighting significant improvements across diverse datasets.

Evolutionary transfer optimization (ETO), which combines evolutionary algorithms with knowledge transfer across related tasks to enhance search performance, has gained widespread attention from researchers in recent years. Multiform transfer optimization (MFTO) stands out as a representative transfer paradigm of ETO, aiming to exploit alternative formulations of the target task of interest. By leveraging useful knowledge acquired from alternative formulations to assist in solving the target task, MFTO has proven effective in tackling complex optimization problems, contributing to the growth of MFTO research. This paper provides a review of existing research progress in MFTO. Firstly, we introduce the fundamental aspects of MFTO, including the general framework and core components. Subsequently, we summarize the advances in MFTO from the perspectives of problems to be solved and the way of constructing alternative formulations. Lastly, we discuss promising future research directions. It is hoped that this survey can provide a thorough understanding of the MFTO framework and facilitate the development of more advanced MFTO algorithms and applications.

In cases of frequent problem-solving of multiobjective optimization tasks from a domain due to changing conditions or problem features, a growing number of individual tasks will be solved and stored in a database, providing an opportunity for a target task at hand to achieve better optimization performance through knowledge transfer from the previously-solved tasks, which is also known as sequential transfer optimization. Despite a variety of transfer algorithms that have been developed over the years, the research on the design of benchmark problems for evaluating such algorithms received far less attention. Oftentimes, the source and target tasks in existing test problems are manually assembled or extended from specific practical problems, limiting their ability to represent the diverse yet complex source-target similarity relationships in real-world problems. In light of this, we propose design methods to generate multiobjective sequential transfer optimization problems (MSTOPs) systematically in this work, wherein the Pareto manifolds of individual tasks and the manifold-based similarity between the tasks can be customized with ease, enabling a broad spectrum of representation of the diverse similarity relationships between the source-target Pareto manifolds of MSTOPs. Lastly, a benchmark suite with 12 test problems is developed using the proposed methods, which would serve as an arena for electing superior multiobjective sequential transfer optimization algorithms. The source code is available at https://github.com/XmingHsueh/MSTOP.

Evolutionary multitasking (EMT), as a very popular research topic in the evolutionary computation community, has been used to solve high-dimensional FS problems and has shown good performance recently. However, most of the existing EMT-based methods still have two drawbacks. First, they only consider using filter-based task generation strategies to retain highly relevant features for generating the additional tasks, whereas the redundancy between features is ignored. Second, they always consider a complete variable vector (e.g., global optimum or mean positional information of a population at current generation) as positive knowledge and transfer it, which greatly weakens the variety of transferred knowledge and increases the possibility of falling into local optimality. To deal with these two drawbacks, we propose a new EMT-assisted multitask particle swarm optimization (MPSO) algorithm with two innovations for high-dimensional FS. First, we propose a dual clustering-based task generation strategy to generate tasks by considering both feature relevance and redundancy. Second, we propose a fine-grain knowledge transfer strategy to realize explicit transfer of knowledge between different tasks. Experimental results on 15 public datasets show the effectiveness and competitiveness of our proposed MPSO algorithm over other state-of-the-art FS methods in dealing with high-dimensional FS problems.

Deep neural networks are typically trained using global error signals that backpropagate (BP) end-to-end, which is not only biologically implausible but also suffers from the update locking problem and requires huge memory consumption. Local learning, which updates each layer independently with a gradient-isolated auxiliary network, offers a promising alternative to address the above problems. However, existing local learning methods are confronted with a large accuracy gap with the BP counterpart, particularly for large-scale networks. This is due to the weak coupling between local layers and their subsequent network layers, as there is no gradient communication across layers. To tackle this issue, we put forward an augmented local learning method, dubbed AugLocal. AugLocal constructs each hidden layer’s auxiliary network by uniformly selecting a small subset of layers from its subsequent network layers to enhance their synergy. We also propose to linearly reduce the depth of auxiliary networks as the hidden layer goes deeper, ensuring sufficient network capacity while reducing the computational cost of auxiliary networks. Our extensive experiments on four image classification datasets (i.e., CIFAR-10, SVHN, STL-10, and ImageNet) demonstrate that AugLocal can effectively scale up to tens of local layers with a comparable accuracy to BP-trained networks while reducing GPU memory usage by around 40%. The proposed AugLocal method, therefore, opens up a myriad of opportunities for training high-performance deep neural networks on resource-constrained platforms. Code is available at \url{https://github.com/ChenxiangMA/AugLocal}.

To relieve the growing burden of mental disorders, deep learning techniques have emerged as a promising tool to aid clinicians by detecting abnormal patterns in neuroimaging data. However, the efficacy of such models is contingent upon access to vast pools of patient data, which is impractical for individual healthcare institutions. Moreover, the privacy-preserving policy regulations governing medical images further complicate the pooling of information necessary for training robust models. Federated Learning (FL) offers a solution to this dilemma by aggregating the local model updates without compromising patient privacy. However, current studies fail to adequately account for the need to personalize models according to the diverse structures of local data. In this work, an effective heterogeneous structured FL framework using graph convolutional aggregation dubbed GAHFL is proposed to diagnose mental disorders on functional magnetic resonance imaging data. In addition, we propose to perform the global model self-evaluation to enable the training to emphasize the samples that are difficult to classify. To solve the catastrophic forgetting problem, we build a historical logit pool to awaken the global model’s recognition ability by performing a server knowledge self-distillation. Empirical evaluations demonstrate that the proposed framework achieves averaged diagnosis AUC values of 69.01% and 69.04% with different sizes of public datasets of ABIDE-I and ADHD-200 datasets, respectively. The ablation studies and robustness validation test further demonstrate the superior performance of our framework.

Integrating personalization into federated learning is crucial for addressing data heterogeneity and surpassing the limitations of a single aggregated model. Personalized federated learning excels at capturing inter-client similarities and meeting diverse client needs through custom-made models. However, even with personalized approaches, it’s essential to aggregate knowledge among clients to ensure universal benefits. This paper proposes Federated Dual Objectives and Dual Models (FedDodm), a novel approach that employs two independent models to separately address explicit personalization and implicit generalization objectives in personalized federated learning. By treating these objectives as distinct loss functions and training models accordingly, we achieve a balance between the two through a fusion method. Extensive experiments across various models and learning tasks demonstrate that FedDodm outperforms state-of-the-art federated learning approaches, marking a significant advancement in effectively integrating personalized and generalized knowledge.

The brain-inspired Spiking Neural Networks (SNNs) have garnered considerable research interest due to their superior performance and energy efficiency in processing temporal signals. Recently, a novel multi-compartment spiking neuron model, namely the Two-Compartment LIF (TC-LIF) model, has been proposed and exhibited a remarkable capacity for sequential modelling. However, training the TC-LIF model presents challenges stemming from the large memory consumption and the issue of vanishing gradient associated with the Backpropagation Through Time (BPTT) algorithm. To address these challenges, online learning methodologies emerge as a promising solution. Yet, to date, the application of online learning methods in SNNs has been predominantly confined to simplified Leaky Integrate-and-Fire (LIF) neuron models. In this paper, we present a novel online learning method specifically tailored for networks of TC-LIF neurons. Additionally, we propose a refined TC-LIF neuron model called Adaptive TC-LIF, which is carefully designed to enhance temporal information integration in online learning scenarios. Extensive experiments, conducted on various sequential benchmarks, demonstrate that our approach successfully preserves the superior sequential modeling capabilities of the TC-LIF neuron while incorporating the training efficiency and hardware friendliness of online learning. As a result, it offers a multitude of opportunities to leverage neuromorphic solutions for processing temporal signals.

The heterogeneity of medical images poses significant challenges to accurate disease diagnosis. To tackle this issue, the impact of such heterogeneity on the causal relationship between image features and diagnostic labels should be incorporated into model design, which however remains underexplored. In this paper, we propose a mixed prototype correction for causal inference (MPCCI) method, aimed at mitigating the impact of unseen confounding factors on the causal relationships between medical images and disease labels, so as to enhance the diagnostic accuracy of deep learning models. The MPCCI comprises a causal inference component based on front-door adjustment and an adaptive training strategy. The causal inference component employs a multi-view feature extraction (MVFE) module to establish mediators, and a mixed prototype correction (MPC) module to execute causal interventions. Moreover, the adaptive training strategy incorporates both information purity and maturity metrics to maintain stable model training. Experimental evaluations on four medical image datasets, encompassing CT and ultrasound modalities, demonstrate the superior diagnostic accuracy and reliability of the proposed MPCCI. The code will be available at https://github.com/Yajie-Zhang/MPCCI.

Recently, brain-inspired spiking neural networks (SNNs) have demonstrated promising capabilities in solving pattern recognition tasks. However, these SNNs are grounded on homogeneous neurons that utilize a uniform neural coding for information representation. Given that each neural coding scheme possesses its own merits and drawbacks, these SNNs encounter challenges in achieving optimal performance such as accuracy, response time, efficiency, and robustness, all of which are crucial for practical applications. In this study, we argue that SNN architectures should be holistically designed to incorporate heterogeneous coding schemes. As an initial exploration in this direction, we propose a hybrid neural coding and learning framework, which encompasses a neural coding zoo with diverse neural coding schemes discovered in neuroscience. Additionally, it incorporates a flexible neural coding assignment strategy to accommodate task-specific requirements, along with novel layer-wise learning methods to effectively implement hybrid coding SNNs. We demonstrate the superiority of the proposed framework on image classification and sound localization tasks. Specifically, the proposed hybrid coding SNNs achieve comparable accuracy to state-of-the-art SNNs, while exhibiting significantly reduced inference latency and energy consumption, as well as high noise robustness. This study yields valuable insights into hybrid neural coding designs, paving the way for developing high-performance neuromorphic systems.

Bilevel optimization is a special type of optimization in which one problem is embedded within another. The bilevel optimization problem (BLOP) of which both levels are multiobjective functions is usually called the multiobjective BLOP (MBLOP). The expensive computation and nested features make it challenging to solve. Most existing studies look for complete lower-level solutions for every upper-level variable. However, not every lower-level solution will participate in the bilevel Pareto-optimal front. Under a limited computational budget, instead of wasting resources to find complete lower-level solutions that may not be in the feasible region or inducible region of the MBLOP, it is better to concentrate on finding the solutions with better performance. Bearing these considerations in mind, we propose a multiobjective bilevel optimization solving routine combined with a knee point driven algorithm. Specifically, the proposed algorithm aims to quickly find feasible solutions considering the lower-level constraints in the first stage and then concentrates the computational resources on finding solutions with better performance. Besides, we develop several multiobjective bilevel test problems with different properties, such as scalable, deceptive, convexity, and (dis)continuous. Finally, the performance of the algorithm is validated on a practical petroleum refining bilevel problem, which involves a multiobjective environmental regulation problem and a petroleum refining operational problem. Comprehensive experiments fully demonstrate the effectiveness of our presented algorithm in solving MBLOPs.

Evolutionary multitask optimization is an emerging research topic that aims to solve multiple tasks simultaneously. A general challenge in solving multitask optimization problems (MTOPs) is how to effectively transfer common knowledge between/among tasks. However, knowledge transfer in existing algorithms generally has two limitations. First, knowledge is only transferred between the aligned dimensions of different tasks rather than between similar or related dimensions. Second, the knowledge transfer among the related dimensions belonging to the same task is ignored. To overcome these two limitations, this article proposes an interesting and efficient idea that divides individuals into multiple blocks and transfers knowledge at the block-level, called the block-level knowledge transfer (BLKT) framework. BLKT divides the individuals of all the tasks into multiple blocks to obtain a block-based population, where each block corresponds to several consecutive dimensions. Similar blocks coming from either the same task or different tasks are grouped into the same cluster to evolve. In this way, BLKT enables the transfer of knowledge between similar dimensions that are originally either aligned or unaligned or belong to either the same task or different tasks, which is more rational. Extensive experiments conducted on CEC17 and CEC22 MTOP benchmarks, a new and more challenging compositive MTOP test suite, and real-world MTOPs all show that the performance of BLKT-based differential evolution (BLKT-DE) is superior to the compared state-of-the-art algorithms. In addition, another interesting finding is that the BLKT-DE is also promising in solving single-task global optimization problems, achieving competitive performance with some state-of-the-art algorithms.

Neural architecture search (NAS) can automatically design architectures for deep neural networks (DNNs) and has become one of the hottest research topics in the current machine learning community. However, NAS is often computationally expensive because a large number of DNNs require to be trained for obtaining performance during the search process. Performance predictors can greatly alleviate the prohibitive cost of NAS by directly predicting the performance of DNNs. However, building satisfactory performance predictors highly depends on enough trained DNN architectures, which are difficult to obtain due to the high computational cost. To solve this critical issue, we propose an effective DNN architecture augmentation method named graph isomorphism-based architecture augmentation method (GIAug) in this article. Specifically, we first propose a mechanism based on graph isomorphism, which has the merit of efficiently generating a factorial of n (i.e., n ) diverse annotated architectures upon a single architecture having n nodes. In addition, we also design a generic method to encode the architectures into the form suitable to most prediction models. As a result, GIAug can be flexibly utilized by various existing performance predictors-based NAS algorithms. We perform extensive experiments on CIFAR-10 and ImageNet benchmark datasets on small-, medium- and large-scale search space. The experiments show that GIAug can significantly enhance the performance of the state-of-the-art peer predictors. In addition, GIAug can save three magnitude order of computation cost at most on ImageNet yet with similar performance when compared with state-of-the-art NAS algorithms.

Dynamic environments pose great challenges for expensive optimization problems, as the objective functions of these problems change over time and thus require remarkable computational resources to track the optimal solutions. Although data-driven evolutionary optimization and Bayesian optimization (BO) approaches have shown promise in solving expensive optimization problems in static environments, the attempts to develop such approaches in dynamic environments remain rarely explored. In this article, we propose a simple yet effective meta-learning-based optimization framework for solving the expensive dynamic optimization problems. This framework is flexible, allowing any off-the-shelf continuously differentiable surrogate model to be used in a plug-in manner, either in data-driven evolutionary optimization or BO approaches. In particular, the framework consists of two unique components: 1) the meta-learning component, in which a gradient-based meta-learning approach is adopted to learn experience (effective model parameters) across different dynamics along the optimization process and 2) the adaptation component, where the learned experience (model parameters) is used as the initial parameters for fast adaptation in the dynamic environment based on few shot samples. By doing so, the optimization process is able to quickly initiate the search in a new environment within a strictly restricted computational budget. Experiments demonstrate the effectiveness of the proposed algorithm framework compared to several state-of-the-art algorithms on common benchmark test problems under different dynamic characteristics.

Presents corrections to the paper, (Corrections to "Toward Adaptive Knowledge Transfer in Multifactorial Evolutionary Computation").

Nested evolutionary algorithms (EAs) have been regarded as very promising tools for bi-level optimization. Due to the nested structure, the upper level population evaluation requires a set of complete lower level optimizations, thereby reducing the efficiency and practicability of EA methods. In this paper, a multi-objective transformation-based evolutionary algorithm (MOTEA) is proposed to perform multiple lower level optimizations in a parallel and collaborative manner. Specifically, the corresponding multiple lower level optimizations for each generation of the upper level population evaluation are transformed into locating a set of Pareto optimal solutions of a constructed multi-objective optimization problem. By utilizing the built-in implicit parallelism of evolutionary multi-objective optimization, multiple lower level problems can thus be optimized in parallel. Within one multi-objective search population, the collaboration among the parallel lower level optimization can be realized by exploiting and utilizing the implicit similarities among them for better efficiency. The effectiveness and efficiency of the proposed MOTEA are verified by comparing it with four state-of-the-art evolutionary bi-level optimization algorithms on two sets of popular bi-level optimization benchmark test problems and three application problems.

Many practical optimization problems in the fields of transportation, business, engineering, environmental economics, etc., involve more than one level of decision-making and can be modeled as a bi-level optimization problem with a nested structure of decision variables. Existing studies have made remarkable progress on bi-level single-objective problems. However, due to the increased complexities in terms of computation and decision-making, few efforts have been devoted to bi-level multi-objective optimization problems (BLMOPs). This paper proposes an evolutionary multi-form optimization paradigm that explores alternative formulations of the target task to assist in the search with the original formulation, namely BLMFO, for bi-level multi-objective optimization. Firstly, in the proposed framework, alternative formulations of the original problem are derived to facilitate the problem-solving and also alleviate computational overheads. Then, BLMFO performs the evolutionary search in the original problem space and the auxiliary task space simultaneously to combine searching for feasible solutions and exploring regions of promising solutions, thus ensuring the effectiveness of the proposed framework. Further, useful information is transferred across the original and auxiliary tasks via explicit knowledge transfer to enable complementary exploration for better optimization performance. To the best of our knowledge, this work serves as the first attempt to solve BLMOPs via multi-form evolutionary optimization in the literature. The framework is verified using four instantiation groups with different underlying baseline solvers on various benchmarks and practical problems. The experimental results show the effectiveness and superiority of the proposed framework in terms of performance indicators and the quality of final optimized solutions.

Evolutionary multitasking Optimization (EMTO) is a paradigm that optimizes multiple tasks simultaneously to improve the overall performance of all tasks by seamlessly transferring useful knowledge among them. Although EMTO has received significant interest, rare studies consider handling tasks that are multimodal optimization problems (MMOPs) with multiple global optimal solutions. Due to the multiple different modalities of each task, a major challenge of solving multiple MMOPs is how to extract and transfer knowledge across modalities of different tasks. To this end, this paper designs a distributed knowledge transfer based evolutionary multitask multimodal optimization (EMTMO-DKT) approach for solving multiple MMOPs simultaneously by discovering and utilizing local knowledge across modalities of different tasks. Specifically, we first divide the population of each task into multiple subpopulations, where each subpopulation explores a modality. Then, we propose an evolution path based similarity measurement to measure the local similarities between subpopulations of different tasks. Since the modalities can be locally similar across tasks, we develop a subpopulation cross matching strategy according to the obtained similarities to pair subpopulations of different tasks. In this stage, the successfully paired subpopulations are allowed to transfer knowledge. Finally, the knowledge transfer probability self-adjusting strategy is applied to each subpopulation to balance knowledge transfer and self-evolution, so as to improve search efficiency. In this paper, a set of multitask multimodal optimization test problems are constructed to assess the efficacy of compared algorithms. Experimental results on both the benchmark functions and the real-world optimization problem demonstrate that the proposed algorithm can quickly locate more global optima in comparison with state-of-the-art EMTO and multimodal optimization algorithms.

With the rising number of large-scale multiobjective optimization problems (LSMOPs) from academia and industries, some multiobjective evolutionary algorithms (MOEAs) with different decision variable handling strategies have been proposed. Decision variable analysis (DVA) is widely used in large-scale optimization, aiming at identifying the connection between each decision variable and the objectives, and grouping those interacting decision variables to reduce the complexity of LSMOPs. Despite their effectiveness, existing DVA techniques require the unbearable cost of function evaluations for solving LSMOPs. We propose a reformulation-based approach for efficient DVA to address this deficiency. Then a large-scale MOEA is proposed based on reformulated DVA, namely, LERD. Specifically, the DVA process is reformulated into an optimization problem with binary decision variables, aiming to approximate different grouping results. Afterwards, each group of decision variables is used for convergence-related or diversity-related optimization. The effectiveness and efficiency of the reformulation-based DVA are validated by replacing the corresponding DVA techniques in two large-scale MOEAs. Experiments in comparison with six state-of-the-art large-scale MOEAs on LSMOPs with up to 2000 decision variables have shown the promising performance of LERD.

Evolutionary multitasking (EMT) has attracted much attention in the community of evolutionary computation recently. It intends to improve the performance of evolutionary optimization on multiple problems via knowledge learning and transfer across them while the optimization processes progress online. Existing EMT paradigms can be classified as explicit EMT (EEMT) and implicit EMT (IEMT) according to the mechanisms adopted in the knowledge transfer. With additional knowledge learning and transfer modules, the EEMT often brings flexible algorithmic designs and effective knowledge transfer against the IEMT. However, most of the existing EEMT studies are designed for continuous optimization problems. Due to the difficulty of learning problem-specific mappings across combinatorial optimization problems, EEMT for combinatorial optimization is still in the nascent stage. Furthermore, it is worth noting that, with the growing number of tasks in today’s real-world applications and the enlarged number of decision variables in each of the tasks, learning mappings across tasks becomes more challenging. Keeping the above in mind, this paper presents a novel EEMT algorithm with centralized learning for solving the large-scale and multi-objective combinatorial optimization in many-task manner, in which knowledge transfer across tasks is conducted based on a centralized learning model, instead of task-specific mappings which are required in existing EEMT studies. To investigate the performance of the proposed centralized learning assisted EEMT, comprehensive empirical studies have been conducted on the large-scale and multi-objective knapsack problems. Lastly, the efficacy of our proposed method is further validated on a real-world combinatorial optimization application.

Recently, a number of domain adaptation (DA) methods have been proposed for knowledge transfer in evolutionary multitasking (EMT). However, the learned mappings in these methods often have unique biases in representing the connection between source and target tasks. Few studies have paid attention to the complementarity of different mappings in knowledge transfer. To fill this research gap, this article proposes an ensemble method to combine multiple DA methods for knowledge transfer in EMT by considering the efficacy and diversity of these methods. First, a hierarchical clustering method is used to divide the population of each task into multiple clusters. Then, when two parental solutions are selected for knowledge transfer across tasks, the solutions within the same cluster are checked. In particular, if none of these solutions has been transferred before, the efficacy of DA methods is considered first by using roulette wheel selection based on the corresponding performance improvements in the evolutionary optimization process. Otherwise, the diversity of DA methods is emphasized by randomly selecting one of the DA methods for knowledge transfer. The effectiveness of our proposed ensemble method is validated by embedding it into existing state-of-the-art EMT algorithms, and the experimental results show that our algorithm outperforms several recently proposed EMT algorithms on most cases of two multitasking benchmark suites and one practical case.

The ongoing advancements in network architecture design have led to remarkable achievements in deep learning across various challenging computer vision tasks. Meanwhile, the development of neural architecture search (NAS) has provided promising approaches to automating the design of network architectures for lower prediction error. Recently, the emerging application scenarios of deep learning (e.g., autonomous driving) have raised higher demands for network architectures considering multiple design criteria: number of parameters/weights, number of floating-point operations, inference latency, among others. From an optimization point of view, the NAS tasks involving multiple design criteria are intrinsically multiobjective optimization problems; hence, it is reasonable to adopt evolutionary multiobjective optimization (EMO) algorithms for tackling them. Nonetheless, there is still a clear gap confining the related research along this pathway: on the one hand, there is a lack of a general problem formulation of NAS tasks from an optimization point of view; on the other hand, there are challenges in conducting benchmark assessments of EMO algorithms on NAS tasks. To bridge the gap: 1) we formulate NAS tasks into general multiobjective optimization problems and analyze the complex characteristics from an optimization point of view; 2) we present an end-to-end pipeline, dubbedEvoXBench, to generate benchmark test problems for EMO algorithms to run efficiently—without the requirement of GPUs or Pytorch/Tensorflow; and 3) we instantiate two test suites comprehensively covering two datasets, seven search spaces, and three hardware devices, involving up to eight objectives. Based on the above, we validate the proposed test suites using six representative EMO algorithms and provide some empirical analyses. The code ofEvoXBenchis available athttps://github.com/EMI-Group/EvoXBench.

Point cloud registration is an important task in computer vision, where the goal is to estimate a transformation to align a pair of point clouds. Most of the existing registration methods face the problems of poor robustness and getting stuck in local optima. Evolutionary multitasking is an effective paradigm to enhance global search capability and improve convergence characteristics through knowledge transfer across multiple related tasks. Inspired by evolutionary multitasking, this article proposes a multiform optimization approach through evolutionary multitasking for solving the point cloud registration problems. We first construct two related registration tasks with different functional landscapes to form a multiform optimization problem. Compared with methods that only focus on a single registration attribute, the two proposed tasks focus on robustness and precision of registration, respectively. Then, a new two-stage bidirectional knowledge transfer strategy is presented, which can implement efficient knowledge transfer among two related tasks. Finally, both simulations and real experiments show the power of our method. The proposed method is robust to noise, outliers, and partial overlaps and is effective in multiple real registration scenarios, such as object registration, scene reconstruction, and simultaneous localization and mapping.

Knowledge transfer from optimized problems has emerged as a promising technique for enhancing evolutionary search. However, most studies in this domain primarily concentrate on devising knowledge transfer mechanisms for specific problem domains, often lacking the examination of the fundamental aspects of knowledge transfer, i.e., what, when and how to transfer across diverse scenarios. This not only restricts the generality of these algorithms but also hinders their practical applicability. In light of this, this paper: 1) reviews a vast array of techniques associated with the crucial aspects of solution transfer and 2) conducts a series of experiments to explore the underlying transfer mechanisms that enhance the evolutionary search. In particular, we first define solution transferability in the context of evolutionary search, which provides a new perspective in understanding what, when and how to transfer in enhancing evolutionary search. Next, through comprehensive experiments, we find that the approximation and evaluation of solution transferability is of great importance in designing what, when and how to transfer towards enhanced evolutionary search. Furthermore, our empirical study also discusses the counterintuitive performance improvements unrelated to the search experience of source tasks. The source code for reproducing our experiments is available at https://github.com/XmingHsueh/STO-EC.

Evolutionary neural architecture search (ENAS) methods have been successfully used to design convolutional neural network (CNN) architectures automatically. These methods have achieved excellent performance in creating a specific neural architecture for a single task but are less efficient for multiple tasks. Existing ENAS frameworks always repeatedly perform the search from scratch for each task, even though these tasks may be solved by similar CNN architectures. This work presents an evolutionary multi-task convolutional neural architecture search (MTNAS) framework to enable efficient architecture searches in multi-task scenarios by incorporating architectural similarities. The proposed MTNAS constructs architectures for different tasks simultaneously by implementing a knowledge-sharing mechanism among multiple search processes. Specifically, promising architectures found in one search process can be transferred and reused to generate high-quality architectures for others. Furthermore, we devise an adaptive strategy to dynamically adjust the frequency of knowledge transfer, aiming to alleviate the potential effect of negative transfer. Extensive experiments demonstrate that MTNAS can outperform state-of-the-art NAS methods or achieve comparable performance in different tasks but with 2× less search cost.

Dynamic pickup and delivery problems (DPDPs) with various constraints, such as docks, time windows, capacity, and last-in-first-out loading, have posed significant challenges for existing vehicle routing algorithms, as most of them only optimize a single weighted objective function, which makes it difficult to maintain the solutions’ diversity and may easily become stuck in local optima. To alleviate this issue, this paper introduces a decomposition-based multiobjective evolutionary algorithm with tabu search for solving the above DPDPs. First, our algorithm leverages multiobjectivization and reformulates the DPDP as a multiobjective optimization problem (MOP), which is further decomposed into multiple subproblems. Then, these subproblems are approached simultaneously and collaboratively by using a crossover process to enhance the diversity of the solutions, followed by using an efficient tabu search to speed up the convergence. In this way, our algorithm can better balance the trade-off between exploration and exploitation for solving this MOP, and then one promising solution can be selected from the population to complete some pickup and delivery tasks in an interval of the DPDP. Simulation results on 64 test problems from a practical scenario of Huawei demonstrate that the proposed algorithm outperforms other competitive algorithms for tackling DPDPs. Additionally, more experiments are conducted on 20 large-scale distribution problems within JD Logistics to validate the generalization capability of our algorithm.

Facing the increasing worldwide prevalence of mental disorders, the symptom-based diagnostic criteria struggle to address the urgent public health concern due to the global shortfall in well-qualified professionals. Thanks to the recent advances in neuroimaging techniques, functional magnetic resonance imaging (fMRI) has surfaced as a new solution to characterize neuropathological biomarkers for detecting functional connectivity (FC) anomalies in mental disorders. However, the existing computer-aided diagnosis models for fMRI analysis suffer from unstable performance on large datasets. To address this issue, we propose an efficient multitask learning (MTL) framework for joint diagnosis of multiple mental disorders using resting-state fMRI data. A novel multiobjective evolutionary clustering algorithm is presented to group regions of interests (ROIs) into different clusters for FC pattern analysis. On the optimal clustering solution, the multicluster multigate mixture-of-expert model is used for the final classification by capturing the highly consistent feature patterns among related diagnostic tasks. Extensive simulation experiments demonstrate that the performance of the proposed framework is superior to that of the other state-of-the-art methods. Moreover, the potential for practical application of the framework is also validated in terms of limited computational resources, real-time analysis, and insufficient training data. The proposed model can identify the remarkable interpretative biomarkers associated with specific mental disorders for clinical interpretation analysis.

The globally rising prevalence of mental disorders leads to shortfalls in timely diagnosis and therapy to reduce patients' suffering. Facing such an urgent public health problem, professional efforts based on symptom criteria are seriously overstretched. Recently, the successful applications of computer-aided diagnosis approaches have provided timely opportunities to relieve the tension in healthcare services. Particularly, multimodal representation learning gains increasing attention thanks to the high temporal and spatial resolution information extracted from neuroimaging fusion. In this work, we propose an efficient multimodality fusion framework to identify multiple mental disorders based on the combination of functional and structural magnetic resonance imaging. A multioutput conditional generative adversarial network (GAN) is developed to address the scarcity of multimodal data for augmentation. Based on the augmented training data, the multiheaded gating fusion model is proposed for classification by extracting the complementary features across different modalities. The experiments demonstrate that the proposed model can achieve robust accuracies of 75.1 ± 1.5 %, 72.9 ± 1.1 %, and 87.2 ± 1.5 % for autism spectrum disorder (ASD), attention deficit/hyperactivity disorder, and schizophrenia, respectively. In addition, the interpretability of our model is expected to enable the identification of remarkable neuropathology diagnostic biomarkers, leading to well-informed therapeutic decisions.

Neuroimaging techniques have been widely adopted to detect the neurological brain structures and functions of the nervous system. As an effective noninvasive neuroimaging technique, functional magnetic resonance imaging (fMRI) has been extensively used in computer-aided diagnosis (CAD) of mental disorders, e.g., autism spectrum disorder (ASD) and attention deficit/hyperactivity disorder (ADHD). In this study, we propose a spatial-temporal co-attention learning (STCAL) model for diagnosing ASD and ADHD from fMRI data. In particular, a guided co-attention (GCA) module is developed to model the intermodal interactions of spatial and temporal signal patterns. A novel sliding cluster attention module is designed to address global feature dependency of self-attention mechanism in fMRI time series. Comprehensive experimental results demonstrate that our STCAL model can achieve competitive accuracies of 73.0 ± 4.5%, 72.0 ± 3.8%, and 72.5 ± 4.2% on the ABIDE I, ABIDE II, and ADHD-200 datasets, respectively. Moreover, the potential for feature pruning based on the co-attention scores is validated by the simulation experiment. The clinical interpretation analysis of STCAL can allow medical professionals to concentrate on the discriminative regions of interest and key time frames from fMRI data.

