To relieve intensive human-expertise required to design optimization algorithms, recent Meta-Black-Box Optimization (MetaBBO) researches leverage generalization strength of meta-learning to train neural network-based algorithm design policies over a predefined training problem set, which automates the adaptability of the low-level optimizers on unseen problem instances. Currently, a common training problem set choice in existing MetaBBOs is well-known benchmark suites CoCo-BBOB. Although such choice facilitates the MetaBBO's development, problem instances in CoCo-BBOB are more or less limited in diversity, raising the risk of overfitting of MetaBBOs, which might further results in poor generalization. In this paper, we propose an instance generation approach, termed as LSRE, which could generate diverse training problem instances for MetaBBOs to learn more generalizable policies. LSRE first trains an autoencoder which maps high-dimensional problem features into a 2-dimensional latent space. Uniform-grid sampling in this latent space leads to hidden representations of problem instances with sufficient diversity. By leveraging a genetic-programming approach to search function formulas with minimal L2-distance to these hidden representations, LSRE reverse engineers a diversified problem set, termed as Diverse-BBO. We validate the effectiveness of LSRE by training various MetaBBOs on Diverse-BBO and observe their generalization performances on either synthetic or realistic scenarios. Extensive experimental results underscore the superiority of Diverse-BBO to existing training set choices in MetaBBOs. Further ablation studies not only demonstrate the effectiveness of design choices in LSRE, but also reveal interesting insights on instance diversity and MetaBBO's generalization.

Many optimization tasks involve streaming data with unknown concept drifts, posing a significant challenge as Streaming Data-Driven Optimization (SDDO). Existing methods, while leveraging surrogate model approximation and historical knowledge transfer, are often under restrictive assumptions such as fixed drift intervals and fully environmental observability, limiting their adaptability to diverse dynamic environments. We propose TRACE, a TRAnsferable Concept-drift Estimator that effectively detects distributional changes in streaming data with varying time scales. TRACE leverages a principled tokenization strategy to extract statistical features from data streams and models drift patterns using attention-based sequence learning, enabling accurate detection on unseen datasets and highlighting the transferability of learned drift patterns. Further, we showcase TRACE's plug-and-play nature by integrating it into a streaming optimizer, facilitating adaptive optimization under unknown drifts. Comprehensive experimental results on diverse benchmarks demonstrate the superior generalization, robustness, and effectiveness of our approach in SDDO scenarios.

Low-Rank Adaptation (LoRA) has emerged as a prominent solution to mitigate the communication and computation costs in federated fine-tuning of Large Language Models (LLMs).However, we observe that even within lowrank adapters, a substantial portion of parameters manifest negligible updates during federated training, leading to redundant communication and wasted local computation.To address this, we propose GMFL, a plug-andplay layer freezing mechanism designed to seamlessly integrate with existing federated fine-tuning frameworks.Specifically, the server monitors the global update magnitude of each LoRA layer to dynamically generate freezing masks.These masks are updated periodically with a fixed freezing rate, ensuring stable convergence by robustly identifying "saturated" layers.Theoretical analysis confirms the convergence of GMFL, where the freezing mechanism yields a bounded error that scales with client heterogeneity.Extensive experiments across multiple tasks (GLUE, Commonsense Reasoning, Math Reasoning and General Generation) demonstrate that GMFL reduces communication overhead and lowers computational costs while preserving the performance of the underlying federated fine-tuning methods.Our work provides a practical, versatile solution for deploying large-scale federated LLM fine-tuning in resource-constrained environments.

Dynamic Optimization Problems (DOPs) are challenging to address due to their complex nature, i.e., dynamic environment variation. Evolutionary Computation methods are generally advantaged in solving DOPs since they resemble dynamic biological evolution. However, existing evolutionary dynamic optimization methods rely heavily on human-crafted adaptive strategy to detect environment variation in DOPs, and then adapt the searching strategy accordingly. These hand-crafted strategies may perform ineffectively at out-of-box scenarios. In this paper, we propose a reinforcement learning-assisted approach to enable automated variation detection and self-adaption in evolutionary algorithms. This is achieved by borrowing the bi-level learning-to-optimize idea from recent Meta-Black-Box Optimization works. We use a deep Q-network as optimization dynamics detector and searching strategy adapter: It is fed as input with current-step optimization state and then dictates desired control parameters to underlying evolutionary algorithms for next-step optimization. The learning objective is to maximize the expected performance gain across a problem distribution. Once trained, our approach could generalize toward unseen DOPs with automated environment variation detection and self-adaption. To facilitate comprehensive validation, we further construct an easy-to-difficult DOPs testbed with diverse synthetic instances. Extensive benchmark results demonstrate flexible searching behavior and superior performance of our approach in solving DOPs, compared to state-of-the-art baselines. Our code is publicly available here: https://github.com/MetaEvo/Meta-DO

Recent research in Cooperative Coevolution (CC) has achieved promising progress in solving large-scale global optimization problems. However, existing CC paradigms have a primary limitation in that they require deep expertise for selecting or designing effective variable decomposition strategies. Inspired by advancements in Meta-Black-Box Optimization, this paper introduces LCC, a pioneering learning-based cooperative coevolution framework that dynamically schedules decomposition strategies during optimization processes. The decomposition strategy selector is parameterized through a neural network, which processes a meticulously crafted set of optimization status features to determine the optimal strategy for each optimization step. The network is trained via the Proximal Policy Optimization method in a reinforcement learning manner across a collection of representative problems, aiming to maximize the expected optimization performance. Extensive experimental results demonstrate that LCC not only offers certain advantages over state-of-the-art baselines in terms of optimization effectiveness and resource consumption, but it also exhibits promising transferability towards unseen problems.