The purpose of this article is to address unsupervised domain adaptation (UDA) where a labeled source domain and an unlabeled target domain are given. Recent advanced UDA methods attempt to remove domain-specific properties by separating domain-specific information from domain-invariant representations, which heavily rely on the designed neural network structures. Meanwhile, they do not consider class discriminate representations when learning domain-invariant representations. To this end, this article proposes a co-training framework for heterogeneous heuristic domain adaptation (CO-HHDA) to address the above issues. First, a heterogeneous heuristic network is introduced to model domain-specific characters. It allows structures of heuristic network to be different between domains to avoid underfitting or overfitting. Specially, we initialize a small structure that is shared between domains and increase a subnetwork for the domain which preserves rich specific information. Second, we propose a co-training scheme to train two classifiers, a source classifier and a target classifier, to enhance class discriminate representations. The two classifiers are designed based on domain-invariant representations, where the source classifier learns from the labeled source data, and the target classifier is trained from the generated target pseudolabeled data. The two classifiers teach each other in the training process with high-quality pseudolabeled data. Meanwhile, an adaptive threshold is presented to select reliable pseudolabels in each classifier. Empirical results on three commonly used benchmark datasets demonstrate that the proposed CO-HHDA outperforms the state-of-the-art domain adaptation methods.

Information theoretical-based methods have attracted a great attention in recent years and gained promising results for multilabel feature selection (MLFS). Nevertheless, most of the existing methods consider a heuristic way to the grid search of important features, and they may also suffer from the issue of fully utilizing labeling information. Thus, they are probable to deliver a suboptimal result with heavy computational burden. In this article, we propose a general optimization framework global relevance and redundancy optimization (GRRO) to solve the learning problem. The main technical contribution in GRRO is a formulation for MLFS while feature relevance, label relevance (i.e., label correlation), and feature redundancy are taken into account, which can avoid repetitive entropy calculations to obtain a global optimal solution efficiently. To further improve the efficiency, we extend GRRO to filter out inessential labels and features, thus facilitating fast MLFS. We call the extension as GRROfast, in which the key insights are twofold: 1) promising labels and related relevant features are investigated to reduce ineffective calculations in terms of features, even labels and 2) the framework of GRRO is reconstructed to generate the optimal result with an ensemble. Moreover, our proposed algorithms have an excellent mechanism for exploiting the inherent properties of multilabel data; specifically, we provide a formulation to enhance the proposal with label-specific features. Extensive experiments clearly reveal the effectiveness and efficiency of our proposed algorithms.

This article suggests a new dynamic multiobjective evolutionary algorithm (DMOEA) with Knowledge Transfer and Maintenance, called KTM-DMOEA, which aims to alleviate the negative transfer and enhance the optimization efficiency. Two strategies, i.e., knowledge transfer prediction (KTP) and knowledge maintenance sampling (KMS), are proposed to excavate useful knowledge from historical environments. Particularly, KTP is a discriminative predictor designed to reduce the feature and distribution divergences across distinct environments, which classifies high-quality solutions from a large number of randomly generated solutions in new environment. Moreover, KMS is a generative predictor by modeling the distribution of elitist solutions in last environment, which can sample superior solutions in new environment according to the dynamic change trends. In this way, the advantages of KTP and KMS strategies are combined to produce a superior initial population in new environment, which help to alleviate the negative transfer and resultantly enhance the overall performance of KTM-DMOEA. When compared to several recently reported DMOEAs, the experimental results validate the advantages of KTM-DMOEA in tackling most cases of benchmark and real-world problems.

Graph meta-learning has become a preferable paradigm for graph-based node classification with long-tail distribution, owing to its capability of capturing the intrinsic manifold of support and query nodes. Despite the remarkable success, graph meta-learning suffers from severe performance degradation when training on graph data with structural noise. In this work, we observe that the structural noise may impair the smoothness of the intrinsic manifold supporting the support and query nodes, leading to the poor transferable priori of the meta-learner. To address the issue, we propose a new approach for graph meta-learning that is robust against structural noise, called Proxy subgraph-based Manifold Calibration method (Pro-MC). Concretely, a subgraph generator is designed to generate proxy subgraphs that can calibrate the smoothness of the manifold. The proxy subgraph compromises two types of subgraphs with two biases, thus preventing the manifold from being rugged and straightforward. By doing so, our proposed meta-learner can obtain generalizable and transferable prior knowledge. In addition, we provide a theoretical analysis to illustrate the effectiveness of Pro-MC. Experimental results have demonstrated that our approach can achieve state-of-the-art performance under various structural noises.

Soft object manipulation tasks in domestic scenes pose a significant challenge for existing robotic skill learning techniques due to their complex dynamics and variable shape characteristics. Since learning new manipulation skills from human demonstration is an effective way for robot applications, developing prior knowledge of the representation and dynamics of soft objects is necessary. In this regard, we propose a pretrained soft object manipulation skill learning model, namely SoftGPT, that is trained using large amounts of exploration data, consisting of a three-dimensional heterogeneous graph representation and a GPT-based dynamics model. For each downstream task, a goal-oriented policy agent is trained to predict the subsequent actions, and SoftGPT generates the consequences of these actions. Integrating these two approaches establishes a thinking process in the robot's mind that provides rollout for facilitating policy learning. Our results demonstrate that leveraging prior knowledge through this thinking process can efficiently learn various soft object manipulation skills, with the potential for direct learning from human demonstrations.

The high prevalence of mental disorders gradually poses a huge pressure on the public healthcare services. Deep learning-based computer-aided diagnosis (CAD) has emerged to relieve the tension in healthcare institutions by detecting abnormal neuroimaging-derived phenotypes. However, training deep learning models relies on sufficient annotated datasets, which can be costly and laborious. Semi-supervised learning (SSL) and transfer learning (TL) can mitigate this challenge by leveraging unlabeled data within the same institution and advantageous information from source domain, respectively. This work is the first attempt to propose an effective semi-supervised transfer learning (SSTL) framework dubbed S3TL for CAD of mental disorders on fMRI data. Within S3TL, a secure cross-domain feature alignment method is developed to generate target-related source model in SSL. Subsequently, we propose an enhanced dual-stage pseudo-labeling approach to assign pseudo-labels for unlabeled samples in target domain. Finally, an advantageous knowledge transfer method is conducted to improve the generalization capability of the target model. Comprehensive experimental results demonstrate that S3TL achieves competitive accuracies of 69.14%, 69.65%, and 72.62% on ABIDE-I, ABIDE-II, and ADHD-200 datasets, respectively. Furthermore, the simulation experiments also demonstrate the application potential of S3TL through model interpretation analysis and federated learning extension.

Variable grouping provides an efficient approach to large-scale optimization, and multipopulation strategies are effective for both large-scale optimization and dynamic optimization. However, variable grouping is not well studied in large-scale dynamic optimization when cooperating with multipopulation strategies. Specifically, when the numbers/sizes of the variable subcomponents are large, the performance of the algorithms will be substantially degraded. To address this issue, we propose a bilevel variable grouping (BLVG)-based framework. First, the primary grouping applies a state-of-the-art variable grouping method based on variable interaction analysis to group the variables into subcomponents. Second, the secondary grouping further groups the subcomponents into variable cells, that is, combination variable cells and decomposition variable cells. We then tailor a multipopulation strategy to process the two types of variable cells efficiently in a cooperative coevolutionary (CC) way. As indicated by the empirical study on large-scale dynamic optimization problems (DOPs) of up to 300 dimensions, the proposed framework outperforms several state-of-the-art frameworks for large-scale dynamic optimization.

Blood pressure (BP) is one of the most important indicators of health. BP that is too high or too low causes varying degrees of diseases, such as renal impairment, cerebrovascular incidents, and cardiovascular diseases. Since traditional cuff-based BP measurement techniques have the drawbacks of patient discomfort and the impossibility of continuous BP monitoring, noninvasive cuffless continuous BP measurement has become a popular topic. The common noninvasive approach uses machine-learning (ML) algorithms to estimate BP by using the features extracted from simultaneous photoplethysmogram (PPG) and electrocardiogram (ECG) signals, such as the pulse transit time and pulse wave velocity. This study investigates the BP estimation performance of the novel dendritic neural regression (DNR) method proposed by us. Unlike conventional neural networks, DNR utilizes the multiplication operator as the excitation function in each dendritic branch, inspired by biological neuron phenomena, and can effectively capture nonlinear relationships between distinct input features. In addition, AMSGrad is used as the optimization algorithm to further enhance the dendritic neural model's performance. The experimental results show that by being fed a combination of the raw features extracted from the ECG and PPG signals and the components of the BP mathematical models, DNR can increase the accuracy of systolic BP, diastolic BP, and mean arterial pressure estimation significantly, which are superior to the state-of-the-art ML techniques. According to the British Hypertension Society protocol, DNR achieves a grade of A for the long-term BP estimation. Considering its architectural simplicity and powerful performance, the proposed method can be regarded as a reliable tool for estimating long-term continuous BP in a noninvasive cuffless way.

The dendritic neural model (DNM) is computationally faster than other machine-learning techniques, because its architecture can be implemented by using logic circuits and its calculations can be performed entirely in binary form. To further improve the computational speed, a straightforward approach is to generate a more concise architecture for the DNM. Actually, the architecture search is a large-scale multiobjective optimization problem (LSMOP), where a large number of parameters need to be set with the aim of optimizing accuracy and structural complexity simultaneously. However, the issues of irregular Pareto front, objective discontinuity, and population degeneration strongly limit the performances of conventional multiobjective evolutionary algorithms (MOEAs) on the specific problem. Therefore, a novel competitive decomposition-based MOEA is proposed in this study, which decomposes the original problem into several constrained subproblems, with neighboring subproblems sharing overlapping regions in the objective space. The solutions in the overlapping regions participate in environmental selection for the neighboring subproblems and then propagate the selection pressure throughout the entire population. Experimental results demonstrate that the proposed algorithm can possess a more powerful optimization ability than the state-of-the-art MOEAs. Furthermore, both the DNM itself and its hardware implementation can achieve very competitive classification performances when trained by the proposed algorithm, compared with numerous widely used machine-learning approaches.

Many real-world optimization problems require searching for multiple optimal solutions simultaneously, which are called multimodal optimization problems (MMOPs). For MMOPs, the algorithm is required both to enlarge population diversity for locating more global optima and to enhance refine ability for increasing the accuracy of the obtained solutions. Thus, numerous niching techniques have been proposed to divide the population into different niches, and each niche is responsible for searching on one or more peaks. However, it is often a challenge to distinguish proper individuals as niche centers in existing niching approaches, which has become a key issue for efficiently solving MMOPs. In this article, the niche center distinguish (NCD) problem is treated as an optimization problem and an NCD-based differential evolution (NCD-DE) algorithm is proposed. In NCD-DE, the niches are formed by using an internal genetic algorithm (GA) to online solve the NCD optimization problem. In the internal GA, a fitness-entropy measurement objective function is designed to evaluate whether a group of niche centers (i.e., encoded by a chromosome in the internal GA) is promising. Moreover, to enhance the exploration and exploitation abilities of NCD-DE in solving the MMOPs, a niching and global cooperative mutation strategy that uses both niche and population information is proposed to generate new individuals. The proposed NCD-DE is compared with some state-of-the-art and recent well-performing algorithms. The experimental results show that NCD-DE achieves better or competitive performance on both the accuracy and completeness of the solutions than the compared algorithms.

Cooperative coevolution (CC) algorithms based on variable decomposition methods are efficient in solving large-scale optimization problems (LSOPs). However, many decomposition methods, such as the differential grouping (DG) method and its variants, are based on the theorem of function additively separable, which may not work well on problems that are not additively separable and will result in a bottleneck for CC to solve various LSOPs. This deficiency motivates us to study how the decomposition method can decompose more kinds of separable functions, such as the multiplicatively separable function, to improve the general problem-solving ability of CC on LSOPs. With this concern, this article makes the first attempt to decompose multiplicatively separable functions and proposes a novel method called dual DG (DDG) for better LSOP decomposition and optimization. The novelty and advantage of DDG are that it can be suitable for not only additively separable functions but also multiplicatively separable functions, which can considerably expand the application scope of CC. In this article, we will first define the multiplicatively separable function, and then mathematically show its relationship to the additively separable function and how they can be transformed into each other. Based on this, the DDG can use two kinds of differences to detect the separable structure of both additively and multiplicatively separable functions. In addition, the time complexity of DDG is analyzed and a DDG-based CC algorithm framework is developed for solving LSOPs. To verify the superiority of DDG, experiments and comparisons with some state-of-the-art and champion algorithms are conducted not only on 30 LSOPs based on the test suite of the IEEE CEC large-scale global optimization competition, but also on a case study of the parameter optimization for a neural network-based application.

Decomposition methods have been widely employed in evolutionary algorithms for tackling multiobjective optimization problems (MOPs) due to their good mathematical explanation and promising performance. However, most decomposition methods only use a single ideal or nadir point to guide the evolution, which are not so effective for solving MOPs with extremely convex/concave Pareto fronts (PFs). To solve this problem, this article proposes an effective method to adapt decomposed directions (ADDs) for solving MOPs. Instead of using one single ideal or nadir point, each weight vector has one exclusive ideal point in our method for decomposition, in which the decomposed directions are adapted during the search process. In this way, the adapted decomposed directions can evenly and entirely cover the PF of the target MOP. The effectiveness of our method is analyzed theoretically and verified experimentally when embedding it into three representative multiobjective evolutionary algorithms (MOEAs), which can significantly improve their performance. When compared to seven competitive MOEAs, the experiments also validate the advantages of our method for solving 39 artificial MOPs with various PFs and one real-world MOP.

The radial basis function (RBF) model and the Kriging model have been widely used in the surrogate-assisted evolutionary algorithms (SAEAs). Based on their characteristics, a global and local surrogate-assisted differential evolution algorithm (GL-SADE) for high-dimensional expensive problems is proposed in this article, in which a global RBF model is trained with all samples to estimate a global trend, and then its optima is used to significantly accelerate the convergence process. A local Kriging model prefers to select points with good predicted fitness and great uncertainty, which can effectively prevent the search from getting trapped into local optima. When the local Kriging model finds the best solution so far, a reward search strategy is executed to further exploit the local Kriging model. The experiments on a set of benchmark functions with dimensions varying from 30 to 200 are conducted to evaluate the performance of the proposed algorithm. The experimental results of the proposed algorithm are compared to four state-of-the-art algorithms to show its effectiveness and efficiency in solving high-dimensional expensive problems. Besides, GL-SADE is applied to an airfoil optimization problem to show its effectiveness.

Surrogate-assisted evolutionary algorithms (SAEAs) have shown promising performance for solving expensive optimization problems (EOPs) whose true evaluations are computationally or physically expensive. However, most existing SAEAs only focus on the problems with low dimensionality and they rarely consider solving large-scale EOPs (LSEOPs). To fill this research gap, this article proposes an ensemble surrogate-based coevolutionary optimizer for tackling LSEOPs. First, some local surrogate models are trained with low-dimensional data subsets by using feature selection on the large-scale decision variables, a part of which are used to build a selective ensemble surrogate for better approximating the target LSEOP. Then, a coevolutionary optimizer guided by the ensemble surrogate is designed by running two populations to cooperatively solve the target LSEOP and the simplified auxiliary problem. The information of offspring from the two populations is shared to facilitate the coevolution process, which can exploit the searching experience from the simplified auxiliary problem to help solving the target LSEOP. Finally, an effective infill selection criterion is used to update the ensemble surrogate and enhance its approximate performance. To evaluate the performance of the proposed algorithm, a number of well-known benchmark problems are used and the experimental results validate our superior performance over nine state-of-the-art SAEAs on most cases.

The evolutionary multitask optimization (EMTO) algorithm is a promising approach to solve many-task optimization problems (MaTOPs), in which similarity measurement and knowledge transfer (KT) are two key issues. Many existing EMTO algorithms estimate the similarity of population distribution to select a set of similar tasks and then perform KT by simply mixing individuals among the selected tasks. However, these methods may be less effective when the global optima of the tasks greatly differ from each other. Therefore, this article proposes to consider a new kind of similarity, namely, shift invariance, between tasks. The shift invariance is defined that the two tasks are similar after linear shift transformation on both the search space and the objective space. To identify and utilize the shift invariance between tasks, a two-stage transferable adaptive differential evolution (TRADE) algorithm is proposed. In the first evolution stage, a task representation strategy is proposed to represent each task by a vector that embeds the evolution information. Then, a task grouping strategy is proposed to group the similar (i.e., shift invariant) tasks into the same group while the dissimilar tasks into different groups. In the second evolution stage, a novel successful evolution experience transfer method is proposed to adaptively utilize the suitable parameters by transferring successful parameters among similar tasks within the same group. Comprehensive experiments are carried out on two representative MaTOP benchmarks with a total of 16 instances and a real-world application. The comparative results show that the proposed TRADE is superior to some state-of-the-art EMTO algorithms and single-task optimization algorithms.

Multiobjective multitask optimization (MMO) attempts to solve several problems simultaneously. This is commonly done by identifying useful knowledge to transfer between tasks, thereby producing optimal solutions more quickly. In this study, an MMO algorithm using transfer rank and a KNN model is proposed to achieve this goal. The definition of transfer rank is first introduced for quantifying the priority of transfer solutions, to improve the probability of a positive result. The solution with the higher rank was assumed to be the most suitable for transfer, as solutions were sorted in descending order based on transfer rank. Priority was given to previous and positive-transfer solutions and those with the same transfer rank were distinguished using a KNN model classifier. The effectiveness of the proposed algorithm was verified by studying benchmark MMO problems. The experimental results showed the proposed algorithm was more effective than other conventional MMO techniques.

Many-task optimization problem is a kind of challenging multi-task optimization problem with more than three tasks. Two significant issues in solving many-task optimization problems are measuring inter-task similarity and transferring knowledge among similar tasks. However, most existing algorithms only use a single similarity measurement, which cannot accurately measure the inter-task similarity because the inter-task similarity is a concept with multiple different aspects. To address this limitation, this paper proposes a bi-objective knowledge transfer framework, which aims firstly to accurately measure different types of inter-task similarity using two different measurements and secondly to effectively transfer knowledge with different types of similarity via specific strategies. To achieve the first goal, a bi-objective measurement is designed to measure inter-task similarity from two different aspects, including shape similarity and domain similarity. To achieve the second goal, a similarity-based adaptive knowledge transfer strategy is designed to choose the suitable knowledge transfer strategy based on the type of inter-task similarity. We compare the bi-objective knowledge transfer framework-based algorithms with several state-of-the-art algorithms on two challenging many-task optimization test suites with 16 instances and on real-world many-task optimization problems with up to 500 tasks. The experimental results show that the proposed algorithms generally outperform the compared algorithms.

Recently, evolutionary multitasking (EMT) has been successfully used in the field of high-dimensional classification. However, the generation of multiple tasks in the existing EMT-based feature selection (FS) methods is relatively simple, using only the Relief-${F}$method to collect related features with similar importance into one task, which cannot provide more diversified tasks for knowledge transfer. Thus, this article devises a new EMT algorithm for FS in high-dimensional classification, which first adopts different filtering methods to produce multiple tasks and then modifies a competitive swarm optimizer (CSO) to efficiently solve these related tasks via knowledge transfer. First, a diversified multiple task generation method is designed based on multiple filtering methods, which generates several relevant low-dimensional FS tasks by eliminating irrelevant features. In this way, useful knowledge for solving simple and relevant tasks can be transferred to simplify and speed up the solution of the original high-dimensional FS task. Then, a CSO is modified to simultaneously solve these relevant FS tasks by transferring useful knowledge among them. Numerous empirical results demonstrate that the proposed EMT-based FS method can obtain a better feature subset than several state-of-the-art FS methods on 18 high-dimensional datasets.

Handling constrained multiobjective optimization problems (CMOPs) is extremely challenging, since multiple conflicting objectives subject to various constraints require to be simultaneously optimized. To deal with CMOPs, numerous constrained multiobjective evolutionary algorithms (CMOEAs) have been proposed in recent years, and they have achieved promising performance. However, there has been few literature on the systematic review of the related studies currently. This article provides a comprehensive survey for evolutionary constrained multiobjective optimization. We first review a large number of CMOEAs through categorization and analyze their advantages and drawbacks in each category. Then, we summarize the benchmark test problems and investigate the performance of different constraint handling techniques (CHTs) and different algorithms, followed by some emerging and representative applications of CMOEAs. Finally, we discuss some new challenges and point out some directions of the future research in the field of evolutionary constrained multiobjective optimization.

Evolutionary transfer optimization (ETO) has been becoming a hot research topic in the field of evolutionary computation, which is based on the fact that knowledge learning and transfer across the related optimization exercises can improve the efficiency of others. However, rare studies employ ETO to solve large-scale multiobjective optimization problems (LMOPs). To fill this research gap, this article proposes a new multitasking ETO algorithm via a powerful transfer learning model to simultaneously solve multiple LMOPs. In particular, inspired by adversarial domain adaptation in transfer learning, a discriminative reconstruction network (DRN) model (containing an encoder, a decoder, and a classifier) is created for each LMOP. At each generation, the DRN is trained by the currently obtained nondominated solutions for all LMOPs via backpropagation with gradient descent. With this well-trained DRN model, the proposed algorithm can transfer the solutions of source LMOPs directly to the target LMOP for assisting its optimization, can evaluate the correlation between the source and target LMOPs to control the transfer of solutions, and can learn a dimensional-reduced Pareto-optimal subspace of the target LMOP to improve the efficiency of transfer optimization in the large-scale search space. Moreover, we propose a real-world multitasking LMOP suite to simulate the training of deep neural networks (DNNs) on multiple different classification tasks. Finally, the effectiveness of the proposed algorithm has been validated in this real-world problem suite and the other two synthetic problem suites.

Recent decades have witnessed great advancements in multiobjective evolutionary algorithms (MOEAs) for multiobjective optimization problems (MOPs). However, these progressively improved MOEAs have not necessarily been equipped with scalable and learnable problem-solving strategies for new and grand challenges brought by the scaling-up MOPs with continuously increasing complexity from diverse aspects, mainly, including expensive cost of function evaluations, many objectives, large-scale search space, time-varying environments, and multitask. Under different scenarios, divergent thinking is required in designing new powerful MOEAs for solving them effectively. In this context, research studies on learnable MOEAs with machine learning techniques have received extensive attention in the field of evolutionary computation. This article begins with a general taxonomy of scaling-up MOPs and learnable MOEAs, followed by an analysis of the challenges that these MOPs pose to traditional MOEAs. Then, we synthetically overview recent advances of learnable MOEAs in solving various scaling-up MOPs, focusing primarily on four attractive directions (i.e., learnable evolutionary discriminators for environmental selection, learnable evolutionary generators for reproduction, learnable evolutionary evaluators for function evaluations, and learnable evolutionary transfer modules for sharing or reusing optimization experience). The insight of learnable MOEAs is offered to readers as a reference to the general track of the efforts in this field.

Most existing evolutionary search strategies are not so efficient when directly handling the decision space of large-scale multiobjective optimization problems (LMOPs). To enhance the efficiency of tackling LMOPs, this article proposes an accelerated evolutionary search (AES) strategy. Its main idea is to learn a gradient-descent-like direction vector (GDV) for each solution via the specially trained feedforward neural network, which may be the learnt possibly fastest convergent direction to reproduce new solutions efficiently. To be specific, a multilayer perceptron (MLP) with only one hidden layer is constructed, in which the number of neurons in the input and output layers is equal to the dimension of the decision space. Then, to get appropriate training data for the model, the current population is divided into two subsets based on the nondominated sorting, and each poor solution in one subset with worse convergence will be paired to an elitist solution in another subset with the minimum angle to it, which is considered most likely to guide it with rapid convergence. Next, this MLP is updated via backpropagation with gradient descent by using the above elaborately prepared dataset. Finally, an accelerated large-scale multiobjective evolutionary algorithm (ALMOEA) is designed by using AES as a reproduction operator. Experimental studies validate the effectiveness of the proposed AES when handling the search space of LMOPs with dimensionality ranging from 1000 to 10000. When compared with six state-of-the-art evolutionary algorithms, the experimental results also show the better efficiency and performance of the proposed optimizer in solving various LMOPs.

Evolutionary large-scale multiobjective optimization (ELMO) has received increasing attention in recent years. This study has compared various existing optimizers for ELMO on different benchmarks, revealing that both benchmarks and algorithms for ELMO still need significant improvement. Thus, a new test suite and a new optimizer framework are proposed to further promote the research of ELMO. More realistic features are considered in the new benchmarks, such as mixed formulation of objective functions, mixed linkages in variables, and imbalanced contributions of variables to the objectives, which are challenging to the existing optimizers. To better tackle these benchmarks, a variable group-based learning strategy is embedded into the new optimizer framework for ELMO, which significantly improves the quality of reproduction in large-scale search space. The experimental results validate that the designed benchmarks can comprehensively evaluate the performance of existing optimizers for ELMO and the proposed optimizer shows distinct advantages in tackling these benchmarks.

When solving constrained multiobjective optimization problems (CMOPs), the utilization of infeasible solutions significantly affects algorithm’s performance because they not only maintain diversity but also provide promising search directions. In light of this situation, this article proposes a new multitasking-constrained multiobjective optimization (MTCMO) framework, in which a dynamic auxiliary task is created to assist in solving a complex CMOP (the main task) via the knowledge transfer. Moreover, the constraint boundary of the auxiliary task reduces dynamically, so that it keeps a high relatedness with the main task to continuously provide supplementary evolutionary directions. Furthermore, an improved$\epsilon $method is designed for the auxiliary task to utilize diverse high-quality infeasible solutions for breaking through infeasible obstacles in the early stage and approaching the feasible boundary from infeasible regions in the later stage. Besides, a new test function with decision space constraints is designed, where one parameter can be adjusted to control the overlap degree between the constrained Pareto front and the unconstrained Pareto front. This function and the other two modified existing functions are used to analyze the characteristics of MTCMO. Finally, compared with 11 state-of-the-art peer methods, the superior or competitive performance of MTCMO is demonstrated on 54 benchmark functions and two real-world applications.

Knowledge transfer (KT) plays a key role in multitask optimization. However, most of the existing KT methods still face two challenges. First, the tasks may commonly have different dimensionalities (DDs), making the KT between heterogeneous search spaces very difficult. Second, the tasks may have different degrees of similarity in different dimensions, making that treating all dimensions with equal importance may be harmful to the KT process. To address these two challenges, this article proposes a novel orthogonal transfer (OT) method that is enabled by a cross-task mapping (CTM) strategy, which can achieve high-quality KT among heterogeneous tasks. For the first challenge, the CTM strategy maps the global best individual of one task from its original search space to the search space of the target task via an optimization process, which can handle the difference in task dimensionality. For the second challenge, the OT method is performed on the CTM-obtained individual and a random individual of the target task to find the best combination of different dimensions in these two individuals rather than treating all the dimensions equally, so as to achieve high-quality KT. To verify the effectiveness of the proposed OT method and the resulted OT-based multitask optimization (OTMTO) algorithm, this article not only uses the existing multitask optimization benchmark but also proposes a new benchmark test suite named multitask optimization problems (MTOPs) with DDs. Comprehensive experimental results on the existing and the proposed benchmarks show that the proposed OT method and the OTMTO algorithm are very advantageous in providing high-quality KT and in handling the heterogeneity of search space in MTOPs compared to the existing competitive evolutionary multitask optimization (EMTO) algorithms.

Genetic programming (GP) has achieved great success for learning scheduling heuristics in dynamic job-shop scheduling (JSS). In theory, generating a large number of offspring for GP, known as brood recombination, can improve its heuristic generation ability. However, it is time consuming to evaluate extra individuals. Phenotypic characterization-based surrogates with K-nearest neighbors have been successfully used for GP to preselect only promising individuals for real fitness evaluations in dynamic JSS. However, sample individuals used by surrogate are from only the current generation, since the fitness of individuals across generations is not comparable due to the rotation of training instances. The surrogate cannot accurately estimate the fitness of an offspring that is far away from all the limited sample individuals at the current generation. This article proposes an effective instance-rotation-based surrogate to address the above issue. Specifically, the surrogate uses the samples extracted from individuals across multiple generations with different instances. More importantly, we propose a fitness mapping strategy to make the fitness evaluated by different instances comparable. The results show that the GP with brood recombination and the proposed surrogate can significantly improve the quality of scheduling heuristics. The results also reveal that the proposed algorithm has successfully reduced the number of omitted promising offspring due to the higher accuracy of the surrogate. The samples in the new surrogate spread better in the phenotypic space, and the nearest neighbor tends to be closer to the predicted offspring. This makes the estimated fitness more accurate.

Multitask learning has been successfully used in handling multiple related tasks simultaneously. In reality, there are often many tasks to be solved together, and the relatedness between them is unknown in advance. In this article, we focus on the multitask genetic programming (GP) for the dynamic flexible job shop scheduling (DFJSS) problems, and address two challenges. The first is how to measure the relatedness between tasks accurately. The second is how to select task pairs to transfer knowledge during the multitask learning process. To measure the relatedness between DFJSS tasks, we propose a new relatedness metric based on the behavior distributions of the variable-length GP individuals. In addition, for more effective knowledge transfer, we develop an adaptive strategy to choose the most suitable assisted task for the target task based on the relatedness information between tasks. The findings show that in all of the multitask scenarios studied, the proposed algorithm can substantially increase the effectiveness of the learned scheduling heuristics for all the desired tasks. The effectiveness of the proposed algorithm has also been verified by the analysis of task relatedness and structures of the evolved scheduling heuristics, and the discussions of population diversity and knowledge transfer.

Neural architecture search (NAS) has attracted much attention in recent years. It automates the neural network construction for different tasks, which is traditionally addressed manually. In the literature, evolutionary optimization (EO) has been proposed for NAS due to its strong global search capability. However, despite the success enjoyed by EO, it is worth noting that existing EO algorithms for NAS are often very computationally expensive, which makes these algorithms unpractical in reality. Keeping this in mind, in this article, we propose an efficient memetic algorithm (MA) for automated convolutional neural network (CNN) architecture search. In contrast to existing EO algorithms for CNN architecture design, a new cell-based architecture search space, and new global and local search operators are proposed for CNN architecture search. To further improve the efficiency of our proposed algorithm, we develop a one-epoch-based performance estimation strategy without any pretrained models to evaluate each found architecture on the training datasets. To investigate the performance of the proposed method, comprehensive empirical studies are conducted against 34 state-of-the-art peer algorithms, including manual algorithms, reinforcement learning (RL) algorithms, gradient-based algorithms, and evolutionary algorithms (EAs), on widely used CIFAR10 and CIFAR100 datasets. The obtained results confirmed the efficacy of the proposed approach for automated CNN architecture design.

Class imbalance is a common issue in the community of machine learning and data mining. The class-imbalance distribution can make most classical classification algorithms neglect the significance of the minority class and tend toward the majority class. In this article, we propose a label enhancement method to solve the class-imbalance problem in a graph manner, which estimates the numerical label and trains the inductive model simultaneously. It gives a new perspective on the class-imbalance learning based on the numerical label rather than the original logical label. We also present an iterative optimization algorithm and analyze the computation complexity and its convergence. To demonstrate the superiority of the proposed method, several single-label and multilabel datasets are applied in the experiments. The experimental results show that the proposed method achieves a promising performance and outperforms some state-of-the-art single-label and multilabel class-imbalance learning methods.

Deep neural networks (DNNs) have achieved great success in many applications. The architectures of DNNs play a crucial role in their performance, which is usually manually designed with rich expertise. However, such a design process is labor-intensive because of the trial-and-error process and also not easy to realize due to the rare expertise in practice. Neural architecture search (NAS) is a type of technology that can design the architectures automatically. Among different methods to realize NAS, the evolutionary computation (EC) methods have recently gained much attention and success. Unfortunately, there has not yet been a comprehensive summary of the EC-based NAS algorithms. This article reviews over 200 articles of most recent EC-based NAS methods in light of the core components, to systematically discuss their design principles and justifications on the design. Furthermore, current challenges and issues are also discussed to identify future research in this emerging field.

Large-scale multiobjective optimization problems (LSMOPs) are characterized as optimization problems involving hundreds or even thousands of decision variables and multiple conflicting objectives. To solve LSMOPs, some algorithms designed a variety of strategies to track Pareto-optimal solutions (POSs) by assuming that the distribution of POSs follows a low-dimensional manifold. However, traditional genetic operators for solving LSMOPs have some deficiencies in dealing with the manifold, which often results in poor diversity, local optima, and inefficient searches. In this work, a generative adversarial network (GAN)-based manifold interpolation framework is proposed to learn the manifold and generate high-quality solutions on the manifold, thereby improving the optimization performance of evolutionary algorithms. We compare the proposed approach with several state-of-the-art algorithms on various large-scale multiobjective benchmark functions. The experimental results demonstrate that significant improvements have been achieved by the proposed framework in solving LSMOPs.

Spiking neural networks (SNNs) represent the most prominent biologically inspired computing model for neuromorphic computing (NC) architectures. However, due to the nondifferentiable nature of spiking neuronal functions, the standard error backpropagation algorithm is not directly applicable to SNNs. In this work, we propose a tandem learning framework that consists of an SNN and an artificial neural network (ANN) coupled through weight sharing. The ANN is an auxiliary structure that facilitates the error backpropagation for the training of the SNN at the spike-train level. To this end, we consider the spike count as the discrete neural representation in the SNN and design an ANN neuronal activation function that can effectively approximate the spike count of the coupled SNN. The proposed tandem learning rule demonstrates competitive pattern recognition and regression capabilities on both the conventional frame- and event-based vision datasets, with at least an order of magnitude reduced inference time and total synaptic operations over other state-of-the-art SNN implementations. Therefore, the proposed tandem learning rule offers a novel solution to training efficient, low latency, and high-accuracy deep SNNs with low computing resources.

This work addresses unsupervised partial domain adaptation (PDA), in which classes in the target domain are a subset of the source domain. The key challenges of PDA are how to leverage source samples in the shared classes to promote positive transfer and filter out the irrelevant source samples to mitigate negative transfer. Existing PDA methods based on adversarial DA do not consider the loss of class discriminative representation. To this end, this article proposes a contrastive learning-assisted alignment (CLA) approach for PDA to jointly align distributions across domains for better adaptation and to reweight source instances to reduce the contribution of outlier instances. A contrastive learning-assisted conditional alignment (CLCA) strategy is presented for distribution alignment. CLCA first exploits contrastive losses to discover the class discriminative information in both domains. It then employs a contrastive loss to match the clusters across the two domains based on adversarial domain learning. In this respect, CLCA attempts to reduce the domain discrepancy by matching the class-conditional and marginal distributions. Moreover, a new reweighting scheme is developed to improve the quality of weights estimation, which explores information from both the source and the target domains. Empirical results on several benchmark datasets demonstrate that the proposed CLA outperforms the existing state-of-the-art PDA methods.

Emulating the spike-based processing in the brain, spiking neural networks (SNNs) are developed and act as a promising candidate for the new generation of artificial neural networks that aim to produce efficient cognitions as the brain. Due to the complex dynamics and nonlinearity of SNNs, designing efficient learning algorithms has remained a major difficulty, which attracts great research attention. Most existing ones focus on the adjustment of synaptic weights. However, other components, such as synaptic delays, are found to be adaptive and important in modulating neural behavior. How could plasticity on different components cooperate to improve the learning of SNNs remains as an interesting question. Advancing our previous multispike learning, we propose a new joint weight-delay plasticity rule, named TDP-DL, in this article. Plastic delays are integrated into the learning framework, and as a result, the performance of multispike learning is significantly improved. Simulation results highlight the effectiveness and efficiency of our TDP-DL rule compared to baseline ones. Moreover, we reveal the underlying principle of how synaptic weights and delays cooperate with each other through a synthetic task of interval selectivity and show that plastic delays can enhance the selectivity and flexibility of neurons by shifting information across time. Due to this capability, useful information distributed away in the time domain can be effectively integrated for a better accuracy performance, as highlighted in our generalization tasks of the image, speech, and event-based object recognitions. Our work is thus valuable and significant to improve the performance of spike-based neuromorphic computing.

Vehicle routing problems (VRPs) are essential in logistics. In the literature, many exact and heuristic optimization algorithms have been proposed to solve the VRPs. These traditional approaches, however, generally start the optimization from scratch and ignore the experiences of solving related VRPs, which may lead to unnecessary computational costs in searching repeated problems and reduce the efficiency of vehicle routing. Recently, transfer optimization (TO) has been presented to speed up vehicle routing by reusing the knowledge learned from similarly solved VRPs. However, existing TO methods build connections across VRPs in a low-dimensional Euclidean space, which has limited modeling ability in the cases of having nonlinear correlations. Keeping this in mind, this article presents a study of TO equipped with the kernel method for fast vehicle routing. In contrast to existing TO methods, in this work, the learning of connections across VRPs for knowledge transfer is conducted in a reproducing kernel Hilbert space (RKHS), which thus has greater modeling capacity in nonlinear customer relationships between VPRs. To evaluate the performance of the proposed method, comprehensive empirical studies have been conducted using well-known VRP benchmarks, against existing state-of-the-art TO methods for vehicle routing. Finally, a well-known real-world VRP application given by a routing company (Jingdong), namely, the package delivery problem (PDP), is investigated to further assess the efficacy of our proposed method.

The Pareto front (PF) estimation has become an emerging strategy for solving multiobjective optimization problems in recent studies. By approximating the geometrical structure of the PF during the evolutionary procedure, some PF estimation approaches have been suggested and shown effectiveness in guiding the search direction of evolutionary algorithms. However, these approaches encounter difficulties in handling irregular PFs, whose geometrical structures are too complex to be properly approximated. To address this issue, this article proposes a novel PF estimation approach based on local models. In contrast to existing approaches estimating the PF via a reference point set or a single model, the proposed approach automatically divides the population into several groups and builds a local model for each group of solutions. In spite of the simplicity of each local model, the combination of all the local models can approximate the PFs with complex geometrical structures. An evolutionary algorithm is then developed based on the local model-based PF estimation approach and a novel fitness function and is compared with four evolutionary algorithms on 39 problems. Statistical results indicate that the proposed algorithm exhibits better performance than the compared algorithms, especially on problems with highly irregular PFs.

Large-scale multiobjective optimization problems (LSMOPs) refer to optimization problems with multiple con-flicting optimization objectives and hundreds or even thousands of decision variables. A key point in solving LSMOPs is how to balance exploration and exploitation so that the algorithm can search in a huge decision space efficiently. Large-scale multi-objective evolutionary algorithms consider the balance between exploration and exploitation from the individual's perspective. However, these algorithms ignore the significance of tackling this issue from the perspective of decision variables, which makes the algorithm lack the ability to search from different dimensions and limits the performance of the algorithm. In this paper, we propose a large-scale multiobjective optimization algorithm based on the attention mechanism, called (LMOAM). The attention mechanism will assign a unique weight to each decision variable, and LMOAM will use this weight to strike a balance between exploration and exploitation from the decision variable level. Nine different sets of LSMOP benchmarks are conducted to verify the algorithm proposed in this paper, and the experimental results validate the effectiveness of our design.

The performance of traditional multiobj ective evolutionary algorithms (MOEAs) often deteriorates rapidly when using them to solve large-scale multiobjective optimization problems (LMOPs). To effectively handle LMOPs, we propose a large-scale MOEA via self-guided problem transformation. In the proposed optimizer, the original large-scale search space is transferred to a lower-dimensional weighted space by the guidance of solutions themselves, aiming to effectively search in the weighted space for speeding up the convergence of the population. Specifically, the variables of the target LMOP are adaptively and randomly divided into multiple equal groups, and then solutions are self-guided to construct the small-scale weighted space correspondingly to these variable groups. In this way, each solution is projected as a self-guided vector with multiple weight variables, and then new weight vectors can be generated by searching in the weighted space. Next, new offspring is produced by inversely mapping the newly generated weight vectors to the original search space of this LMOP. Finally, the proposed optimizer is tested on two different LMOP test suites by comparing them with five competitive large-scale MOEAs. Experimental results show some advantages of the proposed algorithm in solving the considered benchmarks.

This paper investigates crowd counting in the frequency domain, which is a novel direction compared to the traditional view in the spatial domain. By transforming the density map into the frequency domain and using the properties of the characteristic function, we propose a novel method that is simple, effective, and efficient. The solid theoretical analysis ends up as an implementation-friendly loss function, which requires only standard tensor operations in the training process. We prove that our loss function is an upper bound of the pseudo sup norm metric between the ground truth and the prediction density map (over all of their sub-regions), and demonstrate its efficacy and efficiency versus other loss functions. The experimental results also show its competitiveness to the state-of-the-art on five benchmark data sets: ShanghaiTech A & B, UCF-QNRF, JHU++, and NWPU. Our codes will be available at: wb-shu/Crowd_Couniing_in_the_Frequency_Domain

The high prevalence of mental disorders gradually poses a huge pressure on the public healthcare services. Recently, deep learning-based computer-aided diagnosis has been introduced to relieve the tension in healthcare institutions by automatically detecting abnormal neuroimaging-derived pheno-types in patients. However, the training of deep learning models relies on sufficiently large annotated datasets, which can be costly, time-consuming, and laborious. Semi-supervised learning (SSL) can mitigate this challenge by leveraging both labeled and unlabeled samples. In this work, an effective dual-stage pseudo-labeling based classification framework dubbed DSPL is proposed to diagnose mental disorders on functional magnetic resonance imaging data. A bicriteria-based pseudo-labels selection method is developed to filter out inferior pseudo-labeled samples. Subsequently, we further propose a self-mutual learning enhanced pseudo-labeling generation approach to mitigate the adverse effects bought by the noisy pseudo-labeled samples. On real-world datasets, the proposed method achieves diagnosis accuracies of 68.09%, 67.94%, and 68.13% on ABIDE-I, ABIDE-II, and ADHD-200, respectively. Ablation study suggests that each component in DSPL makes a great contribution to performance improvement.

Spiking neural networks (SNNs) have shown clear advantages over traditional artificial neural networks (ANNs) for low latency and high computational efficiency, due to their event-driven nature and sparse communication. However, the training of deep SNNs is not straightforward. In this paper, we propose a novel ANN-to-SNN conversion and layer-wise learning framework for rapid and efficient pattern recognition, which is referred to as progressive tandem learning. By studying the equivalence between ANNs and SNNs in the discrete representation space, a primitive network conversion method is introduced that takes full advantage of spike count to approximate the activation value of ANN neurons. To compensate for the approximation errors arising from the primitive network conversion, we further introduce a layer-wise learning method with an adaptive training scheduler to fine-tune the network weights. The progressive tandem learning framework also allows hardware constraints, such as limited weight precision and fan-in connections, to be progressively imposed during training. The SNNs thus trained have demonstrated remarkable classification and regression capabilities on large-scale object recognition, image reconstruction, and speech separation tasks, while requiring at least an order of magnitude reduced inference time and synaptic operations than other state-of-the-art SNN implementations. It, therefore, opens up a myriad of opportunities for pervasive mobile and embedded devices with a limited power budget.

A single dataset could hide a significant number of relationships among its feature set. Learning these relationships simultaneously avoids the time complexity associated with running the learning algorithm for every possible relationship, and affords the learner with an ability to recover missing data and substitute erroneous ones by using available data. In our previous research, we introduced the gate-layer autoencoders (GLAEs), which offer an architecture that enables a single model to approximate multiple relationships simultaneously. GLAE controls what an autoencoder learns in a time series by switching on and off certain input gates, thus, allowing and disallowing the data to flow through the network to increase network's robustness. However, GLAE is limited to binary gates. In this article, we generalize the architecture to weighted gate layer autoencoders (WGLAE) through the addition of a weight layer to update the error according to which variables are more critical and to encourage the network to learn these variables. This new weight layer can also be used as an output gate and uses additional control parameters to afford the network with abilities to represent different models that can learn through gating the inputs. We compare the architecture against similar architectures in the literature and demonstrate that the proposed architecture produces more robust autoencoders with the ability to reconstruct both incomplete synthetic and real data with high accuracy.

Dynamic multiobjective optimization problem (DMOP) denotes the multiobjective optimization problem, which contains objectives that may vary over time. Due to the widespread applications of DMOP existed in reality, DMOP has attracted much research attention in the last decade. In this article, we propose to solve DMOPs via an autoencoding evolutionary search. In particular, for tracking the dynamic changes of a given DMOP, an autoencoder is derived to predict the moving of the Pareto-optimal solutions based on the nondominated solutions obtained before the dynamic occurs. This autoencoder can be easily integrated into the existing multiobjective evolutionary algorithms (EAs), for example, NSGA-II, MOEA/D, etc., for solving DMOP. In contrast to the existing approaches, the proposed prediction method holds a closed-form solution, which thus will not bring much computational burden in the iterative evolutionary search process. Furthermore, the proposed prediction of dynamic change is automatically learned from the nondominated solutions found along the dynamic optimization process, which could provide more accurate Pareto-optimal solution prediction. To investigate the performance of the proposed autoencoding evolutionary search for solving DMOP, comprehensive empirical studies have been conducted by comparing three state-of-the-art prediction-based dynamic multiobjective EAs. The results obtained on the commonly used DMOP benchmarks confirmed the efficacy of the proposed method.

Performance of multi/many-objective evolutionary algorithms (MOEAs) based on decomposition is highly impacted by the Pareto front (PF) shapes of multi/many-objective optimization problems (MOPs), as their adopted weight vectors may not properly fit the PF shapes. To avoid this mismatch, some MOEAs treat solutions as weight vectors to guide the evolutionary search, which can adapt to the target MOP's PF automatically. However, their performance is still affected by the similarity metric used to select weight vectors. To address this issue, this article proposes a fuzzy decomposition-based MOEA. First, a fuzzy prediction is designed to estimate the population's shape, which helps to exactly reflect the similarities of solutions. Then, N least similar solutions are extracted as weight vectors to obtain N constrained fuzzy subproblems ( N is the population size), and accordingly, a shared weight vector is calculated for all subproblems to provide a stable search direction. Finally, the corner solution for each of m least similar subproblems ( m is the objective number) is preserved to maintain diversity, while one solution having the best aggregated value on the shared weight vector is selected for each of the remaining subproblems to speed up convergence. When compared to several competitive MOEAs in solving a variety of test MOPs, the proposed algorithm shows some advantages at fitting their different PF shapes.

Large-scale multiobjective optimization problems (LMOPs) bring significant challenges for traditional evolutionary operators, as their search capability cannot efficiently handle the huge decision space. Some newly designed search methods for LMOPs usually classify all variables into different groups and then optimize the variables in the same group with the same manner, which can speed up the population's convergence. Following this research direction, this article suggests a differential evolution (DE) algorithm that favors searching the variables with higher importance to the solving of LMOPs. The importance of each variable to the target LMOP is quantized and then all variables are categorized into different groups based on their importance. The variable groups with higher importance are allocated with more computational resources using DE. In this way, the proposed method can efficiently generate offspring in a low-dimensional search subspace formed by more important variables, which can significantly speed up the convergence. During the evolutionary process, this search subspace for DE will be expanded gradually, which can strike a good balance between exploration and exploitation in tackling LMOPs. Finally, the experiments validate that our proposed algorithm can perform better than several state-of-the-art evolutionary algorithms for solving various benchmark LMOPs.

It is known that many-objective optimization problems (MaOPs) often face the difficulty of maintaining good diversity and convergence in the search process due to the high-dimensional objective space. To address this issue, this article proposes a novel multiobjective framework for many-objective optimization (Mo4Ma), which transforms the many-objective space into multiobjective space. First, the many objectives are transformed into two indicative objectives of convergence and diversity. Second, a clustering-based sequential selection strategy is put forward in the transformed multiobjective space to guide the evolutionary search process. Specifically, the selection is circularly performed on the clustered subpopulations to maintain population diversity. In each round of selection, solutions with good performance in the transformed multiobjective space will be chosen to improve the overall convergence. The Mo4Ma is a generic framework that any type of evolutionary computation algorithm can incorporate compatibly. In this article, the differential evolution (DE) is adopted as the optimizer in the Mo4Ma framework, thus resulting in an Mo4Ma-DE algorithm. Experimental results show that the Mo4Ma-DE algorithm can obtain well-converged and widely distributed Pareto solutions along with the many-objective Pareto sets of the original MaOPs. Compared with seven state-of-the-art MaOP algorithms, the proposed Mo4Ma-DE algorithm shows strong competitiveness and general better performance.

The searching ability of the population-based search algorithms strongly relies on the coordinate system on which they are implemented. However, the widely used coordinate systems in the existing multifactorial optimization (MFO) algorithms are still fixed and might not be suitable for various function landscapes with differential modalities, rotations, and dimensions; thus, the intertask knowledge transfer might not be efficient. Therefore, this article proposes a novel intertask knowledge transfer strategy for MFOs implemented upon an active coordinate system that is established on a common subspace of two search spaces. The proper coordinate system might identify some common modality in a proper subspace to some extent. In this article, to seek the intermediate subspace, we innovatively introduce the geodesic flow that starts from a subspace, reaching another subspace in unit time. A low-dimension intermediate subspace is drawn from a uniform distribution defined on the geodesic flow, and the corresponding coordinate system is given. The intertask trial generation method is applied to the individuals by first projecting them on the low-dimension subspace, which reveals the important invariant features of the multiple function landscapes. Since intermediate subspace is generated from the major eigenvectors of tasks' spaces, this model turns out to be intrinsically regularized by neglecting the minor and small eigenvalues. Therefore, the transfer strategy can alleviate the influence of noise led by redundant dimensions. The proposed method exhibits promising performance in the experiments.

Both objective optimization and constraint satisfaction are crucial for solving constrained multiobjective optimization problems, but the existing evolutionary algorithms encounter difficulties in striking a good balance between them when tackling complex feasible regions. To address this issue, this article proposes a two-stage evolutionary algorithm, which adjusts the fitness evaluation strategies during the evolutionary process to adaptively balance objective optimization and constraint satisfaction. The proposed algorithm can switch between the two stages according to the status of the current population, enabling the population to cross the infeasible region and reach the feasible regions in one stage, and to spread along the feasible boundaries in the other stage. Experimental studies on four benchmark suites and three real-world applications demonstrate the superiority of the proposed algorithm over the state-of-the-art algorithms, especially on problems with complex feasible regions.

Evolutionary multitasking (EMT) is a newly emerging research topic in the community of evolutionary computation, which aims to improve the convergence characteristic across multiple distinct optimization tasks simultaneously by triggering knowledge transfer among them. Unfortunately, most of the existing EMT algorithms are only capable of boosting the optimization performance for homogeneous problems which explicitly share the same (or similar) fitness landscapes. Seldom efforts have been devoted to generalize the EMT for solving heterogeneous problems. A few preliminary studies employ domain adaptation techniques to enhance the transferability between two distinct tasks. However, almost all of these methods encounter a severe issue which is the so-called degradation of intertask mapping. Keeping this in mind, a novel rank loss function for acquiring a superior intertask mapping is proposed in this article. In particular, with an evolutionary-path-based representation model for optimization instance, an analytical solution of affine transformation for bridging the gap between two distinct problems is mathematically derived from the proposed rank loss function. It is worth mentioning that the proposed mapping-based transferability enhancement technique can be seamlessly embedded into an EMT paradigm. Finally, the efficacy of our proposed method against several state-of-the-art EMTs is verified experimentally on a number of synthetic multitasking and many-tasking benchmark problems, as well as a practical case study.

Spikes are the currency in central nervous systems for information transmission and processing. They are also believed to play an essential role in low-power consumption of the biological systems, whose efficiency attracts increasing attentions to the field of neuromorphic computing. However, efficient processing and learning of discrete spikes still remain a challenging problem. In this article, we make our contributions toward this direction. A simplified spiking neuron model is first introduced with the effects of both synaptic input and firing output on the membrane potential being modeled with an impulse function. An event-driven scheme is then presented to further improve the processing efficiency. Based on the neuron model, we propose two new multispike learning rules which demonstrate better performance over other baselines on various tasks, including association, classification, and feature detection. In addition to efficiency, our learning rules demonstrate high robustness against the strong noise of different types. They can also be generalized to different spike coding schemes for the classification task, and notably, the single neuron is capable of solving multicategory classifications with our learning rules. In the feature detection task, we re-examine the ability of unsupervised spike-timing-dependent plasticity with its limitations being presented, and find a new phenomenon of losing selectivity. In contrast, our proposed learning rules can reliably solve the task over a wide range of conditions without specific constraints being applied. Moreover, our rules cannot only detect features but also discriminate them. The improved performance of our methods would contribute to neuromorphic computing as a preferable choice.

For dynamic multiobjective optimization problems (DMOPs), it is challenging to track the varying Pareto-optimal front. Most traditional approaches estimate the Pareto-optimal sets in the decision space. However, the obtained solutions do not necessarily satisfy the desired properties of decision makers in the objective space. Inverse model-based algorithms have a great potential to solve such problems. Nonetheless, the existing ones have low precision for handling DMOPs with nonlinear correlations between the objective and decision vectors, which greatly limits the application of the inverse models. In this article, an inverse Gaussian process (IGP)-based prediction approach for solving DMOPs is proposed. Unlike most traditional approaches, this approach exploits the IGP to construct a predictor that maps the historical optimal solutions from the objective space to the decision space. A sampling mechanism is developed for generating sample points in the objective space. Then, the IGP-based predictor is employed to generate an effective initial population by using these sample points. The proposed method by introducing IGP can obtain solutions with better diversity and convergence in the objective space, which is more responsive to the demand of decision makers than the traditional methods. It also has better performance than other inverse model-based methods in solving nonlinear DMOPs. To investigate the performance of the proposed approach, experiments have been conducted on 23 benchmark problems and a real-world raw ore allocation problem in mineral processing. The experimental results demonstrate that the proposed algorithm can significantly improve the dynamic optimization performance and has certain practical significance for solving real-world DMOPs.

When a multiobjective evolutionary algorithm based on decomposition (MOEA/D) is applied to solve problems with discontinuous Pareto front (PF), a set of evenly distributed weight vectors may lead to many solutions assembling in boundaries of the discontinuous PF. To overcome this limitation, this article proposes a mechanism of resetting weight vectors (RWVs) for MOEA/D. When the RWV mechanism is triggered, a classic data clustering algorithm DBSCAN is used to categorize current solutions into several parts. A classic statistical method called principal component analysis (PCA) is used to determine the ideal number of solutions in each part of PF. Thereafter, PCA is used again for each part of PF separately and virtual targeted solutions are generated by linear interpolation methods. Then, the new weight vectors are reset according to the interrelationship between the optimal solutions and the weight vectors under the Tchebycheff decomposition framework. Finally, taking advantage of the current obtained solutions, the new solutions in the decision space are updated via a linear interpolation method. Numerical experiments show that the proposed MOEA/D-RWV can achieve good results for bi-objective and tri-objective optimization problems with discontinuous PF. In addition, the test on a recently proposed MaF benchmark suite demonstrates that MOEA/D-RWV also works for some problems with other complicated characteristics.

In multilabel learning, each training example is represented by a single instance, which is relevant to multiple class labels simultaneously. Generally, all relevant labels are considered to be available for labeled data. However, instances with a full label set are difficult to obtain in real-world applications, thus leading to the weakly multilabel learning problem, that is, relevant labels of training data are partially known and many relevant labels are missing, and even abundant training data are associated with an empty label set. To address the problem, we propose a new multilabel method to learn from weakly labeled data. To be specific, an optimization framework is constructed based on the manifold regularized sparse model, in which the correlations among labels and feature structure are considered to model global and local label correlations, thereby achieving discriminative feature analysis for mapping training data to ground-truth label space. Moreover, the proposed method has an excellent mechanism to conduct semisupervised multilabel learning by exploiting training data with the predicted label set of the unlabeled. Experiments on various real-world tasks reveal that the proposed method outperforms some state-of-the-art methods.

Evolutionary multitask learning has achieved great success due to its ability to handle multiple tasks simultaneously. However, it is rarely used in the hyperheuristic domain, which aims at generating a heuristic for a class of problems rather than solving one specific problem. The existing multitask hyperheuristic studies only focus on heuristic selection, which is not applicable to heuristic generation. To fill the gap, we propose a novel multitask generative hyperheuristic approach based on genetic programming (GP) in this article. Specifically, we introduce the idea in evolutionary multitask learning to GP hyperheuristics with a suitable evolutionary framework and individual selection pressure. In addition, an origin-based offspring reservation strategy is developed to maintain the quality of individuals for each task. To verify the effectiveness of the proposed approach, comprehensive empirical studies have been conducted on the homogeneous and heterogeneous multitask dynamic flexible job shop scheduling. The results show that the proposed algorithm can significantly improve the quality of scheduling heuristics for each task in all the examined scenarios. In addition, the evolved scheduling heuristics verify the mutual help among the tasks in a multitask scenario.

Evolutionary algorithms (EAs) have been recognized as a promising approach for bilevel optimization. However, the population-based characteristic of EAs largely influences their efficiency and effectiveness due to the nested structure of the two levels of optimization problems. In this article, we propose a transfer learning-based parallel EA (TLEA) framework for bilevel optimization. In this framework, the task of optimizing a set of lower level problems parameterized by upper level variables is conducted in a parallel manner. In the meanwhile, a transfer learning strategy is developed to improve the effectiveness of each lower level search (LLS) process. In practice, we implement two versions of the TLEA: the first version uses the covariance matrix adaptation evolutionary strategy and the second version uses the differential evolution as the evolutionary operator in lower level optimization. The experimental studies on two sets of widely used bilevel optimization benchmark problems are conducted, and the performance of the two TLEA implementations is compared to that of four well-established evolutionary bilevel optimization algorithms to verify the effectiveness and efficiency of the proposed algorithm framework.

For solving large-scale multiobjective problems (LSMOPs), the transformation-based methods have shown promising search efficiency, which varies the original problem as a new simplified problem and performs the optimization in simplified spaces instead of the original problem space. Owing to the useful information provided by the simplified searching space, the performance of LSMOPs has been improved to some extent. However, it is worth noting that the original problem has changed after the variation, and there is thus no guarantee of the preservation of the original global or near-global optimum in the newly generated space. In this article, we propose to solve LSMOPs via a multivariation multifactorial evolutionary algorithm. In contrast to existing transformation-based methods, the proposed approach intends to conduct an evolutionary search on both the original space of the LSMOP and multiple simplified spaces constructed in a multivariation manner concurrently. In this way, useful traits found along the search can be seamlessly transferred from the simplified problem spaces to the original problem space toward efficient problem solving. Besides, since the evolutionary search is also performed in the original problem space, preserving the original global optimal solution can be guaranteed. To evaluate the performance of the proposed framework, comprehensive empirical studies are carried out on a set of LSMOPs with two to three objectives and 500–5000 variables. The experimental results highlight the efficiency and effectiveness of the proposed method compared to the state-of-the-art methods for large-scale multiobjective optimization.

Evolutionary multitasking (EMT), which shares knowledge across multiple tasks while the optimization progresses online, has demonstrated superior performance in terms of both optimization quality and convergence speed over its single-task counterpart in solving complex optimization problems. However, most of the existing EMT algorithms only consider handling two tasks simultaneously. As the computational cost incurred in the evolutionary search and knowledge transfer increased rapidly with the number of optimization tasks, these EMT algorithms cannot meet today’s requirements of optimization service on the cloud for many real-world applications, where hundreds or thousands of optimization requests (labeled as large-scale EMT) are often received simultaneously and require to be optimized in a short time. Recently, graphics processing unit (GPU) computing has attracted extensive attention to accelerate the applications possessing large-scale data volume that are traditionally handled by the central processing unit (CPU). Taking this cue, toward large-scale EMT, in this article, we propose a new EMT paradigm based on the island model with the compute unified device architecture (CUDA), which is able to handle a large number of continuous optimization tasks efficiently and effectively. Moreover, under the proposed paradigm, we develop the GPU-basedimplicitandexplicitknowledge transfer mechanisms for EMT. To evaluate the performance of the proposed paradigm, comprehensive empirical studies have been conducted against its CPU-based counterpart in large-scale EMT.

Dynamic multiobjective optimization problems (DMOPs) aim to optimize multiple (often conflicting) objectives that are changing over time. Recently, there are a number of promising algorithms proposed based on transfer learning methods to solve DMOPs. However, it is very challenging to reduce the negative effect in transfer learning and find more effective transferred solutions. To fill this research gap, this article proposes a clustering-based transfer (CBT) learning method to solve DMOPs. When the environment changes, two novel operations (clustering-based selection (CBS) and CBT) are used to guide knowledge transfer. Specifically, CBS aims to find a population with nondominated solutions and dominated solutions as the training data for the new environment. Then, CBT further collects the previous Pareto-optimal solutions and some noise solutions as the training data for the previous environment. Two training data sets from different environments are, respectively, divided into multiple clusters and transfer learning is conducted on two similar clusters with high probability to reduce the negative effect, which can train an accurate prediction model to identify the promising solutions for the new environment. Empirical studies have been conducted on 14 benchmark DMOPs and one real-life path planning problem of unmanned air/ground vehicles, which validate the effectiveness of our proposed method. Especially, our method can significantly reduce negative transfer on 12 out of 14 cases when compared with direct transfer learning.