Cooperative Coevolution (CC) effectively addresses Large-Scale Global Optimization (LSGO) via decomposition but struggles with the emerging class of Heterogeneous LSGO (H-LSGO) problems arising from real-world applications, where subproblems exhibit diverse dimensions and distinct landscapes. The prevailing CC paradigm, relying on a fixed low-dimensional optimizer, often fails to navigate this heterogeneity. To address this limitation, we propose the Learning-Based Heterogeneous Cooperative Coevolution Framework (LH-CC). By formulating the optimization process as a Markov Decision Process, LH-CC employs a meta-agent to adaptively select the most suitable optimizer for each subproblem. We also introduce a flexible benchmark suite to generate diverse H-LSGO problem instances. Extensive experiments on 3000-dimensional problems with complex coupling relationships demonstrate that LH-CC achieves superior solution quality and computational efficiency compared to state-of-the-art baselines. Furthermore, the framework exhibits robust generalization across varying problem instances, optimization horizons, and optimizers. Our findings reveal that dynamic optimizer selection is a pivotal strategy for solving complex H-LSGO problems.

Incomplete multi-view clustering is a prominent research area in multimedia. Among various techniques, self-representation-based approaches have gained attention for effectively capturing global data structures. However, most methods assume different views share a common self-representation matrix, overlooking view-specific characteristics and cross-view complementarity. To address this limitation, we propose a novel incomplete multi-view clustering model, Joint Shared and Private Self-representation Learning (JSPSL), which decomposes the self-representation matrices into shared and private components with mutually exclusive constraints. JSPSL unifies missing view completion and self-representation learning within a single framework, enabling mutual reinforcement. We apply ADMM to efficiently solve our model. Extensive experiments demonstrate that JSPSL consistently outperforms state-of-the-art algorithms.

Recently, combining the strength of large language models (LLMs) and Evolutionary Computation (EC) has shown promising results for addressing optimization problems. It typically involves either iterative next-step solution seeking or directly prompting LLMs to generate critical optimization codes. However, these methods often suffer from low computational efficiency, high sensitivity to prompt design, and a lack of domain-specific knowledge. We introduce LLaMoCo, the first instruction-tuning framework designed to adapt LLMs for solving optimization problems in a code-to-code manner. LLaMoCo features a comprehensive instruction set that includes code-style problem descriptions as input prompts and robust optimization codes from expert EC optimizers as target outputs. We then develop a novel two-phase learning strategy with a contrastive learning-based warm-up to enhance convergence during instruction tuning. Extensive experiments demonstrate that a CodeGen (350M) model tuned by our LLaMoCo yields a powerful domain-specific model for generating high-performance optimizers, achieving superior performance compared to GPT-4 family and other competitors on both synthetic and realistic problem sets.

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.

The fragment reconstruction problem aims to assemble the original object from a collection of fragmented pieces. Traditional manual reconstruction techniques heavily rely on expert knowledge and can potentially damage fragile fragments, necessitating the development of automated reconstruction methods. Current reconstruction algorithms often suffer from the curse of dimensionality, compromising both accuracy and efficiency as the number of fragments increases. These algorithms primarily rely on fragment content, limiting their adaptability and scalability. To address these challenges, this paper introduces a novel reconstruction method grounded in a cooperative coevolutionary (CC) optimization framework. This approach encompasses both the formalization of the fragment reconstruction problem and the development of a tailored algorithm to solve it. Notably, our modeling approach is content-independent, relying solely on the edge shapes of the fragments. With this modeling approach, the solution itself represents the reconstruction process of the fragments. To encode candidate solutions efficiently, we employ a tree structure. This encoding scheme renders traditional CC processes and genetic algorithm operators, such as crossover and mutation, inapplicable. Therefore, this paper proposes a tree-structured CC genetic algorithm (T-CCGA) specifically tailored to our reconstruction task. We aim to overcome the limitations of current reconstruction algorithms and pave the way for more accurate and efficient fragment reconstruction methods. To evaluate the effectiveness of the proposed method, we conducted a series of comprehensive experiments. The results demonstrate that T-CCGA achieves promising outcomes in terms of solution quality, convergence speed, and robustness.

Streaming Data-Driven Evolutionary Algorithms (SDDEAs) have emerged as a crucial paradigm in the area of data-driven optimization. However, current methods face critical limitations when handling unpredictable concept drifts in continuously evolving environments. To address this research gap, we propose DASE, a drift-aware streaming evolutionary algorithm that features two key innovations. First, we introduce a hierarchical confidence drift detector that operates on a moving window over continuous data streams, identifying concept drifts by evaluating statistical deviations in model accuracy. Second, we propose a context-aware warm start mechanism that adaptively transfers knowledge from historical environments to the new environment using environmental similarity-based weighting. These dual innovations not only enables automatic segmentation of streaming data into coherence environments but also enhances optimization performance with the real-time responsiveness. Experimental evaluations on benchmark problems demonstrate that DASE significantly outperforms state-of-the-art algorithms across various drift scenarios, establishing it as a powerful method for addressing challenges in continuously streaming environment.