Knowledge transfer plays a vastly important role in solving multitask optimization problems (MTOPs). Many existing methods transfer task-specific knowledge, such as the high-quality solution from one task to other tasks to enhance the optimization ability, which, however, may not work well or even have a negative effect if the tasks have very different task-specific knowledge. Hence, this article proposes a meta-knowledge transfer (MKT)-based differential evolution (MKTDE) algorithm by using a more general MKT method to solve MTOPs more efficiently. The meta-knowledge defined in this article refers to the knowledge that can evolve task-specific knowledge during the evolutionary search. That is, the meta-knowledge is a kind of “knowledge of knowledge,” which denotes the knowledge of “how to solve problem via evolution” and “the feature/way/method of evolving high-quality solution.” The evolutionary search for solving different tasks can share common meta-knowledge even though these tasks involve heterogeneous data and have very different task-specific knowledge. Therefore, the MKT can associate the heterogeneous multisource data of different tasks via transferring the meta-knowledge to help solve MTOPs more efficiently in a more general way. Moreover, to further enhance the MKTDE, two novel and efficient methods are proposed. One is multiple populations for the multiple tasks framework using a unified search space for making knowledge transfer flexibly. The other is an elite solution transfer method for achieving positive high-quality solution transfer. The superior performance of the proposed MKTDE is verified via extensive numerical experiments on both widely used MTOP benchmark problems and real-world robot navigation problems, with comparisons with some state-of-the-art and the latest well-performing algorithms.

Intensity-modulated radiotherapy (IMRT) is one of the most popular techniques for cancer treatment. However, existing IMRT planning methods can only generate one solution at a time and, consequently, medical physicists should perform the planning process many times to obtain diverse solutions to meet the requirement of a clinical case. Meanwhile, multiobjective evolutionary algorithms (MOEAs) have not been fully exploited in IMRT planning since they are ineffective in optimizing the large number of discrete variables of IMRT. To bridge the gap, this article formulates IMRT planning into a large-scale combinatorial many-objective optimization problem and proposes a coevolutionary algorithm to solve it. In contrast to the existing MOEAs handling high-dimensional search spaces via variable grouping or dimensionality reduction, the proposed algorithm evolves one population with fine encoding for local exploitation and evolves another population with rough encoding for global exploration. Moreover, the convergence speed is further accelerated by two customized local search strategies. The experimental results verify that the proposed algorithm outperforms state-of-the-art MOEAs and IMRT planning methods on a variety of clinical cases.

Evolutionary sequential transfer optimization is a paradigm that leverages search experience from solved source optimization tasks to accelerate the evolutionary search of a target task. Even though many algorithms have been developed, they mainly focus on objective-homogeneous problems, where the source and target tasks possess a similar number of objectives. In this work, we explore objective-heterogeneous problems, in which knowledge transfers across single-objective optimization problems (SOPs), multiobjective optimization problems (MOPs), and many-objective optimization problems (MaOPs). Objective-heterogeneous problems challenge the existing methods due to the diverse search and objective spaces between the source and the target task. To address this issue, we present a decision variable analysis-based transfer method that can conduct knowledge transfer across problems with the different numbers of objectives. We first separate decision variables of MOPs and MaOPs into convergence-related variables (CVs) and diversity-related variables (DVs), according to their roles while treating variables of SOPs as CVs. Then, we propose a convergence transfer module to transfer knowledge of CVs to speed up the convergence. It aligns both solutions and fitness ranks for preserving fitness rank consistency between the source and target tasks, whereby accelerating search speed. Besides, a diversity transfer module is presented to refine the distribution of DVs to maintain the population diversity. The experimental results on objective-heterogeneous test problems and a real-world case study have demonstrated the effectiveness of the proposed algorithm.

Dynamic multiobjective optimization problem (DMOP) denotes the multiobjective optimization problem which varies over time. As changes in DMOP may exist some patterns that are predictable, to solve DMOP, a number of research efforts have been made to develop evolutionary search with prediction approaches to estimate the changes of the problem. A common practice of existing prediction approaches is to predict the change of Pareto-optimal solutions (POS) based on the historical solutions obtained in the decision space. However, the change of a DMOP may occur in both decision and objective spaces. Prediction only in the decision space thus may not be able to give the proper estimation of the problem change. Taking this cue, in this article, we propose an evolutionary search with multiview prediction for solving DMOP. In contrast to existing prediction methods, the proposed approach conducts prediction from the views of both decision and objective spaces. To estimate dynamic changes in DMOP, a kernelized autoencoding model is derived to perform the multiview prediction in a reproducing kernel Hilbert space (RKHS), which holds a closed-form solution. To examine the performance of the proposed method, comprehensive empirical studies on the commonly used DMOP benchmarks, as well as a real-world case study on the movie recommendation problem, are presented. The obtained experimental results verified the efficacy of the proposed method for solving both benchmark and real-world DMOPs.

The Vehicle Routing Problem (VRP) is a well-known NP-hard combinatorial optimization problem, which has wide spread applications in real world, such as logistics, bus route planning, and urban path planning. To solve VRP, traditional optimization methods usually start the search from scratch and ignore the VRPs solved in the past, which could lead to repeated explorations of the search space of related problems, and thus results in slow optimization process involving unnecessary computational cost. Keeping this in mind, to speed up the optimization for vehicle routing, this article presents a new study towards faster vehicle routing by transferring knowledge from customer representations which are learned from past solved VRPs. In particular, we propose to capture the useful traits buried in previous optimized routing solutions by learning a new customer representation, which can be transferred across VRPs, serving as the prior knowledge, to bias the optimization in the target VRP. In contrast to existing approaches, the proposed knowledge transfer is consist of a learning of new customer representation based on the optimized routing solution, which is general to VRPs possessing different structural properties, and a weighted$l_{1}$norm-regularized formulation for building sparse mapping across VRPs, that is easy to solve. Further, the proposed knowledge transfer across VRPs occurs along the whole optimization search process, and is thus able to guide the routing optimization process consistently. To verify the efficacy of the proposed method, by using population-based optimization method as the VRP solver, comprehensive empirical studies on both commonly used VRP benchmarks and real world vehicle routing application are presented.

As transportation system plays a vastly important role in combatting newly-emerging and severe epidemics like the coronavirus disease 2019 (COVID-19), the vehicle routing problem (VRP) in epidemics has become an emerging topic that has attracted increasing attention worldwide. However, most existing VRP models are not suitable for epidemic situations, because they do not consider the prevention cost caused by issues such as viral tests and quarantine during the traveling. Therefore, this paper proposes a multi-objective VRP model for epidemic situations, named VRP4E, which considers not only the traditional travel cost but also the prevention cost of the VRP in epidemic situations. To efficiently solve the VRP4E, this paper further proposes a novel algorithm named multi-objective ant colony system algorithm for epidemic situations, termed MOACS4E, together with three novel designs. First, by extending the efficient “multiple populations for multiple objectives” framework, the MOACS4E adopts two ant colonies to optimize the travel and prevention costs respectively, so as to improve the search efficiency. Second, a pheromone fusion-based solution generation method is proposed to fuse the pheromones from different colonies to increase solution diversity effectively. Third, a solution quality improvement method is further proposed to improve the solutions for the prevention cost objective. The effectiveness of the MOACS4E is verified in experiments on 25 generated benchmarks by comparison with six state-of-the-art and modern algorithms. Moreover, the VRP4E in different epidemic situations and a real-world case in the Beijing-Tianjin-Hebei region, China, are further studied to provide helpful insights for combatting COVID-19-like epidemics.

Existing transfer learning methods that focus on problems in stationary environments are not usually applicable to dynamic environments, where concept drift may occur. To the best of our knowledge, the concept drift-tolerant transfer learning (CDTL), whose major challenge is the need to adapt the target model and knowledge of source domains to the changing environments, has yet to be well explored in the literature. This article, therefore, proposes a hybrid ensemble approach to deal with the CDTL problem provided that data in the target domain are generated in a streaming chunk-by-chunk manner from nonstationary environments. At each time step, a class-wise weighted ensemble is presented to adapt the model of target domains to new environments. It assigns a weight vector for each classifier generated from the previous data chunks to allow each class of the current data leveraging historical knowledge independently. Then, a domain-wise weighted ensemble is introduced to combine the source and target models to select useful knowledge of each domain. The source models are updated with the source instances performed by the proposed adaptive weighted CORrelation ALignment (AW-CORAL). AW-CORAL iteratively minimizes domain discrepancy meanwhile decreases the effect of unrelated source instances. In this way, positive knowledge of source domains can be potentially promoted while negative knowledge is reduced. Empirical studies on synthetic and real benchmark data sets demonstrate the effectiveness of the proposed algorithm.

It has been widely recognized that the efficient training of neural networks (NNs) is crucial to classification performance. While a series of gradient-based approaches have been extensively developed, they are criticized for the ease of trapping into local optima and sensitivity to hyperparameters. Due to the high robustness and wide applicability, evolutionary algorithms (EAs) have been regarded as a promising alternative for training NNs in recent years. However, EAs suffer from the curse of dimensionality and are inefficient in training deep NNs (DNNs). By inheriting the advantages of both the gradient-based approaches and EAs, this article proposes a gradient-guided evolutionary approach to train DNNs. The proposed approach suggests a novel genetic operator to optimize the weights in the search space, where the search direction is determined by the gradient of weights. Moreover, the network sparsity is considered in the proposed approach, which highly reduces the network complexity and alleviates overfitting. Experimental results on single-layer NNs, deep-layer NNs, recurrent NNs, and convolutional NNs (CNNs) demonstrate the effectiveness of the proposed approach. In short, this work not only introduces a novel approach for training DNNs but also enhances the performance of EAs in solving large-scale optimization problems.

Spiking neural networks (SNNs) are considered as a potential candidate to overcome current challenges, such as the high-power consumption encountered by artificial neural networks (ANNs); however, there is still a gap between them with respect to the recognition accuracy on various tasks. A conversion strategy was, thus, introduced recently to bridge this gap by mapping a trained ANN to an SNN. However, it is still unclear that to what extent this obtained SNN can benefit both the accuracy advantage from ANN and high efficiency from the spike-based paradigm of computation. In this article, we propose two new conversion methods, namely TerMapping and AugMapping. The TerMapping is a straightforward extension of a typical threshold-balancing method with a double-threshold scheme, while the AugMapping additionally incorporates a new scheme of augmented spike that employs a spike coefficient to carry the number of typical all-or-nothing spikes occurring at a time step. We examine the performance of our methods based on the MNIST, Fashion-MNIST, and CIFAR10 data sets. The results show that the proposed double-threshold scheme can effectively improve the accuracies of the converted SNNs. More importantly, the proposed AugMapping is more advantageous for constructing accurate, fast, and efficient deep SNNs compared with other state-of-the-art approaches. Our study, therefore, provides new approaches for further integration of advanced techniques in ANNs to improve the performance of SNNs, which could be of great merit to applied developments with spike-based neuromorphic computing.

Traditional neuron models use analog values for information representation and computation, while all-or-nothing spikes are employed in the spiking ones. With a more brain-like processing paradigm, spiking neurons are more promising for improvements in efficiency and computational capability. They extend the computation of traditional neurons with an additional dimension of time carried by all-or-nothing spikes. Could one benefit from both the accuracy of analog values and the time-processing capability of spikes? In this article, we introduce a concept of augmented spikes to carry complementary information with spike coefficients in addition to spike latencies. New augmented spiking neuron model and synaptic learning rules are proposed to process and learn patterns of augmented spikes. We provide systematic insights into the properties and characteristics of our methods, including classification of augmented spike patterns, learning capacity, construction of causality, feature detection, robustness, and applicability to practical tasks, such as acoustic and visual pattern recognition. Our augmented approaches show several advanced learning properties and reliably outperform the baseline ones that use typical all-or-nothing spikes. Our approaches significantly improve the accuracies of a temporal-based approach on sound and MNIST recognition tasks to 99.38% and 97.90%, respectively, highlighting the effectiveness and potential merits of our methods. More importantly, our augmented approaches are versatile and can be easily generalized to other spike-based systems, contributing to a potential development for them, including neuromorphic computing.

Biological systems under a parallel and spike-based computation endow individuals with abilities to have prompt and reliable responses to different stimuli. Spiking neural networks (SNNs) have thus been developed to emulate their efficiency and to explore principles of spike-based processing. However, the design of a biologically plausible and efficient SNN for image classification still remains as a challenging task. Previous efforts can be generally clustered into two major categories in terms of coding schemes being employed: rate and temporal. The rate-based schemes suffer inefficiency, whereas the temporal-based ones typically end with a relatively poor performance in accuracy. It is intriguing and important to develop an SNN with both efficiency and efficacy being considered. In this article, we focus on the temporal-based approaches in a way to advance their accuracy performance by a great margin while keeping the efficiency on the other hand. A new temporal-based framework integrated with the multispike learning is developed for efficient recognition of visual patterns. Different approaches of encoding and learning under our framework are evaluated with the MNIST and Fashion-MNIST data sets. Experimental results demonstrate the efficient and effective performance of our temporal-based approaches across a variety of conditions, improving accuracies to higher levels that are even comparable to rate-based ones but importantly with a lighter network structure and far less number of spikes. This article attempts to extend the advanced multispike learning to the challenging task of image recognition and bring state of the arts in temporal-based approaches to a novel level. The experimental results could be potentially favorable to low-power and high-speed requirements in the field of artificial intelligence and contribute to attract more efforts toward brain-like computing.

Competitive swarm optimizers (CSOs) have shown very promising search efficiency in large-scale decision space. However, they face difficulties when solving large-scale multi-/many-objective optimization problems (LMOPs), as their winner particles are selected by random pairwise competition based on only a single evaluation criterion, which does not provide diverse guidance for LMOPs. To alleviate this issue, this article proposes a comprehensive competitive learning (CCL) strategy for CSOs using three competition mechanisms to guide the particle search. Specifically, environmental competition classifies winner and loser particles from the swarm, while cognitive competition and social competition select one winner particle as the cognitive component and the social component, respectively, to guide the search for loser particles. This competitive learning strategy aims to enhance the search capability of loser particles and provides diverse search directions for solving LMOPs. When compared with eight competitive optimizers, the experimental results validate the high efficiency and effectiveness of our method in solving nine LMOPs with 2–10 objectives and 100–5000 variables.

Evolutionary algorithms and swarm intelligence algorithms have been widely used for constrained optimization problems for decades and numerous techniques for constraint handling have been proposed. The${\varepsilon }$-constrained method is a very effective one. In the literature, the${\varepsilon }$value was usually controlled via an exponential function, which is not competent for solving certain types of constrained optimization problems, e.g., whose global optima are located near the boundary of the feasible and infeasible regions. To solve this problem, this article proposes a new adaptive${\varepsilon }$control method and incorporate it into a basic differential evolution (DE) algorithm: (DE/rand/1/exp). Based on the information of constraint violation in the current population, the adaptive method controls the value of${\varepsilon }$through a simple heuristic rule. Compared with the traditional exponential function-based control methods, the proposed adaptive method can prevent the algorithm from being trapped into local optima while retaining the obtained near-optimal candidate solutions in the infeasible region for generating promising searching paths. Besides, we set the crossover rate (CR) as a more reasonable value for DE/rand/1/exp, which can enhance the efficiency significantly. The well-known 2006 IEEE Congress on Evolutionary Computation (CEC 2006) competition on real-parameter single-objective constrained optimization benchmark is adopted to evaluate the effectiveness of the proposed adaptive${\varepsilon }$-constrained DE. Fifteen constrained engineering optimization problems are collected from the literature to test the proposed algorithm. Moreover, the adaptive${\varepsilon }$control method is extended to an adaptive algorithm to solve the benchmark problems from CEC 2017. The comparison results confirm the superiority of the proposed method.

Since multi-objective optimization (MOO) involves multiple conflicting objectives, the high dimensionality of the solution space has a much more severe impact on multi-objective problems than single-objective optimization. Taking the advantage of random embedding, some related works have been proposed to scale derivative-free MOO methods to high-dimensional functions. However, with the premise of "low effective dimensionality", a single randomly embedded subspace cannot guarantee the effectiveness of obtained solutions. Taking this cue, we propose an evolutionary multitasking paradigm for multi-objective optimization via random embedding (EMT-ReMO) to enhance the efficiency and effectiveness of current embedding-based methods in solving high-dimensional optimization problems with low effective dimensions. In EMT-ReMO, the target problem is firstly embedded into multiple low-dimensional subspaces by using different random embeddings, aiming to build up a multi-task environment for identifying the underlying effective subspace. Then the implicit multi-objective evolutionary multitasking is performed with seamless knowledge transfer to enhance the optimization process. Experimental results obtained on six high-dimensional MOO functions with or without low effective dimensions have confirmed the effectiveness as well as the efficiency of the proposed EMT-ReMO.

Deep neural networks (DNNs) have been frequently and widely applied for intelligent systems such as object detection, natural language understanding and speech recognition. Given a specific problem, we always aim to construct the most suitable DNN to solve it, which requires choosing the most appropriate model architecture and seeking the best model parameters values. However, most existing works focus on model parameters learning under the assumption that the model architecture can be manually specified as per prior knowledge and/or trial-and-error experimentation. To overcome this problem, evolutionary algorithms (EAs) have been widely used to design model architectures automatically. Further, EAs have been used for neural network optimization for more than 30 years. Therefore, in this paper, we review the evolutionary neural architecture search (ENAS) from the view of the advanced techniques. We hope this work can provide a comprehensive understanding of EAs' roles for the readers and focus themselves on ENAS.

The gate assignment problem (GAP) aims at assigning gates to aircraft considering operational efficiency of airport and satisfaction of passengers. Unlike the existing works, we model the GAP as a bi-objective constrained optimization problem. The total walking distance of passengers and the total robust cost of the gate assignment are the two objectives to be optimized, while satisfying the constraints regarding the limited number of flights assigned to apron, as well as three types of compatibility. A set of real instances is then constructed based on the data obtained from the Baiyun airport (CAN) in Guangzhou, China. A two-phase large neighborhood search (2PLNS) is proposed, which accommodates a greedy and stochastic strategy (GSS) for the large neighborhood search; both to speed up its convergence and to avoid local optima. The empirical analysis and results on both the synthetic instances and the constructed real-world instances show a better performance for the proposed 2PLNS as compared to many state-of-the-art algorithms in literature. An efficient way of choosing the tradeoff from a large number of nondominated solutions is also discussed in this article.

Recently, evolutionary multitasking (EMT) has been proposed in the field of evolutionary computation as a new search paradigm, for solving multiple optimization tasks simultaneously. By sharing useful traits found along the evolutionary search process across different optimization tasks, the optimization performance on each task could be enhanced. The autoencoding-based EMT is a recently proposed EMT algorithm. In contrast to most existing EMT algorithms, which conduct knowledge transfer across tasks implicitly via crossover, it intends to perform knowledge transfer explicitly among tasks in the form of task solutions, which enables the employment of task-specific search mechanisms for different optimization tasks in EMT. However, the autoencoding-based explicit EMT can only work on continuous optimization problems. It will fail on combinatorial optimization problems, which widely exist in real-world applications, such as scheduling problem, routing problem, and assignment problem. To the best of our knowledge, there is no existing effort working on explicit EMT for combinatorial optimization problems. Taking this cue, in this article, we thus embark on a study toward explicit EMT for combinatorial optimization. In particular, by using vehicle routing as an illustrative combinatorial optimization problem, the proposed explicit EMT algorithm (EEMTA) mainly contains a weighted l1-norm-regularized learning process for capturing the transfer mapping, and a solution-based knowledge transfer process across vehicle routing problems (VRPs). To evaluate the efficacy of the proposed EEMTA, comprehensive empirical studies have been conducted with the commonly used vehicle routing benchmarks in multitasking environment, against both the state-of-the-art EMT algorithm and the traditional single-task evolutionary solvers. Finally, a real-world combinatorial optimization application, that is, the package delivery problem (PDP), is also presented to further confirm the efficacy of the proposed algorithm.

With the emergence of crowdshipping and sharing economy, vehicle routing problem with occasional drivers (VRPOD) has been recently proposed to involve occasional drivers with private vehicles for the delivery of goods. In this article, we present a generalized variant of VRPOD, namely, the vehicle routing problem with heterogeneous capacity, time window, and occasional driver (VRPHTO), by taking the capacity heterogeneity and time window of vehicles into consideration. Furthermore, to meet the requirement in today's cloud computing service, wherein multiple optimization tasks may need to be solved at the same time, we propose a novel evolutionary multitasking algorithm (EMA) to optimize multiple VRPHTOs simultaneously with a single population. Finally, 56 new VRPHTO instances are generated based on the existing common vehicle routing benchmarks. Comprehensive empirical studies are conducted to illustrate the benefits of the new VRPHTOs and to verify the efficacy of the proposed EMA for multitasking against a state-of-art single task evolutionary solver. The obtained results showed that the employment of occasional drivers could significantly reduce the routing cost, and the proposed EMA is not only able to solve multiple VRPHTOs simultaneously but also can achieve enhanced optimization performance via the knowledge transfer between tasks along the evolutionary search process.

Recently, increasing works have been proposed to drive evolutionary algorithms using machine-learning models. Usually, the performance of such model-based evolutionary algorithms is highly dependent on the training qualities of the adopted models. Since it usually requires a certain amount of data (i.e., the candidate solutions generated by the algorithms) for model training, the performance deteriorates rapidly with the increase of the problem scales due to the curse of dimensionality. To address this issue, we propose a multiobjective evolutionary algorithm driven by the generative adversarial networks (GANs). At each generation of the proposed algorithm, the parent solutions are first classified into real and fake samples to train the GANs; then the offspring solutions are sampled by the trained GANs. Thanks to the powerful generative ability of the GANs, our proposed algorithm is capable of generating promising offspring solutions in high-dimensional decision space with limited training data. The proposed algorithm is tested on ten benchmark problems with up to 200 decision variables. The experimental results on these test problems demonstrate the effectiveness of the proposed algorithm.

Dynamic multiobjective optimization problems (DMOPs) are characterized by optimization functions that change over time in varying environments. The DMOP is challenging because it requires the varying Pareto-optimal sets (POSs) to be tracked quickly and accurately during the optimization process. In recent years, transfer learning has been proven to be one of the effective means to solve dynamic multiobjective optimization. However, the negative transfer will lead the search of finding the POS to a wrong direction, which greatly reduces the efficiency of solving optimization problems. Minimizing the occurrence of negative transfer is thus critical for the use of transfer learning in solving DMOPs. In this article, we propose a new individual-based transfer learning method, called an individual transfer-based dynamic multiobjective evolutionary algorithm (IT-DMOEA), for solving DMOPs. Unlike existing approaches, it uses a presearch strategy to filter out some high-quality individuals with better diversity so that it can avoid negative transfer caused by individual aggregation. On this basis, an individual-based transfer learning technique is applied to accelerate the construction of an initial population. The merit of the IT-DMOEA method is that it combines different strategies in maintaining the advantages of transfer learning methods as well as avoiding the occurrence of negative transfer; thereby greatly improving the quality of solutions and convergence speed. The experimental results show that the proposed IT-DMOEA approach can considerably improve the quality of solutions and convergence speed compared to several state-of-the-art algorithms based on different benchmark problems.

Many real-world optimization problems involve multiple objectives, constraints, and parameters that may change over time. These problems are often called dynamic multiobjective optimization problems (DMOPs). The difficulty in solving DMOPs is the need to track the changing Pareto-optimal front efficiently and accurately. It is known that transfer learning (TL)-based methods have the advantage of reusing experiences obtained from past computational processes to improve the quality of current solutions. However, existing TL-based methods are generally computationally intensive and thus time consuming. This article proposes a new memory-driven manifold TL-based evolutionary algorithm for dynamic multiobjective optimization (MMTL-DMOEA). The method combines the mechanism of memory to preserve the best individuals from the past with the feature of manifold TL to predict the optimal individuals at the new instance during the evolution. The elites of these individuals obtained from both past experience and future prediction will then constitute as the initial population in the optimization process. This strategy significantly improves the quality of solutions at the initial stage and reduces the computational cost required in existing methods. Different benchmark problems are used to validate the proposed algorithm and the simulation results are compared with state-of-the-art dynamic multiobjective optimization algorithms (DMOAs). The results show that our approach is capable of improving the computational speed by two orders of magnitude while achieving a better quality of solutions than existing methods.

Multiobjective multitasking optimization (MTO), which is an emerging research topic in the field of evolutionary computation, was recently proposed. MTO aims to solve related multiobjective optimization problems at the same time via evolutionary algorithms. The key to MTO is the knowledge transfer based on sharing solutions across tasks. Notably, positive knowledge transfer has been shown to facilitate superior performance characteristics. However, how to find more valuable transferred solutions for the positive transfer has been scarcely explored. Keeping this in mind, we propose a new algorithm to solve MTO problems. In this article, if a transferred solution is nondominated in its target task, the transfer is positive transfer. Furthermore, neighbors of this positive-transfer solution will be selected as the transferred solutions in the next generation, since they are more likely to achieve the positive transfer. Numerical studies have been conducted on benchmark problems of MTO to verify the effectiveness of the proposed approach. Experimental results indicate that our proposed framework achieves competitive results compared with the state-of-the-art MTO frameworks.

Evolving production scheduling heuristics is a challenging task because of the dynamic and complex production environments and the interdependency of multiple scheduling decisions. Different genetic programming (GP) methods have been developed for this task and achieved very encouraging results. However, these methods usually have trouble in discovering powerful and compact heuristics, especially for difficult problems. Moreover, there is no systematic approach for the decision makers to intervene and embed their knowledge and preferences in the evolutionary process. This article develops a novel people-centric evolutionary system for dynamic production scheduling. The two key components of the system are a new mapping technique to incrementally monitor the evolutionary process and a new adaptive surrogate model to improve the efficiency of GP. The experimental results with dynamic flexible job shop scheduling show that the proposed system outperforms the existing algorithms for evolving scheduling heuristics in terms of scheduling performance and heuristic sizes. The new system also allows the decision makers to interact on the fly and guide the evolution toward the desired solutions.

Under certain smoothness assumptions, the Pareto set of a continuous multiobjective optimization problem is a piecewise continuous manifold in the decision space, which can be derived from the Karush-Kuhn-Tucker condition. Despite that a number of multiobjective evolutionary algorithms (MOEAs) have been proposed, their performance on multiobjective optimization problems with complicated Pareto sets (MOP-cPS) is still unsatisfying. In this article, we adopt the concept of manifold and propose a manifold learning-inspired mating strategy to enhance the diversity maintenance in MOEAs for solving MOP-cPS efficiently. In the proposed strategy, all of the individuals are first clustered into different manifolds according to their distribution in the objective space, and then the mating reproduction is restricted among individuals in the same manifold. Moreover, we embed the proposed mating strategy in three representative MOEAs and compare the embedded MOEAs with their original versions using the assortative genetic operators on a variety of MOP-cPS. The experimental results demonstrate the significant performance improvements benefitting from the proposed mating restriction strategy.

Due to the curse of dimensionality of search space, it is extremely difficult for evolutionary algorithms to approximate the optimal solutions of large-scale multiobjective optimization problems (LMOPs) by using a limited budget of evaluations. If the Pareto-optimal subspace is approximated during the evolutionary process, the search space can be reduced and the difficulty encountered by evolutionary algorithms can be highly alleviated. Following the above idea, this article proposes an evolutionary algorithm to solve sparse LMOPs by learning the Pareto-optimal subspace. The proposed algorithm uses two unsupervised neural networks, a restricted Boltzmann machine, and a denoising autoencoder to learn a sparse distribution and a compact representation of the decision variables, where the combination of the learnt sparse distribution and compact representation is regarded as an approximation of the Pareto-optimal subspace. The genetic operators are conducted in the learnt subspace, and the resultant offspring solutions then can be mapped back to the original search space by the two neural networks. According to the experimental results on eight benchmark problems and eight real-world problems, the proposed algorithm can effectively solve sparse LMOPs with 10000 decision variables by only 100000 evaluations.

A multifactorial evolutionary algorithm (MFEA) is a recently proposed algorithm for evolutionary multitasking, which optimizes multiple optimization tasks simultaneously. With the design of knowledge transfer among different tasks, MFEA has demonstrated the capability to outperform its single-task counterpart in terms of both convergence speed and solution quality. In MFEA, the knowledge transfer across tasks is realized via the crossover between solutions that possess different skill factors. This crossover is thus essential to the performance of MFEA. However, we note that the present MFEA and most of its existing variants only employ a single crossover for knowledge transfer, and fix it throughout the evolutionary search process. As different crossover operators have a unique bias in generating offspring, the appropriate configuration of crossover for knowledge transfer in MFEA is necessary toward robust search performance, for solving different problems. Nevertheless, to the best of our knowledge, there is no effort being conducted on the adaptive configuration of crossovers in MFEA for knowledge transfer, and this article thus presents an attempt to fill this gap. In particular, here, we first investigate how different types of crossover affect the knowledge transfer in MFEA on both single-objective (SO) and multiobjective (MO) continuous optimization problems. Furthermore, toward robust and efficient multitask optimization performance, we propose a new MFEA with adaptive knowledge transfer (MFEA-AKT), in which the crossover operator employed for knowledge transfer is self-adapted based on the information collected along the evolutionary search process. To verify the effectiveness of the proposed method, comprehensive empirical studies on both SO and MO multitask benchmarks have been conducted. The experimental results show that the proposed MFEA-AKT is able to identify the appropriate knowledge transfer crossover for different optimization problems and even at different optimization stages along the search, which thus leads to superior or competitive performances when compared to the MFEAs with fixed knowledge transfer crossover operators.

Constrained multiobjective optimization problems (CMOPs) widely exist in real-world applications, and they are challenging for conventional evolutionary algorithms (EAs) due to the existence of multiple constraints and objectives. When the number of objectives or decision variables is scaled up in CMOPs, the performance of EAs may degenerate dramatically and may fail to obtain any feasible solutions. To address this issue, we propose a paired offspring generation-based multiobjective EA for constrained large-scale optimization. The general idea is to emphasize the role of offspring generation in reproducing some promising feasible or useful infeasible offspring solutions. We first adopt a small set of reference vectors for constructing several subpopulations with a fixed number of neighborhood solutions. Then, a pairing strategy is adopted to determine some pairwise parent solutions for offspring generation. Consequently, the pairwise parent solutions, which could be infeasible, may guide the generation of well-converged solutions to cross the infeasible region(s) effectively. The proposed algorithm is evaluated on CMOPs with up to 1000 decision variables and ten objectives. Moreover, each component in the proposed algorithm is examined in terms of its effect on the overall algorithmic performance. Experimental results on a variety of existing and our tailored test problems demonstrate the effectiveness of the proposed algorithm in constrained large-scale multiobjective optimization.

Operational researchers and decision modelers have aspired to optimization technologies with a self-adaptive mechanism to cope with new problem formulations. Self-adaptive mechanisms not only free users from low-level and complex development tasks to enhance optimization efficiency but also allow them to focus on addressing high-level real-world operational requirements. In recent years, there has been a growing interest in applying machine learning and artificial intelligence techniques to improve self-adaptive mechanisms. However, learning to optimize hard combinatorial optimization problems remains a challenging task. This article proposes a new genetic programming approach to evolve efficient variable selectors to enhance the search mechanism in constraint programming. Starting with a set of training instances for a specific combinatorial optimization problem, the proposed approach evaluates variable selectors and evolves them to be more efficient over a number of generations. The novelties of our proposed approach are threefold: 1) a new representation of variable selectors; 2) a new mechanism for fitness evaluations; and 3) a preselection technique. We examine performance of the proposed approach on different job-shop scheduling problems, and the results show that variable selectors can be evolved efficiently. In particular, there are substantial reductions in the computational effort required for the search component of the constraint solver as well as increased chances of finding the optimal solutions. Further analyses also confirm the efficacy of our approach in respect to scalability, generalization, and interpretability of the evolved variable selectors.

Multimodal multiobjective optimization problems (MMOPs) widely exist in real-world applications, which have multiple equivalent Pareto-optimal solutions that are similar in the objective space but totally different in the decision space. While some evolutionary algorithms (EAs) have been developed to find the equivalent Pareto-optimal solutions in recent years, they are ineffective to handle large-scale MMOPs having a large number of variables. This article thus proposes an EA for solving large-scale MMOPs with sparse Pareto-optimal solutions, i.e., most variables in the optimal solutions are 0. The proposed algorithm explores different regions of the decision space via multiple subpopulations and guides the search behavior of the subpopulations via adaptively updated guiding vectors. The guiding vector for each subpopulation not only provides efficient convergence in the huge search space but also differentiates its search direction from others to handle the multimodality. While most existing EAs solve MMOPs with 2-7 decision variables, the proposed algorithm is shown to be effective for benchmark MMOPs with up to 500 decision variables. Moreover, the proposed algorithm also produces a better result than state-of-the-art methods for the neural architecture search.

Dynamic flexible job shop scheduling (JSS) is an important combinatorial optimization problem with complex routing and sequencing decisions under dynamic environments. Genetic programming (GP), as a hyperheuristic approach, has been successfully applied to evolve scheduling heuristics for JSS. However, its training process is time consuming, and it faces the retraining problem once the characteristics of job shop scenarios vary. It is known that multitask learning is a promising paradigm for solving multiple tasks simultaneously by sharing knowledge among the tasks. To improve the training efficiency and effectiveness, this article proposes a novel surrogate-assisted evolutionary multitask algorithm via GP to share useful knowledge between different scheduling tasks. Specifically, we employ the phenotypic characterization for measuring the behaviors of scheduling rules and building a surrogate for each task accordingly. The built surrogates are used not only to improve the efficiency of solving each single task but also for knowledge transfer in multitask learning with a large number of promising individuals. The results show that the proposed algorithm can significantly improve the quality of scheduling heuristics for all scenarios. In addition, the proposed algorithm manages to solve multiple tasks collaboratively in terms of the evolved scheduling heuristics for different tasks in a multitask scenario.

Automated construction of deep neural networks (DNNs) has become a research hot spot nowadays because DNN’s performance is heavily influenced by its architecture and parameters, which are highly task-dependent, but it is notoriously difficult to find the most appropriate DNN in terms of architecture and parameters to best solve a given task. In this work, we provide an insight into the automated DNN construction process by formulating it into a multilevel multiobjective large-scale optimization problem with constraints, where the nonconvex, nondifferentiable, and black-box nature of this problem make evolutionary algorithms (EAs) to stand out as a promising solver. Then, we give a systematical review of existing evolutionary DNN construction techniques from different aspects of this optimization problem and analyze the pros and cons of using EA-based methods in each aspect. This work aims to help DNN researchers to better understand why, where, and how to utilize EAs for automated DNN construction and meanwhile, help EA researchers to better understand the task of automated DNN construction so that they may focus more on EA-favored optimization scenarios to devise more effective techniques.

Endmember extraction (EE) plays a crucial part in the hyperspectral unmixing (HU) process. To obtain satisfactory EE results, the EE can be considered as the multiobjective optimization problem to optimize the volume maximization (VM) and root-mean-square error (RMSE) simultaneously. However, it is often quite challenging to balance the conflict of these objectives. In order to tackle the challenges of multiobjective EE, we present a (μ + λ) multiobjective differential evolution algorithm ((μ + λ)-MODE) based on ranking multiple mutations. In the (μ + λ)-MODE algorithm, ranking multiple mutations are adopted to create the mutant vectors via the scaling factor pool to enhance the population diversity. Moreover, mutant vectors employ the binary crossover operator to generate the trial vectors through a crossover control parameter pool in (μ + λ)-MODE to take advantage of the good information of the population. In addition, (μ + λ)-MODE utilizes the fast nondominated sorting approach to sort the parent and trial vectors, and then selects the elitism offspring as the next population via the (μ + λ) selection strategy. Eventually, experimental comparative results in three real HSIs reveal that our proposed (μ + λ)-MODE is superior to other EE methods.

Deep neural networks (DNNs), characterized by sophisticated architectures capable of learning a hierarchy of feature representations, have achieved remarkable successes in various applications. Learning DNN's parameters is a crucial but challenging task that is commonly resolved by using gradient-based backpropagation (BP) methods. However, BP-based methods suffer from severe initialization sensitivity and proneness to getting trapped into inferior local optima. To address these issues, we propose a DNN learning framework that hybridizes CC-based optimization with BP-based gradient descent, called BPCC, and implement it by devising a computationally efficient CC-based optimization technique dedicated to DNN parameter learning. In BPCC, BP will intermittently execute for multiple training epochs. Whenever the execution of BP in a training epoch cannot sufficiently decrease the training objective function value, CC will kick in to execute by using the parameter values derived by BP as the starting point. The best parameter values obtained by CC will act as the starting point of BP in its next training epoch. In CC-based optimization, the overall parameter learning task is decomposed into many subtasks of learning a small portion of parameters. These subtasks are individually addressed in a cooperative manner. In this article, we treat neurons as basic decomposition units. Furthermore, to reduce the computational cost, we devise a maturity-based subtask selection strategy to selectively solve some subtasks of higher priority. Experimental results demonstrate the superiority of the proposed method over common-practice DNN parameter learning techniques.

With the increasing prevalence of autism spectrum disorder (ASD), it is important to identify ASD patients for effective treatment and intervention, especially in early childhood. Neuroimaging techniques have been used to characterize the complex biomarkers based on the functional connectivity anomalies in the ASD. However, the diagnosis of ASD still adopts the symptom-based criteria by clinical observation. The existing computational models tend to achieve unreliable diagnostic classification on the large-scale aggregated data sets. In this work, we propose a novel graph-based classification model using the deep belief network (DBN) and the Autism Brain Imaging Data Exchange (ABIDE) database, which is a worldwide multisite functional and structural brain imaging data aggregation. The remarkable connectivity features are selected through a graph extension of K -nearest neighbors and then refined by a restricted path-based depth-first search algorithm. Thanks to the feature reduction, lower computational complexity could contribute to the shortening of the training time. The automatic hyperparameter-tuning technique is introduced to optimize the hyperparameters of the DBN by exploring the potential parameter space. The simulation experiments demonstrate the superior performance of our model, which is 6.4% higher than the best result reported on the ABIDE database. We also propose to use the data augmentation and the oversampling technique to identify further the possible subtypes within the ASD. The interpretability of our model enables the identification of the most remarkable autistic neural correlation patterns from the data-driven outcomes.

As a group of complex neurodevelopmental disorders, autism spectrum disorder (ASD) has been reported to have a high overall prevalence, showing an unprecedented spurt since 2000. Due to the unclear pathomechanism of ASD, it is challenging to diagnose individuals with ASD merely based on clinical observations. Without additional support of biochemical markers, the difficulty of diagnosis could impact therapeutic decisions and, therefore, lead to delayed treatments. Recently, accumulating evidence have shown that both genetic abnormalities and chemical toxicants play important roles in the onset of ASD. In this work, a new multilabel classification (MLC) model is proposed to identify the autistic risk genes and toxic chemicals on a large-scale data set. We first construct the feature matrices and partially labeled networks for autistic risk genes and toxic chemicals from multiple heterogeneous biological databases. Based on both global and local measure metrics, the simulation experiments demonstrate that the proposed model achieves superior classification performance in comparison with the other state-of-the-art MLC methods. Through manual validation with existing studies, 60% and 50% out of the top-20 predicted risk genes are confirmed to have associations with ASD and autistic disorder, respectively. To the best of our knowledge, this is the first computational tool to identify ASD-related risk genes and toxic chemicals, which could lead to better therapeutic decisions of ASD.

Spiking neural P (SN P) systems are a class of discrete neuron-inspired computation models, where information is encoded by the numbers of spikes in neurons and the timing of spikes. However, due to the discontinuous nature of the integrate-and-fire behavior of neurons and the symbolic representation of information, SN P systems are incompatible with the gradient descent-based training algorithms, such as the backpropagation algorithm, and lack the capability of processing the numerical representation of information. In this work, motivated by the numerical nature of numerical P (NP) systems in the area of membrane computing, a novel class of SN P systems is proposed, called numerical SN P (NSN P) systems. More precisely, information is encoded by the values of variables, and the integrate-and-fire way of neurons and the distribution of produced values are described by continuous production functions. The computation power of NSN P systems is investigated. We prove that NSN P is Turing universal as number generating devices, where the production functions in each neuron are linear functions, each involving at most one variable; as number accepting devices, NSN P systems are proved to be universal as well, even if each neuron contains only one production function. These results show that even if a single neuron is simple in the sense that it contains one or two production functions and the production functions in each neuron are linear functions with one variable, a network of simple neurons are still computationally powerful. With the powerful computation power and the characteristic of continuous production functions, developing learning algorithms for NSN P systems is potentially exploitable.

The capability for environmental sound recognition (ESR) can determine the fitness of individuals in a way to avoid dangers or pursue opportunities when critical sound events occur. It still remains mysterious about the fundamental principles of biological systems that result in such a remarkable ability. Additionally, the practical importance of ESR has attracted an increasing amount of research attention, but the chaotic and nonstationary difficulties continue to make it a challenging task. In this article, we propose a spike-based framework from a more brain-like perspective for the ESR task. Our framework is a unifying system with consistent integration of three major functional parts which are sparse encoding, efficient learning, and robust readout. We first introduce a simple sparse encoding, where key points are used for feature representation, and demonstrate its generalization to both spike- and nonspike-based systems. Then, we evaluate the learning properties of different learning rules in detail with our contributions being added for improvements. Our results highlight the advantages of multispike learning, providing a selection reference for various spike-based developments. Finally, we combine the multispike readout with the other parts to form a system for ESR. Experimental results show that our framework performs the best as compared to other baseline approaches. In addition, we show that our spike-based framework has several advantageous characteristics including early decision making, small dataset acquiring, and ongoing dynamic processing. Our framework is the first attempt to apply the multispike characteristic of nervous neurons to ESR. The outstanding performance of our approach would potentially contribute to draw more research efforts to push the boundaries of spike-based paradigm to a new horizon.

Dynamic multi-objective optimisation has attracted increasing attention in the evolutionary multi-objective optimisation community in recent years. Comparing to its static counterpart, which has been studied for more than half a century, the involvement of dynamic and uncertain features, including but not limited to the changing Pareto-optimal set, Pareto-optimal front and problem formulation, pose significant more challenges to evolutionary algorithms. This will become even more complicated when the underlying problem involves computationally expensive objective functions which are not rare in many realworld application scenarios. In this paper, we pave an initial step towards the study of dynamic multi-objective optimisation with computationally expensive objective functions. More specifically, we use a surrogate assisted evolutionary algorithm, MOEA/DEGO in particular, as the baseline in order to carry out evolutionary optimisation with a limited amount of function evaluations. Furthermore, instead of restart the MOEA/D-EGO from scratch after each change, we use transfer learning to map the previously archived training data to the current landscape in order to jump start the surrogate model building process. By doing so, we can expect a better adaptation to the new environment. Proof-of-concept experiments fully demonstrate the effectiveness of our proposed method.

Evolutionary algorithms (EAs) often lose their superiority and effectiveness when applied to large-scale optimization problems. In the literature, many research studies have been proposed to improve the search performance of EAs, such as cooperative co-evolution, embedding, and new search operator design. Among those, memetic multi-agent optimization (MeMAO) is a recently proposed paradigm for high-dimensional problems by using random embeddings. It demonstrated high efficacy with the assumption of “effective dimension However, as prior knowledge is always unknown for a given problem, this method may fail on the large-scale problems that do not have low effective dimensions. Taking this cue, we propose an evolutionary multitasking (EMT) assisted random embedding method (EMT-RE) for solving large-scale optimization problems. Instead of conducting a search on the randomly embedded space directly, we treat the embedded task as the auxiliary task for the given problem. By performing EMT with both the given problem and the randomly embedded task, not only the useful solutions found along the search can be transferred across tasks toward efficient problem solving, but the effectiveness of the search on problems Without a low effective dimensionality is also guaranteed. To evaluate the performance of newly proposed EMT-RE, comprehensive empirical studies are carried out on 8 synthetic continuous optimization functions with up to 2,000 dimensions.

Optical character rcecognition (OCR) is a process of converting images of typed, handwritten or printed text into machine-encoded one. In recent years, the methods represented by deep learning have greatly improved the performance of OCR systems, but the main challenges of such systems are 1) to accurately perform text detection in complex scenes and 2) to identify and set the optimal parameters to optimize the performance of the system. In this paper, we propose an OCR method based on Neural Architecture Search technique, called AutOCR. The characteristic of the proposed method is the automatic design of text detection framework using an evolutionary computation neural architecture search method. This design can not only accurately recognize the text in a complex environment, but also avoid the process of experts participating in parameter adjustment. We compared it with different methods, and the experimental results proved the effectiveness of our method.

Data-driven defect prediction has become increasingly important in software engineering process. Since it is not uncommon that data from a software project is insufficient for training a reliable defect prediction model, transfer learning that borrows data/konwledge from other projects to facilitate the model building at the current project, namely cross-project defect prediction (CPDP), is naturally plausible. Most CPDP techniques involve two major steps, i.e., transfer learning and classification, each of which has at least one parameter to be tuned to achieve their optimal performance. This practice fits well with the purpose of automated parameter optimization. However, there is a lack of thorough understanding about what are the impacts of automated parameter optimization on various CPDP techniques. In this paper, we present the first empirical study that looks into such impacts on 62 CPDP techniques, 13 of which are chosen from the existing CPDP literature while the other 49 ones have not been explored before. We build defect prediction models over 20 real-world software projects that are of different scales and characteristics. Our findings demonstrate that: (1) Automated parameter optimization substantially improves the defect prediction performance of 77% CPDP techniques with a manageable computational cost. Thus more efforts on this aspect are required in future CPDP studies. (2) Transfer learning is of ultimate importance in CPDP. Given a tight computational budget, it is more cost-effective to focus on optimizing the parameter configuration of transfer learning algorithms (3) The research on CPDP is far from mature where it is 'not difficult' to find a better alternative by making a combination of existing transfer learning and classification techniques. This finding provides important insights about the future design of CPDP techniques.

Information theoretical based methods have attracted a great attention in recent years, and gained promising results to deal with multi-label data with high dimensionality. However, most of the existing methods are either directly transformed from heuristic single-label feature selection methods or inefficient in exploiting labeling information. Thus, they may not be able to get an optimal feature selection result shared by multiple labels. In this paper, we propose a general global optimization framework, in which feature relevance, label relevance (i.e., label correlation), and feature redundancy are taken into account, thus facilitating multi-label feature selection. Moreover, the proposed method has an excellent mechanism for utilizing inherent properties of multi-label learning. Specially, we provide a formulation to extend the proposed method with label-specific features. Empirical studies on twenty multi-label data sets reveal the effectiveness and efficiency of the proposed method. Our implementation of the proposed method is available online at: https://jiazhang-ml.pub/GRRO-master.zip.

Increasing mental disorders have emerged as an urgent public health concern such as autism spectrum disorder (ASD) and attention deficit hyperactivity disorder (ADHD). Related mental disorders may share high overlap in clinical symptoms. Therefore, their diagnosis can be challenging to merely rely on the observation of cognitive phenotypes and behavioral manifestations. Unfortunately, there is no additional support of biochemical markers, laboratory tests, or neuroimaging analysis, which can be used as a diagnostic gold standard currently. Over the past decades, resting-state functional magnetic resonance imaging (rs-fMRI) has been considered as one of the most promising modality to capture the intrinsic neural activation patterns between regions in the brain. In this work, we focus on ASD and ADHD due to their high prevalence and relevance with the aim to exploit the multi-task learning (MTL) paradigm for their diagnosis. To the best of our knowledge, this is the first time to make use of the disease-specific heterogeneities for the MTL classification of ASD and ADHD via rs-fMRI signal. We propose a novel graph-based feature selection method to filter out irrelevant functional connectivity features. Then an efficient structure of multi-gate mixture-of-experts (MMoE) is applied to the MTL classification framework. Finally, the experiment results demonstrate that the proposed model can achieve a reliable classification performance in a short term, yielding the mean accuracies of 0.687±0.005 and 0.650±0.014 in ASD and ADHD datasets, respectively. The graph-based feature selection method and MMoE model are demonstrated to make great contribution to performance improvement.

Cross-Project Defect Prediction (CPDP), which borrows data from similar projects by combining a transfer learner with a classifier, have emerged as a promising way to predict software defects when the available data about the target project is insufficient. However, developing such a model is challenge because it is difficult to determine the right combination of transfer learner and classifier along with their optimal hyper-parameter settings. In this paper, we propose a tool, dubbed BiLO-CPDP, which is the first of its kind to formulate the automated CPDP model discovery from the perspective of bi-level programming. In particular, the bi-level programming proceeds the optimization with two nested levels in a hierarchical manner. Specifically, the upper-level optimization routine is designed to search for the right combination of transfer learner and classifier while the nested lower-level optimization routine aims to optimize the corresponding hyper-parameter settings. To evaluate BiLO-CPDP, we conduct experiments on 20 projects to compare it with a total of 21 existing CPDP techniques, along with its single-level optimization variant and Auto-Sklearn, a state-of-the-art automated machine learning tool. Empirical results show that BiLO-CPDP champions better prediction performance than all other 21 existing CPDP techniques on 70% of the projects, while being overwhelmingly superior to Auto-Sklearn and its single-level optimization variant on all cases. Furthermore, the unique bi-level formalization in BiLO-CPDP also permits to allocate more budget to the upper-level, which significantly boosts the performance.

This paper addresses a class of optimization problems in which either part of the objective function is differentiable while the rest is nondifferentiable or the objective function is differentiable in only part of the domain. Accordingly, we propose a dual-decomposition-based approach that includes both objective decomposition and domain decomposition. In the former, the original objective function is decomposed into several relatively simple subobjectives to isolate the nondifferentiable part of the objective function, and the problem is consequently formulated as a multiobjective optimization problem (MOP). In the latter decomposition, we decompose the domain into two subdomains, that is, the differentiable and nondifferentiable domains, to isolate the nondifferentiable domain of the nondifferentiable subobjective. Subsequently, the problem can be optimized with different schemes in the different subdomains. We propose a population-based optimization algorithm, called the simulated water-stream algorithm (SWA), for solving this MOP. The SWA is inspired by the natural phenomenon of water streams moving toward a basin, which is analogous to the process of searching for the minimal solutions of an optimization problem. The proposed SWA combines the deterministic search and heuristic search in a single framework. Experiments show that the SWA yields promising results compared with its existing counterparts.

A variety of evolutionary algorithms have been proposed for many-objective optimization in recent years. However, the difficulties in balancing the convergence and diversity of the population and selecting promising parents for offspring reproduction remain. In this paper, we propose a subregion division-based evolutionary algorithm with an effective mating selection strategy, termed SdEA, for many-objective optimization. In SdEA, a subregion division approach is proposed to divide the objective space into different subregions for balancing the diversity and convergence of the population. Besides, an effective mating selection strategy is proposed to enhance the diversity of the mating pool solutions, aimed at enhancing the selection probability of solutions in the sparse subregions. The proposed SdEA is compared with five state-of-the-art many-objective evolutionary algorithms on 23 test problems from DTLZ, WFG, and MaF test suites. Experimental results on these problems demonstrate that the proposed algorithm is competitive in solving many-objective problems. Furthermore, the proposed mating selection strategy is embedded in several evolutionary algorithms and experimental results demonstrate its effectiveness on improving the performance of the embedded algorithms.

Dynamic multiobjective optimization requires the robust tracking of varying Pareto-optimal solutions (POS) in a changing environment. When a change is detected in the environment, prediction mechanisms estimate the POS by utilizing information from previous populations to accelerate search toward the true POS. To achieve a robust prediction of POS, a mixture-of-experts-based ensemble framework is proposed. Unlike existing approaches, the framework utilizes multiple prediction mechanisms to improve the overall prediction. A gating network is applied to manage switching among the various predictors based on performance of the predictors at different time intervals of the optimization process. The efficacy of the proposed framework is validated through experimental studies based on 13 dynamic multiobjective benchmark optimization problems. The simulation results show that the proposed framework improves the dynamic optimization performance significantly, particularly for: 1) problems with distinct dynamic POS in decision space over time and 2) problems with highly nonlinear decision variable linkages.

Image change detection detects the regions of change in multiple images of the same scene taken at different times, which plays a crucial role in many applications. The two most popular image change detection techniques are as follows: pixel-based methods heavily rely on accurate image coregistration while object-based approaches can tolerate coregistration errors to some extent but are sensitive to image segmentation or classification errors. To address these issues, we propose an unsupervised image change detection approach based on a novel bipartite differential neural network (BDNN). The BDNN is a deep neural network with two input ends, which can extract the holistic features from the unchanged regions in the two input images, where two learnable change disguise maps (CDMs) are used to disguise the changed regions in the two input images, respectively, and thus demarcate the unchanged regions therein. The network parameters and CDMs will be learned by optimizing an objective function, which combines a loss function defined as the likelihood of the given input image pair over all possible input image pairs and two constraints imposed on CDMs. Compared with the pixel-based and object-based techniques, the BDNN is less sensitive to inaccurate image coregistration and does not involve image segmentation or classification. In fact, it can even skip over coregistration if the degree of transformation (due to the different view angles and/or positions of the camera) between the two input images is not that large. We compare the proposed approach with several state-of-the-art image change detection methods on various homogeneous and heterogeneous image pairs with and without coregistration. The results demonstrate the superiority of the proposed approach.

Ordinal data are common in many data mining and machine learning tasks. Compared to nominal data, the possible values (also called categories interchangeably) of an ordinal attribute are naturally ordered. Nevertheless, since the data values are not quantitative, the distance between two categories of an ordinal attribute is generally not well defined, which surely has a serious impact on the result of the quantitative analysis if an inappropriate distance metric is utilized. From the practical perspective, ordinal-and-nominal-attribute categorical data, i.e., categorical data associated with a mixture of nominal and ordinal attributes, is common, but the distance metric for such data has yet to be well explored in the literature. In this paper, within the framework of clustering analysis, we therefore first propose an entropy-based distance metric for ordinal attributes, which exploits the underlying order information among categories of an ordinal attribute for the distance measurement. Then, we generalize this distance metric and propose a unified one accordingly, which is applicable to ordinal-and-nominal-attribute categorical data. Compared with the existing metrics proposed for categorical data, the proposed metric is simple to use and nonparametric. More importantly, it reasonably exploits the underlying order information of ordinal attributes and statistical information of nominal attributes for distance measurement. Extensive experiments show that the proposed metric outperforms the existing counterparts on both the real and benchmark data sets.

The main feature of the Dynamic Multi-objective Optimization Problems (DMOPs) is that optimization objective functions will change with times or environments. One of the promising approaches for solving the DMOPs is reusing the obtained Pareto optimal set (POS) to train prediction models via machine learning approaches. In this paper, we train an Incremental Support Vector Machine (ISVM) classifier with the past POS, and then the solutions of the DMOP we want to solve at the next moment are filtered through the trained ISVM classifier. A high-quality initial population will be generated by the ISVM classifier, and a variety of different types of population-based dynamic multi-objective optimization algorithms can benefit from the population. To verify this idea, we incorporate the proposed approach into three evolutionary algorithms, the multi-objective particle swarm optimization(MOPSO), Nondominated Sorting Genetic Algorithm II (NSGA-II), and the Regularity Model-based multi-objective estimation of distribution algorithm(RE-MEDA). We employ experiments to test these algorithms, and experimental results show the effectiveness.

It is not uncommon that meta-heuristic algorithms contain some intrinsic parameters, the optimal configuration of which is crucial for achieving their peak performance. However, evaluating the effectiveness of a configuration is expensive, as it involves many costly runs of the target algorithm. Perhaps surprisingly, it is possible to build a cheap-to-evaluate surrogate that models the algorithm's empirical performance as a function of its parameters. Such surrogates constitute an important building block for understanding algorithm performance, algorithm portfolio/selection, and the automatic algorithm configuration. In principle, many off-the-shelf machine learning techniques can be used to build surrogates. In this paper, we take the differential evolution (DE) as the baseline algorithm for proof-of-concept study. Regression models are trained to model the DE's empirical performance given a parameter configuration. In particular, we evaluate and compare four popular regression algorithms both in terms of how well they predict the empirical performance with respect to a particular parameter configuration, and also how well they approximate the parameter versus the empirical performance landscapes.

Recently, evolutionary multi-tasking (EMT) has been proposed as a new evolutionary search paradigm that op-timizes multiple problems simultaneously. Due to the knowledge transfer across optimization tasks occurs along the evolutionary search process, EMT has been demonstrated to outperform the traditional single-task evolutionary search algorithms on many complex optimization problems, such as multimodal continuous optimization problems, NP-hard combinatorial optimization problems, and constrained optimization problems. Today, EMT has attracted lots of attentions, and many EMT algorithms have been proposed in the literature. The explicit EMT algorithm (EEMTA) is a recent proposed new EMT algorithm. In contrast to most of existing EMT algorithms, which employ a single population using unified space and common search operators for solving multiple problems, the EEMTA uses multiple populations which possess problem-specific solution representations and search mechanisms for different problems in evolutionary multi-tasking, which thus could lead to enhanced optimization performance. However, the original EEMTA was proposed for solving only two tasks. As knowledge transfer from inappropriate tasks may lead to negative effect on the evolutionary optimization process, additional designs of identifying task pairs for knowledge transfer is necessary in EEMTA for evolutionary multi-tasking with tasks more than two. To the best of our knowledge, there is no research effort has been conducted on this issue. Keeping this in mind, in this paper, we present a preliminary study on the task selection in EEMTA for many-task optimization. As task similarity may lose to capture the usefulness between tasks in evolutionary search, instead of using similarity measures for task selection, here we propose a credit assignment approach for selecting proper task to conduct knowledge transfer in explicit evolutionary many-tasking. The proposed approach is based on the feedbacks from the transferred solutions across tasks, which is adaptively updated along the evolutionary search. To confirm the efficacy of the proposed method, empirical studies on the many-task optimization problem, which consists of 7 commonly used optimization benchmarks, have been presented and discussed.

Autoencoders (AE) have been used successfully as unsupervised learners for inferring latent information, learning hidden features and reducing the dimensionality of the data. In this paper, we propose a new AE architecture: Gate-Layer AE (GLAE). The novelty of GLAE lies in its ability to encourage learning of the relationships among different input variables, which affords it with an inherent ability to recover missing variables from the available ones and to act as a concurrent multi-function approximator.GLAE uses a network architecture that associates each input with a binary gate acting as a switch that turns on or off the flow to each input unit, while synchronising its action with data flow to the network. We test GLAE with different coding sizes and compare its performance against the Classic AE, Denoising AE and Variational AE. The evaluation uses Electroencephalograph (EEG) data with an aim to reconstruct the EEG signal when some data are missing. The results demonstrate GLAE's superior performance in reconstructing EEG signals with up to 25% missing data in an input stream.

Spikes play an essential role in information transmission in central nervous system, but how neurons learn from them remains a challenging question. Most algorithms studied how to train spiking neurons to process patterns encoded with a sole assumption of either a rate or a temporal code. Is there a general learning algorithm capable of processing both codes regardless of the intense debate on them within neuroscience community? In this paper, we propose several threshold-driven plasticity algorithms to address the above question. In addition to formulating the algorithms, we also provide proofs with respect to several properties, such as robustness and convergence. The experimental results illustrate that our algorithms are simple, effective and yet efficient for training neurons to learn spike patterns. Due to their simplicity and high efficiency, our algorithms would be potentially beneficial for both software and hardware implementations. Neurons with our algorithms can also detect and recognize embedded features from a background sensory activity. With the as-proposed algorithms, a single neuron can successfully perform multicategory classifications by making decisions based on its output spike number in response to each category. Spike patterns being processed can be encoded with both spike rates and precise timings. When afferent spike timings matter, neurons will automatically extract temporal features without being explicitly instructed as to which point to fire.

Decomposition-based evolutionary algorithms have shown great potential in many-objective optimization. However, the lack of theoretical studies on decomposition methods has hindered their further development and application. In this paper, we first theoretically prove that weight sum, Tchebycheff, and penalty boundary intersection decomposition methods are essentially interconnected. Inspired by this, we further show that highly customized dominance relationship can be derived from decomposition for any given decomposition vector. A new evolutionary algorithm is then proposed by applying the customized dominance relationship with adaptive strategy to each subpopulation of multiobjective to multiobjective framework. Experiments are conducted to compare the proposed algorithm with five state-of-the-art decomposition-based evolutionary algorithms on a set of well-known scaled many-objective test problems with 5 to 15 objectives. Simulation results have shown that the proposed algorithm can make better use of the decomposition vectors to achieve better performance. Further investigations on unscaled many-objective test problems verify the robust and generality of the proposed algorithm.

Evolutionary multitasking (EMT) is an emerging research topic in the field of evolutionary computation. In contrast to the traditional single-task evolutionary search, EMT conducts evolutionary search on multiple tasks simultaneously. It aims to improve convergence characteristics across multiple optimization problems at once by seamlessly transferring knowledge among them. Due to the efficacy of EMT, it has attracted lots of research attentions and several EMT algorithms have been proposed in the literature. However, existing EMT algorithms are usually based on a common mode of knowledge transfer in the form of implicit genetic transfer through chromosomal crossover. This mode cannot make use of multiple biases embedded in different evolutionary search operators, which could give better search performance when properly harnessed. Keeping this in mind, this paper proposes an EMT algorithm with explicit genetic transfer across tasks, namely EMT via autoencoding, which allows the incorporation of multiple search mechanisms with different biases in the EMT paradigm. To confirm the efficacy of the proposed EMT algorithm with explicit autoencoding, comprehensive empirical studies have been conducted on both the single- and multi-objective multitask optimization problems.