Recent advances in Meta-learning for Black-Box Optimization (MetaBBO) have shown the potential of using neural networks to dynamically configure evolutionary algorithms (EAs), enhancing their performance and adaptability across various BBO instances. However, they are often tailored to a specific EA, which limits their generalizability and necessitates retraining or redesigns for different EAs and optimization problems. To address this limitation, we introduce ConfigX, a new paradigm of the MetaBBO framework that is capable of learning a universal configuration agent (model) for boosting diverse EAs. To achieve so, our ConfigX first leverages a novel modularization system that enables the flexible combination of various optimization sub-modules to generate diverse EAs during training. Additionally, we propose a Transformer-based neural network to meta-learn a universal configuration policy through multitask reinforcement learning across a designed joint optimization task space. Extensive experiments verify that, our ConfigX, after large-scale pre-training, achieves robust zero-shot generalization to unseen tasks and outperforms state-of-the-art baselines. Moreover, ConfigX exhibits strong lifelong learning capabilities, allowing efficient adaptation to new tasks through fine-tuning. Our proposed ConfigX represents a significant step toward an automatic, all-purpose configuration agent for EAs.

Incomplete Multi-View Clustering (IMVC) addresses the challenge of missing data by leveraging available information and effectively mining cross-view relationships. While contrastive learning has recently been introduced into IMVC for discriminative representation learning, existing methods typically adopt pairwise contrastive strategies with view-specific reconstruction and heuristic fusion schemes. These approaches are generally suboptimal when facing high missing-view ratios and struggle to capture latent cross-view dependencies. To overcome these limitations, we propose ConsensNet, a unified consensus-centric framework for IMVC. This is achieved through a unified architecture that integrates contrastive cross-view alignment, consensus prediction, and attention-aware fusion. By aligning all available views into a shared semantic space, ConsensNet effectively captures latent cross-view dependencies without requiring high-quality view completion. Moreover, the attention-aware fusion mechanism dynamically assigns weights to each view based on its relevance to the consensus, thereby reducing the impact of noisy or weakly correlated views. Extensive experiments on multiple datasets demonstrate that ConsensNet consistently outperforms state-of-the-art IMVC methods, particularly under high missing-view scenarios, highlighting its robustness and practical significance.

Recently, Meta-Black-Box-Optimization (MetaBBO) methods significantly enhance the performance of traditional black-box optimizers through meta-learning flexible and generalizable meta-level policies that excel in dynamic algorithm configuration (DAC) tasks within the low-level optimization, reducing the expertise required to adapt optimizers for novel optimization tasks. Though promising, existing MetaBBO methods heavily rely on human-crafted feature extraction approach to secure learning effectiveness. To address this issue, this paper introduces a novel MetaBBO method that supports automated feature learning during the meta-learning process, termed as RLDE-AFL, which integrates a learnable feature extraction module into a reinforcement learning-based DE method to learn both the feature encoding and meta-level policy. Specifically, we design an attention-based neural network with mantissa-exponent based embedding to transform the solution populations and corresponding objective values during the low-level optimization into expressive landscape features. We further incorporate a comprehensive algorithm configuration space including diverse DE operators into a reinforcement learning-aided DAC paradigm to unleash the behavior diversity and performance of the proposed RLDE-AFL. Extensive benchmark results show that co-training the proposed feature learning module and DAC policy contributes to the superior optimization performance of RLDE-AFL to several advanced DE methods and recent MetaBBO baselines over both synthetic and realistic BBO scenarios.

Detecting potential optimal peak areas and locating the accurate peaks in these areas are two major challenges in Multimodal Optimization problems (MMOPs). To address them, much efforts have been spent on developing novel searching operators, niching strategies and multi-objective problem transformation pipelines. Though promising, existing approaches more or less overlook the potential usage of landscape knowledge. In this paper, we propose a novel optimization framework tailored for MMOPs, termed as APDMMO, which facilitates peak detection via fully leveraging the landscape knowledge and hence capable of providing strong optimization performance on MMOPs. Specifically, we first design a novel surrogate landscape model which ensembles a group of non-linear activation units to improve the regression accuracy on diverse MMOPs. Then we propose a free-of-trial peak detection method which efficiently locates potential peak areas through back-propagation on the learned surrogate landscape model. Based on the detected peak areas, we employ SEP-CMAES for local search within these areas in parallel to further improve the accuracy of the found optima. Extensive benchmarking results demonstrate that APDMMO outperforms several up-to-date baselines. Further ablation studies verify the effectiveness of the proposed novel designs. The source-code is available at https://github.com/GMC-DRL/APDMMO.

Clustered federated learning (FL), which groups clients with similar data distributions for collaborative training, represents a pivotal technique within federated learning for effectively addressing the challenges posed by non-IID data on clients. Existing clustered FL algorithms typically endeavor to learn distribution similarities of clients iteratively or indirectly through representations like gradients and loss. This necessitates resource-intensive pre-training or multiple iterations to attain stable clusters, thereby incurring additional communication cost and computational overhead. To address the above issues, we propose lightweight Clustered Federated Learning via Feature Extraction (FECFL). FECFL adopts a simple but effective client representation, i.e., the features extracted from the clients’ data using identically initialized models without any pre-training, to perform efficient one-shot clustering. Moreover, client data distribution is often dynamic in practice. To tackle distribution shift, we embed a distribution monitoring mechanism in FECFL, enabling adaptive re-grouping for new distributions. Finally, we demonstrate the benefits of FECFL over the baselines by conducting experiments on various datasets and distributions.