Non-negative matrix factorization (NMF) is becoming increasingly popular in many research fields due to its particular properties of semantic interpretability and part-based representation. Sparseness constraints are usually imposed on the NMF problems in order to achieve potential features and sparse representation. These constrained NMF problems are usually reformulated as regularization models to solve conveniently. However, the regularization parameters in the regularization model are difficult to tune and the frequently used sparse-inducing terms in the regularization model generally have bias effects on the induced matrix and need an extra restricted isometry property (RIP). This paper proposes a multiobjective sparse NMF paradigm which refrains from the regularization parameter issues, bias effects, and the RIP condition. A novel multiobjective memetic algorithm is also proposed to generate a set of solutions with diverse sparsity and high factorization accuracy. A masked projected gradient local search scheme is specially designed to accelerate the convergence rate. In addition, a priori knowledge is also integrated in the algorithm to reduce the computational time in discovering our interested region in the objective space. The experimental results show that the proposed paradigm has better performance than some regularization algorithms in producing solutions with different degrees of sparsity as well as high factorization accuracy, which are favorable for making the final decisions.

Imbalanced data with a skewed class distribution are common in many real-world applications. Deep Belief Network (DBN) is a machine learning technique that is effective in classification tasks. However, conventional DBN does not work well for imbalanced data classification because it assumes equal costs for each class. To deal with this problem, cost-sensitive approaches assign different misclassification costs for different classes without disrupting the true data sample distributions. However, due to lack of prior knowledge, the misclassification costs are usually unknown and hard to choose in practice. Moreover, it has not been well studied as to how cost-sensitive learning could improve DBN performance on imbalanced data problems. This paper proposes an evolutionary cost-sensitive deep belief network (ECS-DBN) for imbalanced classification. ECS-DBN uses adaptive differential evolution to optimize the misclassification costs based on the training data that presents an effective approach to incorporating the evaluation measure (i.e., G-mean) into the objective function. We first optimize the misclassification costs, and then apply them to DBN. Adaptive differential evolution optimization is implemented as the optimization algorithm that automatically updates its corresponding parameters without the need of prior domain knowledge. The experiments have shown that the proposed approach consistently outperforms the state of the art on both benchmark data sets and real-world data set for fault diagnosis in tool condition monitoring.

Service composition is a key enabling technology in service-oriented computing for developing versatile applications by integrating various existing interoperable services. Although actively studied, most existing works on service composition neglect the existence of complementarity among candidate services within a service class, so-called internal complementarity. In fact, complementary candidate services within a service class can be composed to form a composite candidate service which may yield better service utility than that provided by any existing candidate service within that service class. This work focuses on web service composition where internal complementarity is more likely to happen. Specifically, we aim at addressing the problem of QoS-aware web service selection with internal complementarity (WSS-IC). We first transform this problem into a multi-choice multi-dimensional knapsack problem (MMKP) and prove such a transformation per se has non-polynomial time complexity in the worse case.Then, we perform complexity analysis to demonstrate that existing approaches to MMKPs are not computationally feasible to resolve QoS-aware WSS-IC. This fact motivates us to propose an iteratively improving framework for deriving the solution iteration by iteration while taking into account both solution structure and QoS constraints. At each iteration, the current solution gets improved by solving a disjunctively constrained knapsack problem. To verify the effectiveness of the proposed framework, two heuristic approaches are implemented under this framework. Experimental results demonstrate that our approaches outperform the compared methods in terms of both solution quality and computation time.

Genetic programming has been considered as a powerful approach to automated design of production scheduling heuristics in recent years. Flexible and variable representations allow genetic programming to discover very competitive scheduling heuristics to cope with a wide range of dynamic production environments. However, evolving sophisticated heuristics to handle multiple scheduling decisions can greatly increase the search space and poses a great challenge for genetic programming. To tackle this challenge, a new genetic programming algorithm is proposed to incrementally construct the map of explored areas in the search space and adaptively guide the search towards potential heuristics. In the proposed algorithm, growing neural gas and principal component analysis are applied to efficiently generate and update the map of explored areas based on the phenotypic characteristics of evolved heuristics. Based on the obtained map, a surrogate assisted model will help genetic programming determine which heuristics to be explored in the next generation. When applied to evolve scheduling heuristics for dynamic flexible job shop scheduling problems, the proposed algorithm shows superior performance as compared to the standard genetic programming algorithm. The analyses also show that the proposed algorithm can balance its exploration and exploitation better than the existing surrogate-assisted algorithm.

Minimax optimization, which is actively involved in numerous robust design problems, aims at pursuing the solutions with best worst-case performances. Although considerable research has been devoted to the development of minimax optimization algorithms, there still exist several fundamental limitations for existing approaches, e.g., restriction on problem types, excessively high computational cost, and low optimization efficiency. To address these issues, a minimax differential evolution algorithm is proposed in this paper. First, a novel bottom-boosting scheme enables the algorithm to identify the promising solutions in a reliable yet efficient manner. After that, a partial-regeneration strategy together with a new mutation operator contribute to an in-depth exploration over solution space. Finally, a proper integration of these newly proposed mechanisms leads to an algorithmic structure that can appropriately handle various types of problems. Empirical comparison with seven famous methods demonstrates the statistical superiority of the proposed algorithm. Successful applications in two open problems of robust design further validate the effectiveness of the new approach.

Automated surface inspection (ASI) is a challenging task in industry, as collecting training dataset is usually costly and related methods are highly dataset-dependent. In this paper, a generic approach that requires small training data for ASI is proposed. First, this approach builds classifier on the features of image patches, where the features are transferred from a pretrained deep learning network. Next, pixel-wise prediction is obtained by convolving the trained classifier over input image. An experiment on three public and one industrial data set is carried out. The experiment involves two tasks: 1) image classification and 2) defect segmentation. The results of proposed algorithm are compared against several best benchmarks in literature. In the classification tasks, the proposed method improves accuracy by 0.66%-25.50%. In the segmentation tasks, the proposed method reduces error escape rates by 6.00%-19.00% in three defect types and improves accuracies by 2.29%-9.86% in all seven defect types. In addition, the proposed method achieves 0.0% error escape rate in the segmentation task of industrial data.

Robust object recognition in spiking neural systems remains a challenging in neuromorphic computing area as it needs to solve both the effective encoding of sensory information and also its integration with downstream learning neurons. We target this problem by developing a spiking neural system consisting of sparse temporal encoding and temporal classifier. We propose a sparse temporal encoding algorithm which exploits both spatial and temporal information derived from an spike-timing-dependent plasticity-based HMAX feature extraction process. The temporal feature representation, thus, becomes more appropriate to be integrated with a temporal classifier based on spiking neurons rather than with nontemporal classifier. The algorithm has been validated on two benchmark data sets and the results show the temporal feature encoding and learning-based method achieves high recognition accuracy. The proposed model provides an efficient approach to perform feature representation and recognition in a consistent temporal learning framework, which is easily adapted to neuromorphic implementations.

This paper presents a voice conversion framework that uses phonetic information in an exemplar-based voice conversion approach. The proposed idea is motivated by the fact that phone-dependent exemplars lead to better estimation of activation matrix, therefore, possibly better conversion. We propose to use the phone segmentation results from automatic speech recognition (ASR) to construct a sub-dictionary for each phone. The proposed framework can work with or without parallel training data. With parallel training data, we found that phonetic sub-dictionary outperforms the state-of-the-art baseline in objective and subjective evaluations. Without parallel training data, we use Phonetic PosteriorGrams (PPGs) as the speaker-independent exemplars in the phonetic sub-dictionary to serve as a bridge between speakers. We report that such technique achieves a competitive performance without the need of parallel training data.

Tool Condition Monitoring (TCM) is an important topic in manufacturing industry, which improves product quality, production efficiency, reduces costs and downtime. This paper develops a new data-driven framework for estimating tool remaining useful life (RUL) in TCM. The framework includes the following modular components: data preprocessing with a proposed adaptive Baysian change point detection (ABCPD) for automatic data alignment, time window process, feature extraction, feature selection and a multi-layer neural network as the main machine learning algorithm. The proposed framework is evaluated on a real-world gun drilling experimental dataset with multiple sensor measurements (i.e. thrust force, torque, 12 vibration signals). Different model selection, sensor selection, feature selection methods have been investigated in this paper. The simulation performance of the proposed framework is studied with the gun drilling dataset and it has been shown that the proposed framework has good performance.

Growing trend of the dynamic multiobjective optimization research in the evolutionary computation community has increased the need for challenging and conceptually simple benchmark test suite to assess the optimization performance of an algorithm. This paper proposes a new dynamic multiobjective benchmark test suite which contains a number of component functions with clearly defined properties to assess the diversity maintenance and tracking ability of a dynamic multiobjective evolutionary algorithm (MOEA). Time-varying fitness landscape modality, tradeoff connectedness, and tradeoff degeneracy are considered as these properties rarely exist in the current benchmark test instances. Cross-problem comparative study is presented to analyze the sensitivity of a given algorithm to certain fitness landscape properties. To demonstrate the use of the proposed benchmark test suite, three evolutionary multiobjective algorithms, namely nondominated sorting genetic algorithm, decomposition-based MOEA, and recently proposed Kalman-filter-based prediction approach, are analyzed and compared. Besides, two problem-specific performance metrics are designed to assess the convergence and diversity performances, respectively. By applying the proposed test suite and performance metrics, microscopic performance details of these algorithms are uncovered to provide insightful guidance to the algorithm designer.

Evolutionary multiobjective optimization in dynamic environments is a challenging task, as it requires the optimization algorithm converging to a time-variant Pareto optimal front. This paper proposes a dynamic multiobjective optimization algorithm which utilizes an inverse model set to guide the search toward promising decision regions. In order to reduce the number of fitness evalutions for change detection purpose, a two-stage change detection test is proposed which uses the inverse model set to check potential changes in the objective function landscape. Both static and dynamic multiobjective benchmark optimization problems have been considered to evaluate the performance of the proposed algorithm. Experimental results show that the improvement in optimization performance is achievable when the proposed inverse model set is adopted.

In recent decades, the field of multiobjective optimization has attracted considerable interest among evolutionary computation researchers. One of the main features that makes evolutionary methods particularly appealing for multiobjective problems is the implicit parallelism offered by a population, which enables simultaneous convergence toward the entire Pareto front. While a plethora of related algorithms have been proposed till date, a common attribute among them is that they focus on efficiently solving only a single optimization problem at a time. Despite the known power of implicit parallelism, seldom has an attempt been made to multitask, i.e., to solve multiple optimization problems simultaneously. It is contended that the notion of evolutionary multitasking leads to the possibility of automated transfer of information across different optimization exercises that may share underlying similarities, thereby facilitating improved convergence characteristics. In particular, the potential for automated transfer is deemed invaluable from the standpoint of engineering design exercises where manual knowledge adaptation and reuse are routine. Accordingly, in this paper, we present a realization of the evolutionary multitasking paradigm within the domain of multiobjective optimization. The efficacy of the associated evolutionary algorithm is demonstrated on some benchmark test functions as well as on a real-world manufacturing process design problem from the composites industry.

Class imbalance problems, where the number of samples in each class is unequal, is prevalent in numerous real world machine learning applications. Traditional methods which are biased toward the majority class are ineffective due to the relative severity of misclassifying rare events. This paper proposes a novel evolutionary cluster-based oversampling ensemble framework, which combines a novel cluster-based synthetic data generation method with an evolutionary algorithm (EA) to create an ensemble. The proposed synthetic data generation method is based on contemporary ideas of identifying oversampling regions using clusters. The novel use of EA serves a twofold purpose of optimizing the parameters of the data generation method while generating diverse examples leveraging on the characteristics of EAs, reducing overall computational cost. The proposed method is evaluated on a set of 40 imbalance datasets obtained from the University of California, Irvine, database, and outperforms current state-of-the-art ensemble algorithms tackling class imbalance problems.

Automated design of dispatching rules for production systems has been an interesting research topic over the last several years. Machine learning, especially genetic programming (GP), has been a powerful approach to dealing with this design problem. However, intensive computational requirements, accuracy and interpretability are still its limitations. This paper aims at developing a new surrogate assisted GP to help improving the quality of the evolved rules without significant computational costs. The experiments have verified the effectiveness and efficiency of the proposed algorithms as compared to those in the literature. Furthermore, new simplification and visualisation approaches have also been developed to improve the interpretability of the evolved rules. These approaches have shown great potentials and proved to be a critical part of the automated design system.

Differential evolution (DE) is a popular population-based metaheuristic approach for solving numerical optimization problems. In recent years, considerable research has been devoted to the development of new mutation strategies and parameter adaptation mechanisms. However, as one of the basic algorithmic components of DE, the crossover operation has not been sufficiently examined in existing works. Most of the main DE variants solely employ traditional binomial recombination, which has intrinsic limitations in handling dependent subsets of variables. To fill this research niche, we propose a multiple exponential recombination that inherits all the main advantages of existing crossover operators while possessing a stronger ability in managing dependent variables. Multiple segments of the involved solutions will be exchanged during the proposed operator. The properties of the new scheme are examined both theoretically and empirically. Experimental results demonstrate the robustness of the proposed operator in solving problems with unknown variable interrelations.

For accurate prognostics, users have to determine the current health of the system and predict future degradation pattern of the system. An increasingly popular approach toward tackling prognostic problems involves the use of switching models to represent various degradation phases, which the system undergoes. Such approaches have the advantage of determining the exact degradation phase of the system and being able to handle nonlinear degradation models through piecewise linear approximation. However, limitations of such existing methods include, limited applicability due to the discretization of predicted remaining useful life, insufficient robustness due to the use of single models and others. This paper circumvents these limitations by proposing a hybrid of ensemble methods with switching methods. The proposed method first implements a switching Kalman filter (SKF) to classify between various linear degradation phases, then predict the future propagation of fault dimension using appropriate Kalman filters for each phase. This proposed method achieves both continuous and discrete prediction values representing the remaining life and degradation phase of the system, respectively. The proposed framework is shown via a case study on benchmark simulated aeroengine data sets. The evaluation of the proposed framework shows that the proposed method achieves better accuracy and robustness against noise compared with other methods reported in the literature. The results also indicate the effectiveness of the SKF in detecting the switching point between various degradation modes.

In numerous industrial applications where safety, efficiency, and reliability are among primary concerns, condition-based maintenance (CBM) is often the most effective and reliable maintenance policy. Prognostics, as one of the key enablers of CBM, involves the core task of estimating the remaining useful life (RUL) of the system. Neural networks-based approaches have produced promising results on RUL estimation, although their performances are influenced by handcrafted features and manually specified parameters. In this paper, we propose a multiobjective deep belief networks ensemble (MODBNE) method. MODBNE employs a multiobjective evolutionary algorithm integrated with the traditional DBN training technique to evolve multiple DBNs simultaneously subject to accuracy and diversity as two conflicting objectives. The eventually evolved DBNs are combined to establish an ensemble model used for RUL estimation, where combination weights are optimized via a single-objective differential evolution algorithm using a task-oriented objective function. We evaluate the proposed method on several prognostic benchmarking data sets and also compare it with some existing approaches. Experimental results demonstrate the superiority of our proposed method.

Workload is the amount of cognitive effort executed by a certain subject. Several attempts have been done in order to measure workload level. However, there exists a difficulty in analyzing workload: the problem of individuality, or variability among different individuals and how they respond to similar tasks. In order to have a more objective measure of workload level, the authors employed a more direct analysis upon the system that does cognitive work itself. The use of electroencephalogram (EEG) was employed to measure brain signals and process them to get an objective estimation of workload level. In this study, the authors evaluated the workload level related to complex training-based type task. Piloting simulation task was used to represent such type of task. The authors assess the EEG channel connections and found important connections for the estimation of workload level. This information can be used to build a more an EEG-based workload level estimator that is more efficient, i.e. less channels needed be used to accurately construct the estimation. The authors also found the significant brain signal frequency band that is related to the measure of workload in complex tasks. The problem of individual differences was also resolved using the proposed algorithm.

Autonomous robots such are unmanned aerial and unmanned ground vehicles are increasingly utilized in patrolling, surveillance, search and rescue and in missions that are hazardous for humans. Path-planning, path-generation and following a planned path successfully are fundamental requirements for autonomous operation of unmanned robots. Though the operational principle of aerial and ground robots are different, the algorithms for path-planning and path-following can be generalized. Vector Directed Path Generation and Tracking (VDPGT) proposed in this work is a platform independent path-generation and path-following algorithm. VDPGT is designed to dynamically adapt the shortest path to a destination. Simulation studies carried out on two ground robots (Turtlebot and Clearpath Husky), two aerial robots (AR Drone and Hector-quadrotor) and realtime experiments on Turtlebot and AR Drone demonstrate the platform independent nature of VDPGT.

In this paper, we propose a novel grid-based differential evolution (DE) algorithm termed as GrDE to handle many-objective optimization problems. For this algorithm, a novel differential evolution variant is formulated by first synthesizing an opposition-based self-adaptive DE operator with a local mutation operator, and then incorporating it into a grid-based framework. The proposed algorithm is being investigated through a comparative study with five other state-of-the-art evolutionary multi-objective optimization (EMO) algorithms using a total of 20 test instances from the DTLZ test suite. Through the experimental results that are presented by employing the Inverted Generational Distance (IGD) performance indicator, it is seen that GrDE is able to achieve competitive, if not better, performance when compared to the other algorithms used in this study.

Effectively utilising available resources is an important task of a reservation system to help service providers improve their profits and customer satisfaction. Reservation with slack is an interesting and challenging combinatorial optimization problem with many potential applications in practice. However, this problem has not received enough attentions in the literature. This study proposes a new mixed integer linear programming model for reservation with slack and develops a new hybrid genetic algorithm to deal with this problem. The results show that the proposed method is very competitive as compared to the exact optimisation method and the composite dispatching rule in terms of effectiveness and efficiency. While exact method can only solve very small instances with no more than 20 activities, the proposed algorithm can handle very large scale instances with hundreds of activities in a short running time. Analyses are also provided in this paper to examine the influence of decoding methods, local search heuristics and diversification on the performance of the proposed algorithm.

In recent years, many new variants of Differential Evolution (DE) have been proposed for real number function optimization, and most of these variants employ binomial recombination as their crossover operators. By contrast, another classical crossover operator, exponential recombination, received less attention. This paper examines the explorative ability of exponential recombination in handling high-dimensional multimodal problems. Based on the analysis, a new variant of DE with a hybrid crossover operation is proposed. DE/best/1, a greedy mutation strategy rarely used in tackling multimodal problems, is utilized in our algorithm to help combine the two basic recombination operators. Empirical results demonstrate that the proposed algorithm is powerful in solving high-dimensional multimodal problems.

Neural information recorded from electroencephalogram (EEG) provides new possibilities for diagnosis of brain abnormalities, cognitive monitoring, etc. However, many artifacts, such as eye blink and muscle movements, impact and contaminate EEG data. While traditional techniques proposed for artifact removal identified artifact on two-way data, (spatial x temporal), multidimensional nature of EEG data (spatial x temporal x spectral x condition x trial) is overlooked. In this work, we investigate the use of multiway analysis/tensor factorization on the extended EEG tensor (spatial x temporal x spectral), which is constructed from continuous wavelet transform, using Block Term Decomposition (BTD) of rank-(Lr, Lr, 1) for artifact removal. Eight different carefully designed experiments to study artifact typically produced by voluntarily, and sometimes involuntarily, behaviors using a subject were performed and analyzed. After the BTD decomposition, artifacted components are automatically identified removed using spatial and temporal features. The reconstructed signal from proposed method suppresses artifact while retains the signal texture of eight types of artifact investigated.

This paper develops a framework for determining the Remaining Useful Life (RUL) of aero-engines. The framework includes the following modular components: creating a moving time window, a suitable feature extraction method and a multi-layer neural network as the main machine learning algorithm. The proposed framework is evaluated on the publicly available C-MAPSS dataset. The prognostic accuracy of the proposed algorithm is also compared against other state-of-the-art methods available in the literature and it has been shown that the proposed framework has the best overall performance.

The recently introduced DeepIR model is proven effective for text classification [1]. In this paper, a modified DeepIR model is proposed by introducing a new document probability. This probability employs composite log likelihood method. An experiment using the modified DeepIR model is conducted on five text classification data sets. The proposed model shows considerable improvements in multi-class classification and minor improvements in binary-class classification. We further analyze the result to explain the performance increase.

Many real-world problems are usually unbalanced, where datasets present skewed class distributions, such as failure diagnosis, spam detection, anomaly detection, fraud detection, oil spillage detection and medical diagnosis, etc. Deep Belief Network (DBN) is a competitive machine learning technique with good performance in many applications. However, some machine learning methods are likely to give poor performance with imbalanced data between classes since they assume equal costs for each class intrinsically. To deal with this problem, existing researches only focus on sampling based approaches and lack of studies about cost-sensitive based approaches. This paper proposes cost-sensitive Deep Belief Networks for such imbalanced classification problems. The proposed approach is extended to multi-class scenario. Unequalized misclassification costs between classes have been applied to DBN. Extensive comparison with extreme learning machines is provided as a proof of the ability of the proposed approach to perform competitively on imbalanced datasets. An evolutionary algorithm is also implemented to optimize the misclassification costs for each class in cost matrix.

Evolutionary algorithms are effective in solving static multiobjective optimization problems resulting in the emergence of a number of state-of-the-art multiobjective evolutionary algorithms (MOEAs). Nevertheless, the interest in applying them to solve dynamic multiobjective optimization problems has only been tepid. Benchmark problems, appropriate performance metrics, as well as efficient algorithms are required to further the research in this field. One or more objectives may change with time in dynamic optimization problems. The optimization algorithm must be able to track the moving optima efficiently. A prediction model can learn the patterns from past experience and predict future changes. In this paper, a new dynamic MOEA using Kalman filter (KF) predictions in decision space is proposed to solve the aforementioned problems. The predictions help to guide the search toward the changed optima, thereby accelerating convergence. A scoring scheme is devised to hybridize the KF prediction with a random reinitialization method. Experimental results and performance comparisons with other state-of-the-art algorithms demonstrate that the proposed algorithm is capable of significantly improving the dynamic optimization performance.

Convergence performance and parametric sensitivity are two issues that tend to be neglected when extending differential evolution (DE) to multiobjective optimization (MO). To fill this research gap, we develop two novel mutation operators and a new parameter adaptation mechanism. A multiobjective DE variant is obtained through integration of the proposed strategies. The main innovation of this paper is the simultaneous use of individuals across generations from an objective-based perspective. Good convergence-diversity tradeoff and satisfactory exploration-exploitation balance are achieved via the hybrid cross-generation mutation operation. Furthermore, the cross-generation adaptation mechanism enables the individuals to self-adapt their associated parameters not only optimization stage-wise but also objective-space-wise. Empirical results indicate the statistical superiority of the proposed algorithm over several state-of-the-art evolutionary algorithms in handling MO problems.

This paper proposes a biologically plausible network architecture with spiking neurons for sequence recognition. This architecture is a unified and consistent system with functional parts of sensory encoding, learning, and decoding. This is the first systematic model attempting to reveal the neural mechanisms considering both the upstream and the downstream neurons together. The whole system is a consistent temporal framework, where the precise timing of spikes is employed for information processing and cognitive computing. Experimental results show that the system is competent to perform the sequence recognition, being robust to noisy sensory inputs and invariant to changes in the intervals between input stimuli within a certain range. The classification ability of the temporal learning rule used in the system is investigated through two benchmark tasks that outperform the other two widely used learning rules for classification. The results also demonstrate the computational power of spiking neurons over perceptrons for processing spatiotemporal patterns. In summary, the system provides a general way with spiking neurons to encode external stimuli into spatiotemporal spikes, to learn the encoded spike patterns with temporal learning rules, and to decode the sequence order with downstream neurons. The system structure would be beneficial for developments in both hardware and software.

Challenging multi-modal optimization problems have been very successfully solved by evolutionary computation (EC) techniques. To date, many methods have been proposed on evolutionary optimization for both single and multiobjective large scale problems. In the age of Big Data, there is an urge to take evolutionary optimization techniques to the next level for solving problems with even larger scales: thousands and millions of variables. These problems arise in many domains ranging from bioinformatics, to neuroscience and social simulations. In this paper, we investigate the use of EC to solve Big electroencephalography (EEG) data optimization problems with thousands of variables. The optimization problem attempts to identify maximum information that should be kept from a signal while minimizing the artifact. The high level of epistasis inherent in a signal can slow down the evolution. Therefore, we investigate the advantages of optimizing the problem in the frequency domain with different thresholds as opposed to the time domain. We propose synthetic EEG data sets of various scale and noise level. These data sets were the basis for the Optimization of Big Data 2015 Competition (BigOpt), CEC 2015. Two state-of-art multiobjective evolutionary algorithms (MOEAs) were evaluated. The results of this work suggest that frequency representation of the signals facilitates dimensionality reduction for big scale optimization of time series data, and hence provides faster and better quality solutions for EEG data cleaning. Moreover, the results suggest that existing state-of-art multiobjective evolutionary computation methods are extremely slow. Methods that can optimize the problem faster and with high quality are needed.

Genetic programming based hyper-heuristics have been an suitable approach to designing powerful dispatching rules for dynamic job shop scheduling. However, most current methods only focus on a single objective while practical problems almost always involve multiple conflicting objectives. Some efforts have been made to design non-dominated dispatching rules but using genetic programming to deal with multiple objectives is still very challenging because of the large search space and the stochastic characteristics of job shops. This paper investigates different strategies to utilise computational budgets when evolving dispatching rules with genetic programming. The results suggest that using local search heuristics can enhance the quality of evolved dispatching rules. Moreover, the results show that there are some differences in evolving rules for single objectives and for multiple objectives and that it is difficult to efficiently estimate the Pareto dominance of rules.

Order acceptance and scheduling is an interesting and chal- lenging scheduling problem in which two decisions need to be handled simultaneously. While the exact methods are not efficient and sometimes impractical, existing meta-heuristics proposed in the literature still have troubles dealing with large problem instances. In this paper, a dispatching rule based genetic algorithm is proposed to combine the advan- tages of existing dispatching rules/heuristics, genetic algo- rithm and local search. The results indicates that the pro- posed methods are effective and efficient when compared to a number of existing heuristics with a wide range of problem instances.

Proper tuning of control parameters is critical to the performance of a multi-objective evolutionary algorithm (MOEA). However, the developments of tuning methods for multi-objective optimization are insufficient compared to single-objective optimization. To circumvent this issue, this paper proposes a novel framework that can self-adapt the parameter values from an objective-based perspective. Optimal parametric setups for each objective will be efficiently estimated by combining single-objective tuning methods with a grouping mechanism. Subsequently, the position information of individuals in objective space is utilized to achieve a more efficient adaptation among multiple objectives. The new framework is implemented into two classical Differential-Evolution-based MOEAs to help to adapt the scaling factor F in an objective-wise manner. Three state-of-the-art single-objective tuning methods are applied respectively to validate the robustness of the proposed mechanisms. Experimental results demonstrate that the new framework is effective and robust in solving multi-objective optimization problems.

Early diagnosis that can detect faults from some symptoms accurately is critical, because it provides the potential benefits such as reducing maintenance costs, improving productivity and avoiding serious damages. Degradation pattern classification for early diagnosis has not been explored in many researches yet. This paper will use hybrid ensemble model for degradation pattern classification. Supervised training of deep models (e.g. Many-layered Neural Nets) is difficult for optimization problem with unlabeled datasets or insufficient data sample. Shallow models (SVMs, Neural Networks, etc...) are unlikely candidates for learning high-level abstractions, since they are affected by the curse of dimensionality. Therefore, deep learning network (DBN), an unsupervised learning model, in diagnosis problem has been investigated to do classification. Few researches have been done for exploring the effects of DBN in diagnosis. In this paper, an ensemble of DBNs with MOEA/D has been applied for diagnosis to handle failure degradation with multivariate sensory data. Turbofan engine degradation dataset is employed to demonstrate the efficacy of the proposed model. We believe that deep learning with multi-objective ensemble for degradation pattern classification can shed new light on failure diagnosis, and our work presented the applicability of this method to diagnosis as well as prognostics.

Dispatching rules have been commonly used in practice for making sequencing and scheduling decisions. Due to specific characteristics of each manufacturing system, there is no universal dispatching rule that can dominate in all situations. Therefore, it is important to design specialized dispatching rules to enhance the scheduling performance for each manufacturing environment. Evolutionary computation approaches such as tree-based genetic programming (TGP) and gene expression programming (GEP) have been proposed to facilitate the design task through automatic design of dispatching rules. However, these methods are still limited by their high computational cost and low exploitation ability. To overcome this problem, we develop a new approach to automatic programming via iterated local search (APRILS) for dynamic job shop scheduling. The key idea of APRILS is to perform multiple local searches started with programs modified from the best obtained programs so far. The experiments show that APRILS outperforms TGP and GEP in most simulation scenarios in terms of effectiveness and efficiency. The analysis also shows that programs generated by APRILS are more compact than those obtained by genetic programming. An investigation of the behavior of APRILS suggests that the good performance of APRILS comes from the balance between exploration and exploitation in its search mechanism.

Inspired by biological evolution, a plethora of algorithms with evolutionary features have been proposed. These algorithms have strengths in certain aspects, thus yielding better optimization performance in a particular problem. However, in a wide range of problems, none of them are superior to one another. Synergetic combination of these algorithms is one of the potential ways to ameliorate their search ability. Based on this idea, this paper proposes an adaptive memetic computing as the synergy of a genetic algorithm, differential evolution, and estimation of distribution algorithm. The ratio of the number of fitter solutions produced by the algorithms in a generation defines their adaptability features in the next generation. Subsequently, a subset of solutions undergoes local search using the evolutionary gradient search algorithm. This memetic technique is then implemented in two prominent frameworks of multiobjective optimization: the domination- and decomposition-based frameworks. The performance of the adaptive memetic algorithms is validated in a wide range of test problems with different characteristics and difficulties.

Many diversity metrics have been proposed for offline diversity measurement of the whole population in multiobjective optimization. Most of the existing methods require knowledge of the exact Pareto optimal front or the ideal vector. For this reason, there is no direct approach to use the diversity metrics in an online manner. In this paper we propose an online diversity metric that is inspired by the geometrical interpretation of convergence and diversity. In addition, the proposed method is able to measure the diversity loss caused by any individual in the population. This information is useful in the selection process as the algorithm can perform a diversity-preservation selection based on the measured diversity loss contributed by each individual. To demonstrate the effectiveness of the proposed metric in enhancing the diversification of the solution set, we implement the metric on the well-known multiobjective evolutionary algorithm with decomposition. The simulation results show the applicability and usability of the proposed online diversity measurement.