Recent decomposition-based neural multi-objective combinatorial optimization (MOCO) methods struggle to achieve desirable performance. Even equipped with complex learning techniques, they often suffer from significant optimality gaps in weight-specific subproblems. To address this challenge, we propose a neat weight embedding method to learn weight-specific representations, which captures weight-instance interaction for the subproblems and was overlooked by most current methods. We demonstrate the potentials of our method in two instantiations. First, we introduce a succinct addition model to learn weight-specific node embeddings, which surpassed most existing neural methods. Second, we design an enhanced conditional attention model to simultaneously learn the weight embedding and node embeddings, which yielded new state-of-the-art performance. Experimental results on classic MOCO problems verified the superiority of our method. Remarkably, our method also exhibits favorable generalization performance across problem sizes, even outperforming the neural method specialized for boosting size generalization.

Recent research in Meta-Black-Box-Optimization (MetaBBO) have shown that meta-trained neural networks can effectively guide the design of black-box optimizers, significantly reducing the need for expert tuning and delivering robust performance across complex problem distributions. Despite their success, a paradox remains: MetaBBO still rely on human-crafted Exploratory Landscape Analysis features to inform the meta-level agent about the low-level optimization progress. To address the gap, this paper proposes Neural Exploratory Landscape Analysis (NeurELA), a novel framework that dynamically profiles landscape features through a two-stage, attention-based neural network, executed in an entirely end-to-end fashion. NeurELA is pre-trained over a variety of MetaBBO algorithms using a multi-task neuroevolution strategy. Extensive experiments show that NeurELA achieves consistently superior performance when integrated into different and even unseen MetaBBO tasks and can be efficiently fine-tuned for further performance boost. This advancement marks a pivotal step in making MetaBBO algorithms more autonomous and broadly applicable. The source code of NeurELA can be accessed at https://anonymous.4open.science/r/Neur-ELA-303C.

Recent progress in Meta-Black-Box-Optimization (MetaBBO) has demonstrated that using RL to learn a meta-level policy for dynamic algorithm configuration (DAC) over an optimization task distribution could significantly enhance the performance of the low-level BBO algorithm. However, the online learning paradigms in existing works makes the efficiency of MetaBBO problematic. To address this, we propose an offline learning-based MetaBBO framework in this paper, termed Q-Mamba, to attain both effectiveness and efficiency in MetaBBO. Specifically, we first transform DAC task into long-sequence decision process. This allows us further introduce an effective Q-function decomposition mechanism to reduce the learning difficulty within the intricate algorithm configuration space. Under this setting, we propose three novel designs to meta-learn DAC policy from offline data: we first propose a novel collection strategy for constructing offline DAC experiences dataset with balanced exploration and exploitation. We then establish a decomposition-based Q-loss that incorporates conservative Q-learning to promote stable offline learning from the offline dataset. To further improve the offline learning efficiency, we equip our work with a Mamba architecture which helps long-sequence learning effectiveness and efficiency by selective state model and hardware-aware parallel scan respectively. Through extensive benchmarking, we observe that Q-Mamba achieves competitive or even superior performance to prior online/offline baselines, while significantly improving the training efficiency of existing online baselines. We provide sourcecodes of Q-Mamba https://github.com/MetaEvo/Q-Mamba.

Existing neural methods for the Travelling Salesman Problem (TSP) mostly aim at finding a single optimal solution. To discover diverse yet high-quality solutions for Multi-Solution TSP (MSTSP), we propose a novel deep reinforcement learning based neural solver, which is primarily featured by an encoder-decoder structured policy. Concretely, on the one hand, a Relativization Filter (RF) is designed to enhance the robustness of the encoder to affine transformations of the instances, so as to potentially improve the quality of the found solutions. On the other hand, a Multi-Attentive Adaptive Active Search (MA3S) is tailored to allow the decoders to strike a balance between the optimality and diversity. Experimental evaluations on benchmark instances demonstrate the superiority of our method over recent neural baselines across different metrics, and its competitive performance against state-of-the-art traditional heuristics with significantly reduced computational time, ranging from 1.3× to 15× faster. Furthermore, we demonstrate that our method can also be applied to the Capacitated Vehicle Routing Problem (CVRP).

Lifelong Multi-Agent Path Finding (LMAPF) focuses on planning conflict-free paths for agents, like autonomous vehicles, that are continuously assigned new tasks. The synergy of search-based and learning-based methods holds promise for striking a balance in-between effectiveness and efficiency but still faces several challenges such as inferior initial paths, weak search-learning synergy and low sample utilization rate. To address these issues, this paper proposes a new synergized LMAPF approach, named Synergistic Multi-Agent Path Optimization (SMAPO), which consists of two tightly-coupled phases: Primordial Planning and Decision Refinement. In the Primordial Planning phase, we introduce a novel load-balanced A* algorithm that integrates planned and perceived congestion costs, which enhances initial solution quality by evenly distributing spatiotemporal traffic loads, thereby mitigating potential conflicts. In the Decision Refinement phase, we propose a novel Encoder-Decoder based neural network to learn a collaborative optimization policy through multi-agent reinforcement learning. In addition, we leverage dual transformations to augment trajectory samples during online learning, enhancing both the sample utilization rate and overall learning stability. Extensive experiments reveal that our SMAPO is superior to the state-of-the-art baselines in effectiveness, efficiency, and generalization capability. Source code is available at https://github.com/ByteUser-blues/SMAPO.