Convergence and diversity are two crucial issues in evolutionary multiobjective optimization. To enhance the diversity property of Multiobjective Evolutionary Algorithm (MOEA), a novel selection method is implemented on decomposition-based MOEA (MOEA/D). The selection method incorporates the concept of maximum diversity loss, which quantifies the diversity loss of each individual in every generation. By monitoring tolerance of the diversity loss, the diversity of the solutions in each generation can be preserved. To further enhance the algorithm's search ability, a new hybrid recombination strategy is implemented by taking the advantage of different recombination operators. In terms of Inverted Generational Distance (IGD), the experiment results shown that the proposed algorithm, namely DHRS-MOEA/D, performed significantly better than many state-of-the-art MOEAs in most of the CEC-09 and WFG test problems.

Convergence speed and parametric sensitivity are two issues that tend to be neglected when extending Differential Evolution (DE) for multi-objective optimization. To fill in this gap, we propose a multi-objective DE variant with an extraordinary mutation strategy and unfixed parameters. Wise tradeoff between convergence and diversity is achieved via the novel cross-generation mutation operators. In addition, a dynamic mechanism enables the parameters to evolve continuously during the optimization process. Empirical results show that the proposed algorithm is powerful in handling multi-objective problems.

In this paper, we present a new learning rule for classification of spatiotemporal spike patterns. This rule is derived from the common Widrow-Hoff rule, and it can be used for both the association and the classification. We mainly focus on investigating its classification ability in this paper. Through experimental simulations, it can be seen that this rule can successfully train the neuron to reproduce the desired spikes. In the classification task, the neuron is capable to classify different categories with the learning rule. We have proposed two decision-making schemes which are the absolute confidence and the relative confidence criteria. The classification performance is largely improved by the relative confidence criterion. The performance of this rule on classification of spatiotemporal spike patterns is also investigated and benchmarked by the tempotron rule.

Due-date assignment plays an important role in scheduling systems and strongly influences the delivery performance of job shops. Because of the stochastic and dynamic nature of job shops, the development of general due-date assignment models (DDAMs) is complicated. In this study, two genetic programming (GP) methods are proposed to evolve DDAMs for job shop environments. The experimental results show that the evolved DDAMs can make more accurate estimates than other existing dynamic DDAMs with promising reusability. In addition, the evolved operation-based DDAMs show better performance than the evolved DDAMs employing aggregate information of jobs and machines.

A scheduling policy strongly influences the performance of a manufacturing system. However, the design of an effective scheduling policy is complicated and time consuming due to the complexity of each scheduling decision, as well as the interactions among these decisions. This paper develops four new multi-objective genetic programming-based hyperheuristic (MO-GPHH) methods for automatic design of scheduling policies, including dispatching rules and due-date assignment rules in job shop environments. In addition to using three existing search strategies, nondominated sorting genetic algorithm II, strength Pareto evolutionary algorithm 2, and harmonic distance-based multi-objective evolutionary algorithm, to develop new MO-GPHH methods, a new approach called diversified multi-objective cooperative evolution (DMOCC) is also proposed. The novelty of these MO-GPHH methods is that they are able to handle multiple scheduling decisions simultaneously. The experimental results show that the evolved Pareto fronts represent effective scheduling policies that can dominate scheduling policies from combinations of existing dispatching rules with dynamic/regression-based due-date assignment rules. The evolved scheduling policies also show dominating performance on unseen simulation scenarios with different shop settings. In addition, the uniformity of the scheduling policies obtained from the proposed method of DMOCC is better than those evolved by other evolutionary approaches.

The recent identification of neural cliques, which are network-level memory coding units in the hippocampus, enables population codes to be the neuronal representation of memory. It has been discovered that the timing of spikes plays an important role in the neural computation and information processing in the brain. Moreover, these memory-coding units have been observed organizing in a hierarchical manner in the brain. Inspired by these exciting findings, we present a hierarchically organized memory model with spiking neurons, which can store both associative memory and episodic memory with temporal population codes. The basic structure of the hierarchical model is composed of three layers with different functions and can be extended to more complicated networks by duplicating and connecting the basic three-layer network. With a spike-timing based learning algorithm, the spiking neural network with theta and gamma oscillations is able to store spatiotemporal memory items within gamma cycles, and links these memories into a sequence. The spiking-timing-dependent plasticity (STDP) contributes to the formation of both associative memory and episodic memory via fast and slow N-methyl-D-aspartate (NMDA) channels, respectively.

Many real-world optimization problems are subjected to uncertainties that may be characterized by the presence of noise in the objective functions. The estimation of distribution algorithm (EDA), which models the global distribution of the population for searching tasks, is one of the evolutionary computation techniques that deals with noisy information. This paper studies the potential of EDAs; particularly an EDA based on restricted Boltzmann machines that handles multi-objective optimization problems in a noisy environment. Noise is introduced to the objective functions in the form of a Gaussian distribution. In order to reduce the detrimental effect of noise, a likelihood correction feature is proposed to tune the marginal probability distribution of each decision variable. The EDA is subsequently hybridized with a particle swarm optimization algorithm in a discrete domain to improve its search ability. The effectiveness of the proposed algorithm is examined via eight benchmark instances with different characteristics and shapes of the Pareto optimal front. The scalability, hybridization, and computational time are rigorously studied. Comparative studies show that the proposed approach outperforms other state of the art algorithms.

During the past few decades, remarkable progress has been made in solving pattern recognition problems using networks of spiking neurons. However, the issue of pattern recognition involving computational process from sensory encoding to synaptic learning remains underexplored, as most existing models or algorithms target only part of the computational process. Furthermore, many learning algorithms proposed in the literature neglect or pay little attention to sensory information encoding, which makes them incompatible with neural-realistic sensory signals encoded from real-world stimuli. By treating sensory coding and learning as a systematic process, we attempt to build an integrated model based on spiking neural networks (SNNs), which performs sensory neural encoding and supervised learning with precisely timed sequences of spikes. With emerging evidence of precise spike-timing neural activities, the view that information is represented by explicit firing times of action potentials rather than mean firing rates has been receiving increasing attention. The external sensory stimulation is first converted into spatiotemporal patterns using a latency-phase encoding method and subsequently transmitted to the consecutive network for learning. Spiking neurons are trained to reproduce target signals encoded with precisely timed spikes. We show that when a supervised spike-timing-based learning is used, different spatiotemporal patterns are recognized by different spike patterns with a high time precision in milliseconds.

In contrast to the numerous research works that integrate a niching scheme with an existing single-objective evolutionary algorithm to perform multimodal optimization, a few approaches have recently been taken to recast multimodal optimization as a multiobjective optimization problem to be solved by modified multiobjective evolutionary algorithms. Following this promising avenue of research, we propose a novel biobjective formulation of the multimodal optimization problem and use differential evolution (DE) with nondominated sorting followed by hypervolume measure-based sorting to finally detect a set of solutions corresponding to multiple global and local optima of the function under test. Unlike the two earlier multiobjective approaches (biobjective multipopulation genetic algorithm and niching-based nondominated sorting genetic algorithm II), the proposed multimodal optimization with biobjective DE (MOBiDE) algorithm does not require the actual or estimated gradient of the multimodal function to form its second objective. Performance of MOBiDE is compared with eight state-of-the-art single-objective niching algorithms and two recently developed biobjective niching algorithms using a test suite of 14 basic and 15 composite multimodal problems. Experimental results supported by nonparametric statistical tests suggest that MOBiDE is able to provide better and more consistent performance over the existing well-known multimodal algorithms for majority of the test problems without incurring any serious computational burden.

Designing effective dispatching rules is an important factor for many manufacturing systems. However, this time-consuming process has been performed manually for a very long time. Recently, some machine learning approaches have been proposed to support this task. In this paper, we investigate the use of genetic programming for automatically discovering new dispatching rules for the single objective job shop scheduling problem (JSP). Different representations of the dispatching rules in the literature are newly proposed in this paper and are compared and analysed. Experimental results show that the representation that integrates system and machine attributes can improve the quality of the evolved rules. Analysis of the evolved rules also provides useful knowledge about how these rules can effectively solve JSP.

Estimation of distribution algorithms are gaining increased research interest due to their advantage in exploiting linkage information. This paper examines the sampling techniques of a restricted Boltzmann machine-based multi-objective (MO) estimation of distribution algorithm (REDA). The behaviors of the sampling techniques in terms of energy levels are rigorously investigated, and a sampling mechanism that exploits the energy information of the solutions in a trained network is proposed to improve the search capability of the algorithm. The REDA is then hybridized, with a genetic algorithm and a local search based on an evolutionary gradient approach, to enhance the exploration and exploitation capabilities of the algorithm. Thirty-one benchmark test problems, which consist of different difficulties and characteristics, are used to examine the efficiency of the proposed algorithm. Empirical studies show that the proposed algorithm gives promising results in terms of inverted generational distance and nondominance ratio in most of the test problems.

Primates perform remarkably well in cognitive tasks such as pattern recognition. Motivated by recent findings in biological systems, a unified and consistent feedforward system network with a proper encoding scheme and supervised temporal rules is built for solving the pattern recognition task. The temporal rules used for processing precise spiking patterns have recently emerged as ways of emulating the brain's computation from its anatomy and physiology. Most of these rules could be used for recognizing different spatiotemporal patterns. However, there arises the question of whether these temporal rules could be used to recognize real-world stimuli such as images. Furthermore, how the information is represented in the brain still remains unclear. To tackle these problems, a proper encoding method and a unified computational model with consistent and efficient learning rule are proposed. Through encoding, external stimuli are converted into sparse representations, which also have properties of invariance. These temporal patterns are then learned through biologically derived algorithms in the learning layer, followed by the final decision presented through the readout layer. The performance of the model with images of digits from the MNIST database is presented. The results show that the proposed model is capable of recognizing images correctly with a performance comparable to that of current benchmark algorithms. The results also suggest a plausibility proof for a class of feedforward models of rapid and robust recognition in the brain.

A scheduling policy (SP) strongly influences the performance of a manufacturing system. However, the design of an effective SP is complicated and time-consuming due to the complexity of each scheduling decision as well as the interactions between these decisions. This paper proposes novel multi-objective genetic programming based hyper-heuristic methods for automatic design of SPs including dispatching rules (DRs) and due-date assignment rules (DDARs) in job shop environments. The experimental results show that the evolved Pareto front contains effective SPs that can dominate various SPs from combinations of existing DRs with dynamic and regression-based DDARs. The evolved SPs also show promising performance on unseen simulation scenarios with different shop settings. On the other hand, the proposed Diversified Multi-Objective Cooperative Coevolution (DMOCC) method can effectively evolve Pareto fronts of SPs compared to NSGA-II and SPEA2 while the uniformity of SPs obtained by DMOCC is better than those evolved by NSGA-II and SPEA2.

The multi-objective multiple traveling salesman problem (MmTSP) is a generalization of the classical multi-objective traveling salesman problem. In this paper, a formulation of the MmTSP, which considers the weighted sum of the total traveling costs of all salesmen and the highest traveling cost of any single salesman, is proposed. An estimation of distribution algorithm (EDA) based on restricted Boltzmann machine is used for solving the formulated problem. The EDA is developed in the decomposition framework of multi-objective optimization. Due to the limitation of EDAs in generating a wide range of solutions, the EDA is hybridized with the evolutionary gradient search. Simulation studies are carried out to examine the optimization performances of the proposed algorithm on MmTSP with different number of objective functions, salesmen and problem sizes.

Under the framework of evolutionary paradigms, many variations of evolutionary algorithms have been designed. Each of the algorithms performs well in certain cases and none of them are dominating one another. This study is based on the idea of synthesizing different evolutionary algorithms so as to complement the limitations of each algorithm. On top of this idea, this paper proposes an adaptive mechanism that synthesizes a genetic algorithm, differential evolution and estimation of distribution algorithm. The adaptive mechanism takes into account the ratio of the number of promising solutions generated from each optimizer in an early stage of evolutions so as to determine the proportion of the number of solutions to be produced by each optimizer in the next generation. Furthermore, the adaptive algorithm is also hybridized with the evolutionary gradient search to further enhance its search ability. The proposed hybrid adaptive algorithm is developed in the domination-based and decomposition-based multi-objective frameworks. An extensive experimental study is carried out to test the performances of the proposed algorithms in 38 state-of-the-art benchmark test instances.

10.1109/IJCNN.2012.6252369

Many conventional methods have been widely studied to solve the pattern recognition task, but most of them lack the biological plausibility. This paper presents a spiking neural network of integrate-and-fire neurons to perform pattern recognition. A biologically plausible supervised synaptic learning rule is used so that neurons can efficiently make a decision. The whole system contains encoding, learning and readout. It can classify complex patterns of activities stored in a vector, as well as the real-world stimuli. We test the performance of the network with digital images from the MNIST and images of alphabetic letters. It turns out to be able to classify these patterns correctly. In addition, the synaptic dynamics is shown to be compatible with many experimental observations on induction of long-term modifications, like spike-timing-dependent plasticity (STDP).

Evolutionary multiobjective optimization with decomposition, in which the algorithm is not required to differentiate between the dominated and nondominated solutions, is one of the promising approaches in dealing with multiple conflicting objectives. In this paper, the estimation of distribution algorithm (EDA) is integrated into the decomposition framework. The search behavior of the algorithm is further enhanced by hybridizing local search metaheuristic approaches with the decomposition EDA. Three local search techniques, including hill climbing, simulated annealing, and evolutionary gradient search, are considered. A novel multiobjective formulation of the multiple traveling salesman problem is proposed. The hybrid algorithms are used to solve the formulated problem with different number of objective functions, salesmen, and problem sizes. The effectiveness and efficiency of the algorithms are tested and benchmarked against several state-of-the-art multiobjective evolutionary paradigms.

Games are played by a wide variety of audiences. Different individuals will play with different gaming styles and employ different strategic approaches. This often involves interacting with nonplayer characters that are controlled by the game AI. From a developer's standpoint, it is important to design a game AI that is able to satisfy the variety of players that will interact with the game. Thus, an adaptive game AI that can scale the difficulty of the game according to the proficiency of the player has greater potential to customize a personalized and entertaining game experience compared to a static game AI. In particular, dynamic game difficulty scaling refers to the use of an adaptive game AI that performs game adaptations in real time during the game session. This paper presents two adaptive algorithms that use ideas from reinforcement learning and evolutionary computation to improve player satisfaction by scaling the difficulty of the game AI while the game is being played. The effects of varying the learning and mutation rates are examined and a general rule of thumb for the parameters is proposed. The proposed algorithms are demonstrated to be capable of matching its opponents in terms of mean scores and winning percentages. Both algorithms are able to generalize well to a variety of opponents.

Memetic computation is a paradigm that uses the notion of meme(s) as units of information encoded in computational representations for the purpose of problem-solving. It covers a plethora of potentially rich meme-inspired computing methodologies, frameworks and operational algorithms including simple hybrids, adaptive hybrids and memetic automaton. In this paper, a comprehensive multi-facet survey of recent research in memetic computation is presented.

The five papers in this special issue focus on memetic computation.

Estimation of distribution algorithms are increasingly gaining research interest due to their linkage information exploration feature. Two main mechanisms which contribute towards the success of the algorithms are probabilistic modeling and sampling method. Recent attention has been directed towards the development of probabilistic building technique. However, research on the sampling approach is less developed. Thus, this paper carries out an investigation on sampling technique for a novel multi-objective estimation of distribution algorithm - multi-objective restricted Boltzmann machine. Two variants of a new sampling technique based on energy value of the solutions in the trained network are proposed to improve the efficiency of the algorithm. Probabilistic information which is usually clamped into marginal probability distribution may hinder the algorithm in producing solutions that have high linkage dependency between variables. The proposed approach will overcome this limitation of probabilistic modeling in restricted Boltzmann machine. The empirical investigation shows that the proposed algorithm gives promising result in term of convergence and convergence rate.

Restricted Boltzmann machine is an energy-based stochastic neural network with unsupervised learning. This network consists of a layer of hidden unit and visible unit in an undirected generative network. In this paper, restricted Boltzmann machine is modeled as estimation of distribution algorithm in the context of multi-objective optimization. The probabilities of the joint configuration over the visible and hidden units in the network are trained until the distribution over the global state reach a certain degree of thermal equilibrium. Subsequently, the probabilistic model is constructed using the energy function of the network. Moreover, the proposed algorithm incorporates clustering in phenotype space and other canonical operators. The effects on the stability of the trained network and clustering in optimization are rigorously examined. Experimental investigations are conducted to analyze the performance of the algorithm in scalable problems with high numbers of objective functions and decision variables.

This paper presents an evolutionary, game theoretic approach to simulate and study the collective outcome of public goods (PG) provisioning in an agent-based model. Using asymmetric information as the basis for decision making, distinct groups are configured to interact in an iteratedNplayer PG game, where coevolutionary learning is used as the adaptation tool to the dynamic environment. Impact of information type, number of players, group size, rate of interaction, number of available choices, nature of PG provision, and selection schemes are studied under a variety of settings. Simulation results reveal interesting dynamics of strategy and usage profiles, level of derived welfare, and the evolution of cooperation. Analysis of simulated attributes offers a more holistic understanding into the nature of collective action and insights of how the effects of social dilemma can be mitigated. This might provide a good guide to achieve efficient PG provision in the practical context.

In addition to the need for satisfying several competing objectives, many real-world applications are also dynamic and require the optimization algorithm to track the changing optimum over time. This paper proposes a new coevolutionary paradigm that hybridizes competitive and cooperative mechanisms observed in nature to solve multiobjective optimization problems and to track the Pareto front in a dynamic environment. The main idea of competitive-cooperative coevolution is to allow the decomposition process of the optimization problem to adapt and emerge rather than being hand designed and fixed at the start of the evolutionary optimization process. In particular, each species subpopulation will compete to represent a particular subcomponent of the multiobjective problem, while the eventual winners will cooperate to evolve for better solutions. Through such an iterative process of competition and cooperation, the various subcomponents are optimized by different species subpopulations based on the optimization requirements of that particular time instant, enabling the coevolutionary algorithm to handle both the static and dynamic multiobjective problems. The effectiveness of the competitive-cooperation coevolutionary algorithm (COEA) in static environments is validated against various multiobjective evolutionary algorithms upon different benchmark problems characterized by various difficulties in local optimality, discontinuity, nonconvexity, and high-dimensionality. In addition, extensive studies are also conducted to examine the capability of dynamic COEA (dCOEA) in tracking the Pareto front as it changes with time in dynamic environments.

This paper focuses on the development of a spatial evolutionary multiagent social network for studying the macroscopic-behavioral dynamics of civil violence, as a result of microscopic game-theoretic interactions between goal-oriented agents. Agents are modeled from multidisciplinary perspectives and their strategies are evolved over time via collective coevolution and independent learning. Spatial and temporal simulation results reveal fascinating global emergence phenomena and interesting patterns of group movement and autonomous behavioral development. Extensions of differing complexity are also used to investigate the impact of various decision parameters on the outcome of unrest. Analysis of the results provides new insights into the intricate dynamics of civil upheavals and serves as an avenue to gain a more holistic understanding of the fundamental nature of civil violence.

This paper examines the comparative performance and adaptability of evolutionary, learning, and memetic strategies to different environment settings in the iterated prisoner's dilemma (IPD). A memetic adaptation framework is developed for IPD strategies to exploit the complementary features of evolution and learning. In the paradigm, learning serves as a form of directed search to guide evolving strategies to attain eventual convergence towards good strategy traits, while evolution helps to minimize disparity in performance among learning strategies. Furthermore, a double-loop incremental learning scheme (ILS) that incorporates a classification component, probabilistic update of strategies and a feedback learning mechanism is proposed and incorporated into the evolutionary process. A series of simulation results verify that the two techniques, when employed together, are able to complement each other's strengths and compensate for each other's weaknesses, leading to the formation of strategies that will adapt and thrive well in complex, dynamic environments.

This brief investigates continuous attractors of the well-developed model in visual cortex, i.e., the linear threshold (LT) neural networks, based on a parameterized 2-D model. On the basis of existing results on nondegenerate equilibria in mathematics, we further discuss degenerate equilibria for such networks and present properties and distributions of the equilibria, which enables us to draw the coexistence conditions of nondegenerate and degenerate equilibria (e.g., singular lines). Our theoretical results provide a useful framework for precise tuning on the network parameters, e.g., the feedbacks and visual inputs. Simulations are also presented to illustrate the theoretical findings.

Attractor dynamics is a crucial problem for attractor neural networks, as it is the underling computational mechanism for memory storage and retrieval in neural systems. This brief studies a class of attractor network consisting of linearized threshold neurons, and analyzes global attractors based on a parameterized 2-D model. On the basis of previous results on nondegenerate and degenerate equilibria in mathematics, we further elucidate all possible nontrivial global attractors. Our theoretical result provides precise descriptions on how the changes of network parameters affect the attractors' distribution and landscape, and it may give a feasible solution towards specifying attractors by specifying weights. Simulations are presented to illustrate the theoretical results.

This paper presents a novel approach of hybridizing two conventional machine learning algorithms for dimension reduction. Genetic algorithm (GA) and support vector machines (SVMs) are integrated effectively based on a wrapper approach. Specifically, the GA component searches for the best attribute set using principles of evolutionary process, after which the reduced dataset is presented to the SVMs. Simulation results show that GA-SVM hybrid is able to produce good classification accuracy and a high level of consistency. In addition, improvements are made to the hybrid by using a correlation measure between attributes as a fitness measure to replace the weaker members in the population with newly formed chromosomes. This correlation measure injects greater diversity and increases the overall fitness of the population.

Evolutionary gradient search is a hybrid algorithm that exploits the complementary features of gradient search and evolutionary algorithm to achieve a level of efficiency and robustness that cannot be attained by either techniques alone. Unlike the conventional coupling of local search operators and evolutionary algorithm, this algorithm follows a trajectory based on the gradient information that is obtain via the evolutionary process. In this paper, we consider how gradient information can be obtained and used in the context of multi-objective optimization problems. The different types of gradient information are used to guide the evolutionary gradient search to solve multi-objective problems. Experimental studies are conducted to analyze and compare the effectiveness of various implementations.

An adaptive game AI has the potential of tailoring a uniquely entertaining and meaningful game experience to a specific player. An online adaptive AI should be able to profile its opponent efficiently during the early phase of the game and adapts its own playing style to the level of the player so that the player feels entertained playing against it. This paper presents an online adaptive algorithm that uses ideas from evolutionary computation to match the skill level of the opponent during the game. The proposed algorithms demonstrated using a car racing simulator is capable of matching its opponents in terms of both mean score and winning percentages.

This paper proposes a new memetic evolutionary approach for rule extraction from datasets. The evolutionary algorithm integrated an adaptive micro-search intensity scheme inspired by artificial immune system (AIS) for local fine-tuning of the rules. In addition, the rules are encoded using variable length representation allowing easy adaptation. Through the structural mutation and crossover operators, the appropriate number of rules is optimized. Simulation results of the proposed method on real world benchmarking datasets demonstrated the effectiveness of the algorithm.

Evolutionary algorithms are a class of stochastic search methods that attempts to emulate the biological process of evolution, incorporating concepts of selection, reproduction, and mutation. In recent years, there has been an increase in the use of evolutionary approaches in the training of artificial neural networks (ANNs). While evolutionary techniques for neural networks have shown to provide superior performance over conventional training approaches, the simultaneous optimization of network performance and architecture will almost always result in a slow training process due to the added algorithmic complexity. In this paper, we present a geometrical measure based on the singular value decomposition (SVD) to estimate the necessary number of neurons to be used in training a single-hidden-layer feedforward neural network (SLFN). In addition, we develop a new hybrid multiobjective evolutionary approach that includes the features of a variable length representation that allow for easy adaptation of neural networks structures, an architectural recombination procedure based on the geometrical measure that adapts the number of necessary hidden neurons and facilitates the exchange of neuronal information between candidate designs, and a microhybrid genetic algorithm ( microHGA) with an adaptive local search intensity scheme for local fine-tuning. In addition, the performances of well-known algorithms as well as the effectiveness and contributions of the proposed approach are analyzed and validated through a variety of data set types.

Binary representation suffers from the problem of positional dependence, where the amplitude of phenotype variation is dependent on the position of the altered genotype bits. However, this is contrary to conventional variation operations that treat each genotype bit equally. Positional dependence can be attributed to the poor locality, which results in neighboring genotypes having low correlation in the phenotype space, reducing the effectiveness of systematic local search and evolutionary search based on small mutation steps. For this purpose, this paper will propose an alternative genotype-phenotype mapping for binary representation that introduces redundancy into the mapping and removes the exponential orderings between the alleles, hence improving the locality between the genotype and phenotype search space. Empirical study conducted based on distribution, locality, and mutation innovation revealed key algorithmic characteristics of the proposed code, and its practicality is validated by comparative studies based on different benchmark optimization problems. Possible approaches to resolve the overrepresentation problem due to redundancy will be suggested, exhibiting its flexibility and variability in implementation.

This paper considers a berth allocation problem (BAP) which requires the detemination of exact berthing times and positions of incoming ships in a container port. The problem is solved by optimizing the berth schedule so as to minimize concurrently the three objectives of mak span, number of crossings, and waitimg time. These objectives represent the interests of both port and ship operators. A multi-objective evolutionary algorithm (MOEA) that incorporates the concept of Pareto optimality is proposed for solving the multi-objective BAP. The MOEA is equipped with a novel solution decoding scheme which is specifically designed to optimize the use of berth space. The MOEA is also able to function in a dynamic context which is of more relevance to a real-world situation.

Apart from the need to satisfy several competing objectives, many real-world applications are also sensitive to decision or environmental parameter variation which results in large or unacceptable performance variation. While evolutionary optimization techniques have several advantages over operational research methods for robust optimization, it is rarely studied by the evolutionary multi-objective (MO) optimization community. This paper addresses the issue of robust MO optimization by presenting a robust continuous MO test suite with features of noise-induced solution space, fitness landscape and decision space variation. The work presented in this paper should encourage further studies and the development of more effective algorithms for robust MO optimization.

Evolutionary computation algorithms, such as the particle swarm optimization (PSO), have been widely applied in numerical optimizations and real-world product design, not only for their satisfactory performances but also in their relaxing the need for detailed mathematical modelling of complex systems. However, as iterative heuristic searching methods, they often suffer from difficulties in obtaining high quality solutions in an efficient manner. Since unnecessary resources used in computation iterations should be avoided, the determination of a proper termination condition for the algorithms is desirable. In this work, termination is cast as a decision-making process to end the algorithm. Specifically, the non-parametric sign- test is incorporated as a hypothetical test method such that a quantifiable termination in regard to specifiable decision-errors can be assured. Benchmark optimization problems are tackled using the PSO as an illustrative optimizer to demonstrate the effectiveness of the proposed termination condition.

This paper introduces a distributed co- evolutionary particle swarm optimization algorithm (DCPSO). In DCPSO, the population is decomposed into the subpopulations that are each responsible for optimizing one parameter, and co-evolve in a competitive manner. Such co-evolution mechanism with both cooperation and competition are designed to be effective and efficient in solving multi-objective (MO) problems under distributed computation. The competition mechanism also indirectly helps DCPSO to overcome the fault-tolerance constraint in distributed computation. DCPSO shows substantial speedup from non-distributed version by sharing workload among computational nodes. In addition, a dynamic load balancing mechanism is used to further speed up the total runtime by minimizing the amount of idle time in each node.

Coevolutionary architectures have been shown to be effective ways to improve the performance of multiobjective (MO) optimization problems. This paper presents a cooperative coevolutionary algorithm for multiobjective particle swarm optimization (COMOPSO), which applies the divide-and-conquer approach to decompose decision vectors into smaller components and evolves multiple solutions in the form of cooperative subswarms. Representatives from each evolving subswarm are combined to form the solution to the whole system. The fitness of each individual is related to its ability to collaborate with individuals from other species, thereby encouraging the development of cooperative strategies. An adaptive niche sharing algorithm is introduced to handle the selection of the niche radius in a dynamic manner. Coupled with the adaptive niche sharing algorithm COMOPSO demonstrates its effectiveness and efficiency in evolving highly competitive solution sets against various MO algorithms on benchmark problems characterized by different difficulties with consistent results.

Reliability evaluation of power generation systems using probabilistic methods has drawn much attention due to their capacity to account for system uncertainties. However, because of the large number of possible failure states involved in the power system, it is normally not viable to exhaustively enumerate and evaluate all the states which may contribute to system failure. Meanwhile, time-dependent sources such as wind turbine generators are being more significantly integrated into the traditional power grid for cleaner power generation. The intermittency of wind power sources further complicates the reliability evaluation process. In this paper, a binary particle swarm optimization (BPSO) is adopted to derive a set of meaningful system states, which significantly affects the adequacy indices of generation system including loss of load expectation (LOLE), loss of load frequency (LOLF), and expected energy not supplied (EENS). A numerical example is used to verify the applicability and validity of the proposed population-based intelligent search (PIS) based evaluation procedure. Especially, a comparative study in relation to the exact method and Monte Carlo simulation (MCS) is carried out.

In addition to satisfying several competing objectives, many real-world applications are also characterized by a certain degree of noise, manifesting itself in the form of signal distortion or uncertain information. In this paper, extensive studies are carried out to examine the impact of noisy environments in evolutionary multiobjective optimization. Three noise-handling features are then proposed based upon the analysis of empirical results, including an experiential learning directed perturbation operator that adapts the magnitude and direction of variation according to past experiences for fast convergence, a gene adaptation selection strategy that helps the evolutionary search in escaping from local optima or premature convergence, and a possibilistic archiving model based on the concept of possibility and necessity measures to deal with problem of uncertainties. In addition, the performances of various multiobjective evolutionary algorithms in noisy environments, as well as the robustness and effectiveness of the proposed features are examined based upon five benchmark problems characterized by different difficulties in local optimality, nonuniformity, discontinuity, and nonconvexity

In this paper, a new memetic algorithm (MA) for multiobjective (MO) optimization is proposed, which combines the global search ability of particle swarm optimization with a synchronous local search heuristic for directed local fine-tuning. A new particle updating strategy is proposed based upon the concept of fuzzy global-best to deal with the problem of premature convergence and diversity maintenance within the swarm. The proposed features are examined to show their individual and combined effects in MO optimization. The comparative study shows the effectiveness of the proposed MA, which produces solution sets that are highly competitive in terms of convergence, diversity, and distribution.

This paper considers the routing of vehicles with limited capacity from a central depot to a set of geographically dispersed customers where actual demand is revealed only when the vehicle arrives at the customer. The solution to this vehicle routing problem with stochastic demand (VRPSD) involves the optimization of complete routing schedules with minimum travel distance, driver remuneration, and number of vehicles, subject to a number of constraints such as vehicle time window and capacity. To solve such a multiobjective combinatorial optimization problem, this paper presents a multiobjective evolutionary algorithm that incorporates two VRPSD-specific heuristics for local exploitation and a route simulation method to evaluate the fitness of solutions. A novel way of assessing the quality of solutions to the VRPSD on top of comparing their expected costs is also proposed. It is shown that the algorithm is capable of finding useful tradeoff solutions which are robust to the stochastic nature of the problem.

This paper focuses on the design and development of a spatial evolutionary multi-agent social network (EMAS) to investigate the underlying emergent macroscopic behavioral dynamics of civil violence, as a result of the microscopic local movement and game-theoretic interactions between multiple goal-oriented agents. Agents are modeled from multi-disciplinary perspectives and their behavioral strategies are evolved over time via collective co-evolution and independent learning. Experimental results reveal the onset of fascinating global emergent phenomenon as well as interesting patterns of group movement and behavioral development. Analysis of the results provides new insights into the intricate behavioral dynamics that arises in civil upheavals. Collectively, EMAS serves as a vehicle to facilitate the behavioral development of autonomous agents as well as a platform to verify the effectiveness of various violence management policies which is paramount to the mitigation of casualties.

In addition to the need to satisfy several competing objectives, many real-world applications are also characterized by noise. In this paper, three noise-handling features, an experiential learning directed perturbation (ELDP) operator, a gene adaptation selection strategy (GASS) and a possibilistic archiving model are proposed. The ELDP adapts the magnitude and direction of variation according to past experiences for fast convergence while the GASS improves the evolutionary search in escaping from premature convergence in both noiseless and noisy environments. The possibilistic archiving model is based on the concept of possibility and necessity measures to deal with problem of uncertainties. In addition, the performances of various multi-objective evolutionary algorithms in noisy environments as well as the robustness and effectiveness of the proposed features are examined based upon three benchmark problems characterized by different difficulties.

The effects of randomness of control coefficients in particle swarm optimization (PSO) are investigated through empirical studies. The PSO is viewed as a method to solve a coverage problem in the solution space when the global-best particle is reported as the solution. Randomness of the control coefficients, therefore, plays a crucial role in providing an efficient and effective algorithm. Comparisons of performances are made between the uniform and Gaussian distributed random coefficients in adjusting particle velocities. Alternative strategies are also tested, they include: i) pre-assigned randomness through the iterations, ii) selective hybrid random adjustment based on the fitness of the particles. Furthermore, the effect of velocity momentum factor is compared between a constant and random momentum. Numerical results show that performances of the proposed variations are comparable to the conventional implementation for simple test functions. However, enhanced performances using the selective and hybrid strategy are observed for complicate functions.

The bin packing problem is widely found in applications such as loading of tractor trailer trucks, cargo airplanes and ships, where a balanced load provides better fuel efficiency and safer ride. In these applications, there are often conflicting criteria to be satisfied, i.e., to minimize the bins used and to balance the load of each bin, subject to a number of practical constraints. Unlike existing studies that consider only the minimization of bins, a two-objective mathematical model for the bin packing problem with multiple constraints is formulated in this paper. Without the need of combining both objectives into a composite scalar, a hybrid multiobjective particle swarm optimization algorithm (HMOPSO) incorporating the concept of Pareto's optimality to evolve a family of solutions along the trade-off is proposed. The algorithm is also featured with bin packing heuristic, variable length representation, and specialized mutation operator to solve the multiobjective and multi-model combinatorial bin packing problem. Extensive simulations are performed on various test instances, and their performances are compared both quantitatively and statistically with other optimization methods. Each of the proposed features is also explicitly examined to illustrate their usefulness in solving the multiobjective bin packing problem.

One of the major drawbacks of the Hopfield network is that when it is applied to certain polytopes of combinatorial problems, such as the traveling salesman problem (TSP), the obtained solutions are often invalid, requiring numerous trial-and-error setting of the network parameters thus resulting in low-computation efficiency. With this in mind, this article presents a columnar competitive model (CCM) which incorporates a winner-takes-all (WTA) learning rule for solving the TSP. Theoretical analysis for the convergence of the CCM shows that the competitive computational neural network guarantees the convergence of the network to valid states and avoids the tedious procedure of determining the penalty parameters. In addition, its intrinsic competitive learning mechanism enables a fast and effective evolving of the network. Simulation results illustrate that the competitive model offers more and better valid solutions as compared to the original Hopfield network.

Recent advances in evolutionary algorithms show that coevolutionary architectures are effective ways to broaden the use of traditional evolutionary algorithms. This paper presents a cooperative coevolutionary algorithm (CCEA) for multiobjective optimization, which applies the divide-and-conquer approach to decompose decision vectors into smaller components and evolves multiple solutions in the form of cooperative subpopulations. Incorporated with various features like archiving, dynamic sharing, and extending operator, the CCEA is capable of maintaining archive diversity in the evolution and distributing the solutions uniformly along the Pareto front. Exploiting the inherent parallelism of cooperative coevolution, the CCEA can be formulated into a distributed cooperative coevolutionary algorithm (DCCEA) suitable for concurrent processing that allows inter-communication of subpopulations residing in networked computers, and hence expedites the computational speed by sharing the workload among multiple computers. Simulation results show that the CCEA is competitive in finding the tradeoff solutions, and the DCCEA can effectively reduce the simulation runtime without sacrificing the performance of CCEA as the number of peers is increased

The additive recurrent network structure of linear threshold neurons represents a class of biologically-motivated models, where nonsaturating transfer functions are necessary for representing neuronal activities, such as that of cortical neurons. This paper extends the existing results of dynamics analysis of such linear threshold networks by establishing new and milder conditions for boundedness and asymptotical stability, while allowing for multistability. As a condition for asymptotical stability, it is found that boundedness does not require a deterministic matrix to be symmetric or possess positive off-diagonal entries. The conditions put forward an explicit way to design and analyze such networks. Based on the established theory, an alternate approach to study such networks is through permitted and forbidden sets. An application of the linear threshold (LT) network is analog associative memory, for which a simple design method describing the associative memory is suggested in this paper. The proposed design method is similar to a generalized Hebbian approach, but with distinctions of additional network parameters for normalization, excitation and inhibition, both on a global and local scale. The computational abilities of the network are dependent on its nonlinear dynamics, which in turn is reliant upon the sparsity of the memory vectors.

In this letter, we attempt to quantify the significance of increasing the number of neurons in the hidden layer of a feedforward neural network architecture using the singular value decomposition (SVD). Through this, we extend some well-known properties of the SVD in evaluating the generalizability of single hidden layer feedforward networks (SLFNs) with respect to the number of hidden layer neurons. The generalization capability of the SLFN is measured by the degree of linear independency of the patterns in hidden layer space, which can be indirectly quantified from the singular values obtained from the SVD, in a postlearning step. A pruning/growing technique based on these singular values is then used to estimate the necessary number of neurons in the hidden layer. More importantly, we describe in detail properties of the SVD in determining the structure of a neural network particularly with respect to the robustness of the selected model.

This paper investigates the use of evolution and incremental learning to find an optimal strategy in the iterative prisoner's dilemma (IPD) problem, given an environment with a collection of unknown strategies. The Meta-Lamarckian Memetic learning (MLML) scheme is conceptualized based on the biological evolution of man and his abilities to accumulate knowledge and learn from past experiences. Learning was found to be the dominant force for improvement in the short run while improvement in the long run is sustained by the process of evolution. Learning is also much more effective when carried out on an incremental basis as the games progress. A series of simulation results obtained verified that the best performance is attained when a hybrid combination of learning and evolution is carried out on an incremental basis, not just evolution or learning alone.

Many real-world applications involve complex optimization problem with various competing specifications and constraints that are often difficult, if not impossible, to be solved without the aid of powerful and efficient optimization algorithms. Although evolutionary algorithms have proven to be successful with respect to the optimization goals of proximity and diversity, their capability is bottlenecked by the evolutionary operators' abilities to deal with the complicated search spaces. Furthermore, it is well known that the algorithm's performances in different problems are sensitive to the parameter setting of the operators. In an effort to adapt the evolutionary search ability along the different regions of the search space, this paper proposes a dynamic variation operator whose parameter value is deterministically adapted during the algorithm run so as to maintain a balance between the extensive exploration in the early phase and local fine-tuning in the end phase. Comparative studies with some representative variation operators are performed on different benchmark problems to illustrate the effectiveness and efficiency of the proposed operator.

The network of neurons with linear threshold (LT) transfer functions is a prominent model to emulate the behavior of cortical neurons. The analysis of dynamic properties for LT networks has attracted growing interest, such as multistability and boundedness. However, not much is known about how the connection strength and external inputs are related to oscillatory behaviors. Periodic oscillation is an important characteristic that relates to nondivergence, which shows that the network is still bounded although unstable modes exist. By concentrating on a general parameterized two-cell network, theoretical results for geometrical properties and existence of periodic orbits are presented. Although it is restricted to two-dimensional systems, the analysis can provide a useful contribution to analyze cyclic dynamics of some specific LT networks of high dimension. As an application, it is extended to an important class of biologically motivated networks of large scale: the winner-take-all model using local excitation and global inhibition.

The widespread applications of rotating machines, such as turbine machinery, in both industry and commercial life requires advanced technologies to efficiently and effectively test their operational status before they begin their practical productions in the plant. This paper discusses the development of a general flexible automatic test system (ATS) for turbine machinery. In order to meet the demanding test requirements for a large and diverse community of turbine machinery, the proposed automatic test system has a contemporary Windows interface, graphical interaction, and can be easily configured to include functions required by current and emerging test demands. The design and implementation of such a test system is approached from an object-oriented (OO) software engineering point of view for ease of operation, expansion, and maintenance. Practical implementation upon a real industrial plant shows the validity and effectiveness of the implemented ATS for improving the performance and quality of turbine machinery. The obtained test system delivers the performance to meet all rigorous test throughput requirements. Software design in the industrial automation arena becomes more challenging nowadays than ever, due to the increasingly complicated industrial processes and more demanding measurement tasks. This paper presents a flexible automatic test system (ATS) for rotating-turbine machinery based on the systematic object-oriented (OO) software engineering. In this OO method, the process of software development is divided into five major phases: requirement capture, analysis, design, programming, and testing. Requirement capture collects both functional and nonfunctional user requirements for developing the intended system. In the analysis phase, the objects in the problem domain are modeled, and the desired system operations are studied. In the design phase, the results obtained from the analysis phase are converted into a form that can be implemented using programming languages. In the design phase, the issues on how the structures are formed and how they collaborate with one another via interfaces are figured out. In the programming phase, the code for realizing the target system is developed. Finally, in the test phase, the system is tested against the specified requirements to ensure its correctness in both functionality and performance aspects. By adopting the OO software-development method, the flexible ATS for turbine machinery software is developed in an efficient manner. Meanwhile, other novel technologies such as configuration, database management, graphical user interface, Internet, multithreaded programming, and ActiveX Automation are all incorporated into the system development. The method discussed in the paper can be easily extended to the development of other software-intensive industrial automation systems.

This paper presents a distributed coevolutionary classifier (DCC) for extracting comprehensible rules in data mining. It allows different species to be evolved cooperatively and simultaneously, while the computational workload is shared among multiple computers over the Internet. Through the intercommunications among different species of rules and rule sets in a distributed manner, the concurrent processing and computational speed of the coevolutionary classifiers are enhanced. The advantage and performance of the proposed DCC are validated upon various datasets obtained from the UCI machine learning repository. It is shown that the predicting accuracy of DCC is robust and the computation time is reduced as the number of remote engines increases. Comparison results illustrate that the DCC produces good classification rules for the datasets, which are competitive as compared to existing classifiers in literature.

This work presents a new dynamical optimal learning (DOL) algorithm for three-layer linear neural networks and investigates its generalization ability. The optimal learning rates can be fully determined during the training process. The mean squared error is guaranteed to be stably decreased and the learning is less sensitive to initial parameter settings. The simulation results illustrate that the proposed DOL algorithm gives better generalization performance and faster convergence as compared to standard error back propagation algorithm.

This letter presents a new dynamical optimal learning (DOL) algorithm for three-layer linear neural networks and investigates its generalization ability. The optimal learning rates can be fully determined during the training process. The mean squared error (mse) is guaranteed to be stably decreased and the learning is less sensitive to initial parameter settings. The simulation results illustrate that the proposed DOL algorithm gives better generalization performance and faster convergence as compared to standard error back propagation algorithm.

The major drawbacks of the Hopfield network when it is applied to some combinatorial problems, e.g., the traveling salesman problem (TSP), are invalidity of the obtained solutions, trial-and-error setting value process of the network parameters and low-computation efficiency. This letter presents a columnar competitive model (CCM) which incorporates winner-takes-all (WTA) learning rule for solving the TSP. Theoretical analysis for the convergence of the CCM shows that the competitive computational neural network guarantees the convergence to valid states and avoids the onerous procedures of determining the penalty parameters. In addition, its intrinsic competitive learning mechanism enables a fast and effective evolving of the network. The simulation results illustrate that the competitive model offers more and better valid solutions as compared to the original Hopfield network.

This paper considers a transportation problem for moving empty or laden containers for a logistic company. A model for this truck and trailer vehicle routing problem (TTVRP) is first constructed in the paper. The solution to the TTVRP consists of finding a complete routing schedule for serving the jobs with minimum routing distance and number of trucks, subject to a number of constraints such as time windows and availability and multimodal combinatorial optimization problem, a hybrid multiobjective evolutionary algorithm (HMOEA) is applied to find the Pareto optimal routing solutions for the TTVRP. Detailed analysis is performed to extract useful decision-making information from the multiobjective optimization results. The computational results have shown that the HMOEA is effective for solving multiobjective combinatorial problems, such as finding useful trade-off solutions for the TTVRP.

Although evolutionary algorithm is a powerful optimization tool, its computation cost involved in terms of time and hardware increases as the size and complexity of the problem increases. In this paper, a Java-based distributed evolutionary computing package (Paladin-DEC) is presented by exploiting the inherent parallel nature of evolutionary algorithms. The package enhances the concurrent processing and performance of evolutionary algorithms by allowing inter-communications of subpopulations among various computers over the Internet. The Paladin-DEC is incorporated with the features of security, scalability and fault tolerance, and is capable of keeping data integrity throughout the computation. The effectiveness and advantages of the Paladin-DEC are illustrated through a case study of drug scheduling in cancer chemotherapy.

The main objectives of multiobjective evolutionary algorithms are to minimize the distance between the solution set and true Pareto front, to distribute the solutions evenly and to maximize the spread of solution set. This paper addresses these issues by presenting two features that enhance the ability of multiobjective evolutionary algorithms. The first feature is a variant of the mutation operator that adapts the mutation rate along the evolution process to maintain a balance between the introduction of diversity and local fine-tuning. In addition, this adaptive mutation operator adopts a new approach to strike a compromise between the preservation and disruption of genetic information. The second feature is a novel enhanced exploration strategy that encourages the exploration towards less populated areas and hence achieves better discovery of gaps in the generated front. This strategy also preserves nondominated solutions in the evolving population and hence gives good convergence. Comparative studies show that the proposed features are effective.

Evolutionary techniques have become one of the most powerful tools for solving multiobjective optimization (MOO) problems. However the computational cost involved in terms of time and hardware often become surprisingly burdensome as the size and complexity of the problem increases. We propose a distributed cooperative coevolutionary algorithm (DCCEA), which evolves multiple solutions in the form of cooperative subpopulations and exploits the inherent parallelism by sharing the computational workload among computers over the network. Through its multiple features such as archiving, dynamic sharing and extending operator, solutions of DCCEA are not only pushed to the true Pareto front but also well distributed. Simulation results show that DCCEA has a very competitive performance and reduces the runtime effectively.

This paper presents a kind of cooperative co-evolutionary algorithm (CCEA) for multi-objective optimization (MOO). In this algorithm, solutions evolve in the form of cooperative subpopulations. An archive stores non-dominated solutions and helps to evaluate individuals in the subpopulations. The mechanism of niching is applied to maintain the diversity of solutions in the archive. Meanwhile, an extending operator is designed to mine information on solution distribution from the archive and guide the search to regions that are not explored enough. Extensive simulations are performed on different benchmark problems for various multi-objective evolutionary algorithms (MOEAs) and indicate that CCEA is strongly competitive with five recent well-known MOEAs in finding a good non-dominated solution set.

Vehicle routing problem with time windows (VRPTW) involves the routing of a set of vehicles with limited capacity from a central depot to a set of geographically dispersed customers with known demands and predefined time windows. This paper proposes a hybrid multiobjective evolutionary algorithm (HMOEA) that incorporates various heuristics for local exploitation in the evolutionary search and the concept of Pareto's optimality for solving multiobjective optimization in VRPTW problems. The proposed HMOEA optimizes all routing constraints and objectives simultaneously, which improves the routing solutions in many aspects, such as lower routing cost, wider scattering area and better convergence trace.

This paper presents an evolutionary algorithm with a new goal-sequence domination scheme for better decision support in multi-objective optimization. The approach allows the inclusion of advanced hard/soft priority and constraint information on each objective component, and is capable of incorporating multiple specifications with overlapping or non-overlapping objective functions via logical 'OR' and 'AND' connectives to drive the search towards multiple regions of trade-off. In addition, we propose a dynamic sharing scheme that is simple and adaptively estimated according to the on-line population distribution without needing any a priori parameter setting. Each feature in the proposed algorithm is examined to show its respective contribution, and the performance of the algorithm is compared with other evolutionary optimization methods. It is shown that the proposed algorithm has performed well in the diversity of evolutionary search and uniform distribution of non-dominated individuals along the final trade-offs, without significant computational effort. The algorithm is also applied to the design optimization of a practical servo control system for hard disk drives with a single voice-coil-motor actuator. Results of the evolutionary designed servo control system show a superior closed-loop performance compared to classical PID or RPT approaches.

In this paper, we consider a local logistic company that provides transportation service for moving empty and laden containers within Singapore. Due to the limited capacity of its own fleet of vehicles, the company cannot handle all the job orders and have to outsource some orders to other smaller local transportation companies. The current operation of assigning jobs for outsourcing goes through two steps. In the first step, a certain percentage of jobs will be preselected for outsourcing according to some simple rules. Then at the second step, the rest of the jobs will be put into an in-house computer system which assigns jobs to its internal fleet of vehicles according to some greedy rules and the remaining jobs that cannot be served by the internal fleet of vehicles will be outsourced. This paper presents a vehicle capacity planning system (VCPS), which models the problem as a vehicle routing problem with time window constraints (VRPTW) and tabu search (TS) is applied to find a solution for the problem. From the simulation results, some new rules on how to assign jobs for outsourcing are derived, which are shown to be about 8% better than existing rules currently adopted by the company.

Although evolutionary algorithm is a powerful optimization tool, its computation cost involved in terms of time and hardware resources increases as the size or complexity of the problem increases. One promising approach to overcome this limitation is to exploit the inherent parallelism of evolutionary algorithms by creating an infrastructure necessary to support distributed evolutionary computing using existing Internet and hardware resources. This paper presents a Java-based distributed evolutionary computing software (Paladin-DEC), which enhances the concurrent processing and performance of evolutionary algorithms by allowing inter-communications of subpopulations among various computers over the Internet. Such a distributed system enables individuals to migrate among multiple subpopulations according to some patterns to induce diversity of elite individuals periodically, in a way that simulates the species evolve in natural environment. The Paladin-DEC software is capable of keeping data integrity throughout the computation, and is incorporated with the features of robustness, security, fault tolerance, and work balancing. The effectiveness and advantages of the Paladin-DEC are illustrated upon two case studies of drug scheduling in cancer chemotherapy and searching probe sets of yeast genome.

This paper presents the design and implementation of an evolvable hardware based autonomous robot navigation system using intrinsic evolution. Distinguished from the traditional evolutionary approaches based on software simulation, an evolvable robot controller at the hardware gate-level that is capable of adapting dynamic changes in the environments is implemented. In our approach, the concept of Boolean function is used to construct the evolvable controller implemented on an FPGA-based robot turret, and evolutionary computing is applied as a learning tool to guide the artificial evolution at the hardware level. The effectiveness of the proposed evolvable autonomous robotic system is confirmed with the physical real-time implementation of robot navigation behaviors on light source following and obstacle avoidance using a robot with traction fault.

This paper presents the optimal control of drug scheduling in cancer chemotherapy using a distributed evolutionary computing software. Unlike conventional methods that often require gradient information or hybridization of different approaches in drug scheduling, the proposed evolutionary optimization methodology is simple and capable of automatically finding the near-optimal solutions for complex cancer chemotherapy problems. It is shown that different number of variable pairs in evolutionary representation for drug scheduling can be easily implemented via the software, since the computational workload is shared and distributed among multiple computers over the Internet. Simulation results show that the proposed evolutionary approach produces excellent control of drug scheduling in cancer chemotherapy, which are competitive or equivalent to the best solutions published in literature.

In this paper, we present the registration of disparate spatial data. To be specific, we consider the registration of digital terrain elevation data (DTED) to National High Altitude Photography (NHAP). Initially, the DTED is shaded to form a synthetic image, and our registration process maps point in the shaded image to points in the NHAP. For the purpose of comparison, we propose two distinct techniques for matching. The first method is a semi-autonomous. It requires two pairs of user defined matched points to estimate an initial transform as starting point in the search for the best fitting transform using Nelder-Mead Simplex Method. The second method, being more novel in nature, attempts to eliminate the need for any user intervention and registers the two data autonomously by employing the Multi Objective Evolutionary Algorithm (MOEA) toolbox. Both methods worked well in estimating the best fitting affine transform to register the image and elevation data, and the MOEA based autonomous technique outperforms the much simpler single objective based semi autonomous technique.

Genetic programming (GP) has emerged as a promising approach to deal with the classification task in data mining. This paper extends the tree representation of GP to evolve multiple comprehensible IF-THEN classification rules. We introduce a concept mapping technique for the fitness evaluation of individuals. A covering algorithm that employs an artificial immune system-like memory vector is utilized to produce multiple rules as well as to remove redundant rules. The proposed GP classifier is validated on nine benchmark data sets, and the simulation results confirm the viability and effectiveness of the GP approach for solving data mining problems in a wide spectrum of application domains.

Existing multi-objective (MO) evolutionary algorithms apply a fixed search space in the parameter domain. This approach needs a good guess or a-prior knowledge of a promising search area since a wrongly specified range of search space often leads to poor solutions. To address the issue, this paper proposes a novel approach of adaptive search space for MO optimization. Through the method of shrinking and expanding, the technique is capable of directing the evolution to reach more promising search regions even if it is not covered in the initial search space. The role of the inductive learning process is also introduced, which is performed by an exploratory multi-objective evolutionary algorithm to enhance the search from being trapped in local optima as well as to promote the population diversity along the discovered Pareto-optimal front. Features of the proposed approach are experimented and investigated upon benchmark MO optimization problems.

The paper proposes a performance-prioritized computer aided control system design (CACSD) methodology using a high-performance multi-objective evolutionary algorithm toolbox. Unlike conventional mutually independent control schemes, the evolutionary CACSD approach unifies different control laws in both the time and frequency domains based upon performance satisfaction, without the need of aggregating different design criteria into a compromise function or formulating the problem in a specific domain for linear parameterization and deterministic convex optimization. It is shown that control engineers' expertise as well as settings on goal and priority for different preference on each performance requirement can be easily included and modified on-line according to the evolving trade-offs, which makes the controller design interactive, transparent and simple for real-time implementation. Advantages of the proposed evolutionary CACSD methodology are illustrated upon a practical ill-conditioned distillation system, which offers a set of low-order Pareto optimal controllers that satisfy all the required performance specifications in the face of system constraints.

The rapid advances of evolutionary methods for multi-objective (MO) optimization poses the difficulty of keeping track of the developments in this field as well as selecting an appropriate evolutionary approach that best suits the problem in-hand. This paper aims to analyze the strength and weakness of different evolutionary methods proposed in the literature. For this purpose, ten existing well-known evolutionary MO approaches have been experimented and compared extensively on two benchmark problems with different MO optimization difficulties and characteristics. Besides considering the usual two important aspects of MO performance, i.e., the spread across the Pareto-optimal front as well as the ability to attain the global optimum or final trade-offs, this paper also proposes a few useful performance measures for better and comprehensive examination of each approach both quantitatively and qualitatively. Simulation results for the comparisons are commented and summarized.

Many evolutionary algorithm based methods have been proposed for handling constraints in numerical optimization problems. These techniques, however, are often based upon the approach of formulating constraints in the objective domain or repairing/rejecting infeasible solutions through specialized genetic operators. The drawback of these approaches is that the potential for both feasible and infeasible solutions coexist, which often leads to a large search space with complex or discontinuous fitness landscape. These infeasible chromosomes must be evaluated or detected with extra computational effort before they are penalized or eliminated from the population. Moreover, these methods need to ensure the domination of feasible candidate solutions during genetic reproductions in order to eliminate the infeasible ones, which can easily misdirect the evolution towards the local optima whenever a feasible solution is reproduced in problems that contain difficult-to-find feasible regions. This paper describes a constraint handling methodology that formulates the optimization constraints directly into the gene domains in evolutionary algorithms. It allows the constraints to be encoded into the chromosomes and as such, trimming away sections of infeasible regions in constraint optimization problems. This results in a smaller search space and reduces the efforts of evolution in finding the global optimum solution.

In vehicle routing problems with time window constraints (VRPTW), a set of vehicles with limited capacity, are to be routed from a central depot to a set of geographically dispersed customers with known demands and predefined time windows. To solve the problem, the optimized assignment of vehicles to each customer is needed as to achieve the minimal total cost without violating the capacity and time window constraints. Combinatorial optimization problems of this kind are NP-hard and are best solved to the near optimum by heuristics. The authors describe their research on a rare class of genetic algorithms, known as the messy genetic algorithms (mGA) in solving the VRPTW problem. The mGA has the merit of directly realizing the relational search needed in VRPTW representation, which cannot be easily realized using simple heuristic methods. The mGA was applied to solve the benchmark Solomon's 56 VRPTW 100-customer instances, and yielded 23 solutions better than or equivalent to the best solutions ever published in literature.

Evolutionary algorithms have been recognized to be well suited for multiobjective optimization. These methods, however, need to "guess" for an optimal constant population size in order to discover the usually sophisticated tradeoff surface. This paper addresses the issue by presenting a novel incrementing multiobjective evolutionary algorithm (IMOEA) with dynamic population size that is computed adaptively according to the online discovered tradeoff surface and its desired population distribution density. It incorporates the method of fuzzy boundary local perturbation with interactive local fine tuning for broader neighborhood exploration. This achieves better convergence as well as discovering any gaps or missing tradeoff regions at each generation. Other advanced features include a proposed preserved strategy to ensure better stability and diversity of the Pareto front and a convergence representation based on the concept of online population domination to provide useful information. Extensive simulations are performed on two benchmark and one practical engineering design problems.

This paper presents an interactive graphical user interface (GUI) based multiobjective evolutionary algorithm (MOEA) toolbox for effective computer-aided multiobjective (MO) optimization. Without the need of aggregating multiple criteria into a compromise function, it incorporates the concept of Pareto's optimality to evolve a family of nondominated solutions distributing along the tradeoffs uniformly. The toolbox is also designed with many useful features such as the goal and priority settings to provide better support for decision-making in MO optimization, dynamic population size that is computed adaptively according to the online discovered Pareto-front, soft/hard goal settings for constraint handlings, multiple goals specification for logical "AND"/"OR" operation, adaptive niching scheme for uniform population distribution, and a useful convergence representation for MO optimization. The MOEA toolbox is freely available for download at http://vlab.ee.nus.edu.sg/-kctan/moea.htm which is ready for immediate use with minimal knowledge needed in evolutionary computing. To use the toolbox, the user merely needs to provide a simple "model" file that specifies the objective function corresponding to his/her particular optimization problem. Other aspects like decision variable settings, optimization process monitoring and graphical results analysis can be performed easily through the embedded GUIs in the toolbox. The effectiveness and applications of the toolbox are illustrated via the design optimization problem of a practical ill-conditioned distillation system. Performance of the algorithm in MOEA toolbox is also compared with other well-known evolutionary MO optimization methods upon a benchmark problem.

This paper presents a comprehensive Graphical User Interface (GUI) based MOEA Toolbox that implements Multi-Objective Evolutionary Algorithm (MOEA). The toolbox incorporates Pareto cost assignment scheme and other complementary features of hard constraint specification for constraint handling, dynamic population size, fuzzy boundary local perturbation with interactive local fine-tuning, a novel switching preserved strategy and convergence representation for multi-objective optimization. The user only needs a little programming knowledge to write the model file. Other aspects of the simulation like the settings, process monitoring and results analysis are performed on user-friendly and user-interactive GUI windows with easy-to-understand on-line help files. The MOEA Toolbox's performance in a benchmark problem and an actual application has been presented as a demonstration of the toolbox's capabilities.

A new methodology named Evolutionary Artificial Potential Field (EAPF) is proposed for real-time robot path planning. The artificial potential field method is combined with genetic algorithms, to derive optimal potential field functions. The proposed EAPF approach is capable of navigating robot(s) situated among moving obstacles. Potential field functions for obstacles and goal points are also defined. The potential field functions for obstacles contain tunable parameters. The multi-objective evolutionary algorithm (MOEA) is utilized to identify the optimal potential field functions. Fitness functions such as goal-factor, obstacle-factor, smoothness-factor and minimum-pathlength-factor are developed for the MOEA selection criteria. An algorithm named escape-force is introduced to avoid the local minima associated with EAPF. Moving obstacles and moving goal positions were considered to test the robust performance of the proposed methodology. Simulation results show that the proposed methodology is efficient and robust for robot path planning with non-stationary goals and obstacles.

This paper develops a novel genetic algorithm (GA) based methodology for optimal tuning of a reported fuzzy dispatching system for a fleet of automated guided vehicles in a flexible manufacturing environment. The reported dispatching rules are transformed into a continuously adaptive procedure to capitalize the on-line information available from a shop floor at all times. Simulation results obtained show that the GA is very powerful and effective to achieve optimal fuzzy dispatching rules for higher shop floor productivity and operational efficiency.

This paper presents a high performance multi-objective evolutionary algorithm with novel multiple-goal based Pareto cost assignment scheme that is capable of integrating any combination of goal and priority information. In addition, the algorithm is incorporated with a few advanced features for effective multi-objective optimization. These include the development of a dynamic sharing distance computation that is simple and adaptive to the on-line population distribution at each generation; an easy formation to deal with both soft and hard optimization constraints concurrently; a new way of convergence representation for multi-objective optimization based upon the concept of population domination; and a switching criteria preserved strategy to ensure stability and diversity of the multi-objective evolution. The effectiveness of the proposed algorithm is illustrated upon a benchmark optimization problem.