Designing effective black‑box optimizers is hampered by limited problem-specific knowledge and manual control that spans months for almost every detail. In this paper, we present DesignX, the first automated algorithm design framework that generates an effective optimizer specific to a given black-box optimization problem within seconds. Rooted in the first principles, we identify two key sub-tasks: 1) algorithm structure generation and 2) hyperparameter control. To enable systematic construction, a comprehensive modular algorithmic space is first built, embracing hundreds of algorithm components collected from decades of research. We then introduce a dual-agent reinforcement learning system that collaborates on structural and parametric design through a novel cooperative training objective, enabling large-scale meta-training across 10k diverse instances. Remarkably, through days of autonomous learning, the DesignX-generated optimizers continuously surpass human-crafted optimizers by orders of magnitude, either on synthetic testbed or on realistic optimization scenarios such as Protein-docking, AutoML and UAV path planning. Further in-depth analysis reveals DesignX's capability to discover non-trivial algorithm patterns beyond expert intuition, which, conversely, provides valuable design insights for the optimization community. We provide DesignX's Python project at~\url{https://github.com/MetaEvo/DesignX}.

Meta-Black-Box Optimization (MetaBBO) streamlines the automation of optimization algorithm design through meta-learning. It typically employs a bi-level structure: the meta-level policy undergoes meta-training to reduce the manual effort required in developing algorithms for low-level optimization tasks. The original MetaBox (2023) provided the first open-source framework for reinforcement learning-based single-objective MetaBBO. However, its relatively narrow scope no longer keep pace with the swift advancement in this field. In this paper, we introduce MetaBox-v2 (\url{https://github.com/MetaEvo/MetaBox}) as a milestone upgrade with four novel features: 1) a unified architecture supporting RL, evolutionary, and gradient-based approaches, by which we reproduce $23$ up-to-date baselines; 2) efficient parallelization schemes, which reduce the training/testing time by $10-40$x; 3) a comprehensive benchmark suite of $18$ synthetic/realistic tasks ($1900$+ instances) spanning single-objective, multi-objective, multi-model, and multi-task optimization scenarios; 4) plentiful and extensible interfaces for custom analysis/visualization and integrating to external optimization tools/benchmarks. To show the utility of MetaBox-v2, we carry out a systematic case study that evaluates the built-in baselines in terms of the optimization performance, generalization ability and learning efficiency. Valuable insights are concluded from thorough and detailed analysis for practitioners and those new to the field.

The search for multiple optimal solutions in the traveling salesman problem (TSP), as a challenging multimodal optimization problem in the combinatorial domain, has received increasing attention in recent years. Nevertheless, the multisolution TSP (MSTSP) still remains extremely difficult for larger-scale TSP instances. In this article, we propose a niching Lin-Kernighan–Helsgaun (LKH)-based ant colony system (ACS), named nLKH-ACS, taking advantage of LKH’s ability to solve large-scale TSPs, ACS’s search efficiency, and the niching technique for diversity preservation. Specifically, first, to address multisolution problems, we design a niching LKH (nLKH) strategy to generate diverse cost-efficient spanning trees, and adopt the$\alpha $-nearness on each tree to obtain a diverse candidate edge set. The nLKH strategy enhances the ACS by improving pheromone initialization, solution construction, and local search operation using spanning trees and candidate edge sets, thereby strengthening the search capability and diversity. Then, to balance convergence and diversity, an adaptive Gaussian strategy is utilized to update the pheromone matrix. Furthermore, we design an indicator to measure the geometric diversity between pairs of solutions in the MSTSP solution set. The comprehensive experiments on MSTSPs and TSPLIB are conducted to validate the performance of the proposed nLKH-ACS. The experimental results demonstrate the powerful solving capability and excellent diversity of the proposed nLKH-ACS, particularly in finding various optimal solutions in larger-scale TSP instances.

When solving optimization problems with expensive or implicit objective functions, evolutionary algorithms (EAs) commonly utilize surrogate models as cost-effective substitutes for evaluation. This category of algorithms is referred to as data-driven EAs (DDEAs). However, when constructing surrogate models, existing studies rely on the hand-crafted model structure, requiring prior knowledge while leading to the suboptimal fitting ability of the model. To address the issue, this article proposes a novel symbolic regression (SR)-assisted EA, namely SR-DDEA. SR-DDEA employs SR to automatically construct the model structure without prior knowledge and obtain accurate surrogates. Specifically, we develop an efficient gene expression programming algorithm to enhance the expressive ability of surrogates, assisted by a queue-based decoding strategy to improve the efficiency of the model calculations. We also employ a clustering-based selective ensemble method to maximize data utilization and obtain diverse models. Experimental findings on commonly employed benchmarks demonstrate that our algorithm surpasses other cutting-edge offline DDEAs on test problems of different scales and a practical aerodynamic airfoil design challenge.

In recent years, there has been a growing interest in data-driven evolutionary algorithms (DDEAs) employing surrogate models to approximate the objective functions with limited data. However, current DDEAs are primarily designed for lower-dimensional problems and their performance drops significantly when applied to large-scale optimization problems (LSOPs). To address the challenge, this article proposes an offline DDEA named DSKT-DDEA. DSKT-DDEA leverages multiple islands that utilize different data to establish diverse surrogate models, fostering diverse sub-populations and mitigating the risk of premature convergence. In the intra-island optimization phase, a semi-supervised learning method is devised to fine-tune the surrogates. It not only facilitates data argumentation but also incorporates the distribution information gathered during the search process to align the surrogates with the evolving local landscapes. Then, in the inter-island knowledge transfer phase, the algorithm incorporates an adaptive strategy that periodically transfers individual information and evaluates the transfer effectiveness in the new environment, facilitating global optimization efficacy. Experimental results demonstrate that our algorithm is competitive with state-of-the-art DDEAs on problems with up to 1,000 dimensions, while also exhibiting decent parallelism and scalability. Our DSKT-DDEA is open source and accessible at: https://github.com/LabGong/DSKT-DDEA .

The significance of maritime transportation highlights the need to enhance the efficiency of container terminals. This study addresses a challenge within maritime transportation, specifically the continuous berth allocation and time-variant quay crane assignment problem (C/T-V BACAP). We formulate a comprehensive mathematical model of C/T-V BACAP. To solve the problem, we propose an effective memetic algorithm with a heuristic decoding method, named HMA, which comprises three essential components: a three-stage heuristic decoding method, a clustering-based evolutionary strategy, and a target-guided local search operator. The three-stage heuristic decoding method guarantees solution feasibility and high quality through the entire optimization, allowing the following strategies to fully utilize their search capabilities. The clustering-based evolutionary strategy refines the search space and diversifies the promising candidates. Meanwhile, the target-guided local search operator rapidly optimizes the allocation for the challenging vessel. The experimental results demonstrate that the proposed algorithm delivers excellent performance, especially in handling large-scale instances (up to 60 vessels). Our proposed method outperforms the state-of-the-art BACAP algorithms by an average margin of 150% in terms of berth offset and waiting time in most problem instances.

Solving multimodal optimization problems (MMOP) requires finding all optimal solutions, which is challenging in limited function evaluations. Although existing works strike the balance of exploration and exploitation through hand-crafted adaptive strategies, they require certain expert knowledge, hence inflexible to deal with MMOP with different properties. In this paper, we propose RLEMMO, a Meta-Black-Box Optimization framework, which maintains a population of solutions and incorporates a reinforcement learning agent for flexibly adjusting individual-level searching strategies to match the up-to-date optimization status, hence boosting the search performance on MMOP. Concretely, we encode landscape properties and evolution path information into each individual and then leverage attention networks to advance population information sharing. With a novel reward mechanism that encourages both quality and diversity, RLEMMO can be effectively trained using a policy gradient algorithm. The experimental results on the CEC2013 MMOP benchmark underscore the competitive optimization performance of RLEMMO against several strong baselines.

Evolutionary computation (EC) algorithms, renowned as powerful black-box optimizers, leverage a group of individuals to cooperatively search for the optimum. The exploration-exploitation tradeoff (EET) plays a crucial role in EC, which, however, has traditionally been governed by manually designed rules. In this paper, we propose a deep reinforcement learning-based framework that autonomously configures and adapts the EET throughout the EC search process. The framework allows different individuals of the population to selectively attend to the global and local exemplars based on the current search state, maximizing the cooperative search outcome. Our proposed framework is characterized by its simplicity, effectiveness, and generalizability, with the potential to enhance numerous existing EC algorithms. To validate its capabilities, we apply our framework to several representative EC algorithms and conduct extensive experiments on the augmented CEC2021 benchmark. The results demonstrate significant improvements in the performance of the backbone algorithms, as well as favorable generalization across diverse problem classes, dimensions, and population sizes. Additionally, we provide an in-depth analysis of the EET issue by interpreting the learned behaviors of EC.

In recent years, the data-driven optimization area has seen a shift in the research focus from static batched data environment to dynamic streaming data environment. However, this field is hindered by the lack of a comprehensive and standardized test suite. To fill this gap, we introduce SDDObench, the first benchmark tailored for evaluating and comparing the streaming data-driven evolutionary algorithms (SDDEAs). SDDObench comprises two sets of objective functions combined with five different types of concept drifts, which offer the benefit of being inclusive in generating data streams that mimic various real-world situations, while also facilitating straight-forward description and analysis. As a proof-of-concept study, four well-known algorithms are selected to tackle the problems generated by SDDObench. The experiment results and analysis reveal ongoing challenges in attaining good performance for streaming data-driven optimization. Our SDDObench is open-source and accessible at: https://github.com/LabGong/SDDObench.

Recent Meta-learning for Black-Box Optimization (MetaBBO) methods harness neural networks to meta-learn configurations of traditional black-box optimizers. Despite their success, they are inevitably restricted by the limitations of predefined hand-crafted optimizers. In this paper, we present SYMBOL, a novel framework that promotes the automated discovery of black-box optimizers through symbolic equation learning. Specifically, we propose a Symbolic Equation Generator (SEG) that allows closed-form optimization rules to be dynamically generated for specific tasks and optimization steps. Within SYMBOL, we then develop three distinct strategies based on reinforcement learning, so as to meta-learn the SEG efficiently. Extensive experiments reveal that the optimizers generated by SYMBOL not only surpass the state-of-the-art BBO and MetaBBO baselines, but also exhibit exceptional zero-shot generalization abilities across entirely unseen tasks with different problem dimensions, population sizes, and optimization horizons. Furthermore, we conduct in-depth analyses of our SYMBOL framework and the optimization rules that it generates, underscoring its desirable flexibility and interpretability.

Data-efficient image classification poses a challenge in achieving effectiveness with limited data, as evidenced by the current methods based on convolutional neural networks (CNNs) and genetic programming (GP). Existing works employing these two methods encounter limitations, such as a lack of flexibility and an inability to effectively explore the latent features of the data. To tackle these challenges, this paper introduces a genetic programming method for data-efficient image recognition, leveraging novel function sets, terminal sets, and program structures. This method transforms tree-based data structures in GP into trainable CNN architectures. Further, by employing block structures instead of single operations in the search space, the search space is reduced and the stability of the search structures enhanced. Comparative experiments with state-of-the-art neural network methods and GP-based methods on data-efficient classification datasets validate the GP-CNN method offering higher performance.

Semisupervised node classification is a prevalent task on graphs, which involves predicting the labels of unlabeled nodes based on limited labeled data available. At present, centralized approaches to training models for this task are unsustainable due to the increasing demand for computational power, storage capacity, and privacy. An approach of potential is federated graph learning (FGL), which allows multiple clients to collaborate on learning a model while maintaining data privacy. However, current methods suffer from the inability to consider the topology of the graph data and inadequate use of unlabeled data. To address these issues, we propose federated graph augmentation (FedGA) by combining graph neural network (GNN) models to utilize similar topologies existing in different client graphs and augment the client data. Furthermore, we develop FedGA-L based on FedGA, which integrates pseudolabeling and label-injection to improve the utilization of unlabeled data. FedGA-L allows pseudolabels to be used as additional information to enhance data augmentation and further improve the accuracy of node classification. We evaluate the effectiveness of FedGA and FedGA-L through experiments on multiple datasets. The results demonstrate improved accuracy in solving typical classification tasks and their compatibility with a variety of federated learning (FL) frameworks. On widely recognized datasets for graph learning, we achieve an accuracy improvement of 5%–7% compared to vanilla federated learning algorithms.

Current multi-view subspace clustering methods typically consist of a within-view module, which explores inherent characteristics using the self-expressive coefficient matrix, and a cross-view module, which promotes consensus among all views toward similar strengths. However, the self-expressive coefficients are directly influenced by the characteristics and distributions of input features, and coefficient matrices with varying strengths may indicate the same clustering structure. Therefore, directly regularizing the coefficient matrices towards a common matrix is unnecessary and may even diminish the clustering performance. We find that it is the relative data relationship, rather than the absolute similarity, that plays a pivotal role in clustering. Building on this realization, we propose a relative comparison measure that enables a more contextual understanding of the data relationship. Subsequently, we develop a Relative Comparison-based Consensus Learning (RCCL) model for multi-view subspace clustering, which encourages the relative data similarities to be consistent across different views. Our RCCL model advances in identifying the underlying data relationship, avoiding unnecessary constraints on absolute consistency, and thereby delving into the fundamental nature of multi-view consensus. We introduce an elegant transformation operator for relative comparison and solve RCCL under the framework of alternating direction method of multipliers. Extensive experiments unequivocally demonstrated the superiority of RCCL.

Data-driven evolutionary algorithms (DDEAs) have received increasing attention during the past decade, but most existing studies are dedicated to solving relatively small-scale problems. For large-scale optimization problems (LSOPs), special efforts must be made to both the surrogate and the evolutionary components to overcome the “curse of dimensionality”, which remains a challenge in this research area. To address this research limitation, we propose a novel cooperative coevolution-based DDEA (CC-DDEA). First, a hierarchical surrogate-joint learning model is designed to provide fitness approximations at both global and subdivided spaces, thus being able to guide the evolutionary population searching at different granularities. Then, optimization is conducted on both the global level and local sub-space level in the manner of cooperative coevolution. In the local-level search, we introduce a gradient-based operator to accelerate the convergence efficiency of sub-spaces, owing to the differentiable property of our surrogate model. Additionally, the entire framework is used in conjunction with a progressive and dynamic space division strategy, enabling local parallel-to-global unified search and facilitating the final convergence. Experiments on up to 1000-dimensional problems and the comparisons with state-of-the-art DDEAs validate the powerfulness of the proposed algorithm.

Density clustering has shown advantages over other types of clustering methods for processing arbitrarily shaped datasets. In recent years, extensive research efforts has been made on the improvements of DBSCAN or the algorithms incorporating the concept of density peaks. However, these previous studies remain the problems of being sensitive to the parameter settings, and some of them will stuck in weak results when encountering the situations of varying-density distributions. To overcome these issues, we propose an evolution framework named EvoS&R that evolves multiple seeds and the corresponding radii for varying-density data clustering. Compared with the traditional methods, EvoS&R handles the parameter tuning and multi-density fitting problems in an integrated and straightforward manner. Note that, however, the underlying task in EvoS&R is a mixed-variable optimization problem that is challenging in nature. We specifically design a hybrid encoding differential evolution algorithm with novel encoding, mutation, etc., to solve the optimization problem efficiently. Extensive experiments on density-based datasets shows that our algorithm outperforms the other state-of-the-arts in most cases, which validates the effectiveness of the proposed method.

Federated learning (FL) is a distributed machine learning paradigm that can be organized in two layers. In the outer layer of users, there is a model interaction process between the task publisher and users, through which all parties obtain their respective utilities. However, these parties’ utilities are coupled, both depending on the training sample size and local iterations. In the inner layer of users, a user's multiple devices (e.g., computers and smart phones) can be used to jointly train local models efficiently. Yet, due to device heterogeneity, it is challenging for users to determine which devices to participate in local training and allocate how many computing and communication resources to minimize training costs. In this paper, we tackle this novel two-layer optimization problem by designing utility game and resource control strategies. In the outer layer, we model the relationship between the task publisher and users as a Stackelberg game and obtain the optimal solution for both parties by solving a unique Stackelberg equilibrium point; while in the inner layer, we formulate the optimization problem as a mixed integer nonlinear programming problem, which is decomposed into sub-problems and solved by devising resource control algorithm based on successive convex approximation. Finally, extensive experiments show that the proposed algorithms outperform baseline algorithms.

In real scenarios, graph-based multiview clustering has clearly shown popularity owing to the high efficiency in fusing the information from multiple views. Practically, the multiview graphs offer both consistent and inconsistent cues as they usually come from heterogeneous sources. Previous methods illustrated the importance of leveraging the multiview consistency and inconsistency for accurate modeling. However, when fusing the graphs, the inconsistent parts are generally ignored and hence the valued view-specific attributes are lost. To solve this problem, we propose an accurate complementarity learning (ACL) model for graph-based multiview clustering. ACL clearly distinguishes the consistent, complementary, and noise and corruption terms from the initial multiview graphs. In contrast to existing models that overlooked the complementary information, we argue that the view-specific characteristics extracted from the complementary terms are beneficial for affinity learning. In addition, ACL exploits only the positive parts of the complementary information for preserving the evidence on the positive sample relationship, and ignores the negative cues to avoid the vanishing of effective affinity strengths. This way, the learned affinity matrix is able to properly balance the consistent and complementary information. To solve the ACL model, we introduce an efficient alternating optimization algorithm with a varying penalty parameter. Experiments on synthetic and real-world databases clearly demonstrated the superiority of ACL.

The field of visual search has gained significant attention recently, particularly in the context of web search engines and e-commerce product search platforms. However, the abundance of web images presents a challenge for modern image retrieval systems, as they need to find both relevant and diverse images that maximize users’ satisfaction. In response to this challenge, we propose a non-dominated visual diversity re-ranking (NDVDR) method based on the concept of Pareto optimality. To begin with, we employ a fast binary hashing method as a coarse-grained retrieval procedure. This allows us to efficiently obtain a subset of candidate images for subsequent re-ranking. Fed with this initial retrieved image results, the NDVDR performs a fine-grained re-ranking procedure for boosting both relevance and visual diversity among the top-ranked images. Recognizing the inherent conflict nature between the objectives of relevance and diversity, the re-ranking procedure is simulated as the analytical stage of a multi-criteria decision-making process, seeking the optimal tradeoff between the two conflicting objectives within the initial retrieved images. In particular, a non-dominated sorting mechanism is devised that produces Pareto non-dominated hierarchies among images based on the Pareto dominance relation. Additionally, two novel measures are introduced for the effective characterization of the relevance and diversity scores among different images. We conduct experiments on three popular real-world image datasets and compare our re-ranking method with several state-of-the-art image search re-ranking methods. The experimental results validate that our re-ranking approach guarantees retrieval accuracy while simultaneously boosting diversity among the top-ranked images.

Natural image matting has garnered increasing attention in various computer vision applications. The matting problem aims to find the optimal foreground/background (F/B) color pair for each unknown pixel and thus obtain an alpha matte indicating the opacity of the foreground object. This problem is typically modeled as a large-scale pixel pair combinatorial optimization (PPCO) problem. Heuristic optimization is widely employed to tackle the PPCO problem owing to its gradient-free property and promising search ability. However, traditional heuristic methods often encode F/B solutions to a one-dimensional (1D) representation and then evolve the solutions in a 1D manner. This 1D representation destroys the intrinsic two-dimensional (2D) structure of images, where the significant spatial correlations among pixels are ignored. Moreover, the 1D representation also brings operation inefficiency. To address the above issues, this article develops a spatial-aware tensorial evolutionary image matting (TEIM) method. Specifically, the matting problem is modeled as a 2D Spatial-PPCO (S-PPCO) problem, and a global tensorial evolutionary optimizer is proposed to tackle the S-PPCO problem. The entire population is represented as a whole by a third-order tensor, in which individuals are classified into two types: F and B individuals for denoting the 2D F/B solutions, respectively. The evolution process, consisting of three tensorial evolutionary operators, is implemented based on pure tensor computation for efficiently seeking F/B solutions. The local spatial smoothness of images is also integrated into the evaluation process for obtaining a high-quality alpha matte. Experimental results compared with state-of-the-art methods validate the effectiveness of TEIM.

The emergence of networked systems in various fields brings many complex distributed optimization problems, where multiple agents in the system need to optimize a global objective cooperatively when they only have local information. In this work, we take advantage of the intrinsic parallelism of evolutionary computation to address network-based distributed optimization. In the proposed multiagent co-evolutionary algorithm, each agent maintains a subpopulation in which individuals represent solutions to the problem. During optimization, agents perform local optimization on their subpopulations and negotiation through communication with their neighbors. In order to help agents optimize the global objective cooperatively, we design a penalty-based objective function for fitness evaluation, which constrains the subpopulation within a small and controllable range. Further, to make the penalty more targeted, a conflict detection method is proposed to examine whether agents are conflicting on a certain shared variable. Finally, in order to help agents negotiate a consensus solution when only the local objective function is known, we retrofit the processes of negotiating shared variables, namely, evaluation, competition, and sharing. The above approaches form a multiagent co-evolutionary framework, enabling agents to cooperatively optimize the global objective in a distributed manner. Empirical studies show that the proposed algorithm achieves comparable solution quality with the holistic algorithm and better performance than existing gradient-free distributed algorithms on gradient-uncomputable problems.

Evolutionary algorithms, such as differential evolution, excel in solving real-parameter optimization challenges. However, the effectiveness of a single algorithm varies across different problem instances, necessitating considerable efforts in algorithm selection or configuration. This article aims to address the limitation by leveraging the complementary strengths of a group of algorithms and dynamically scheduling them throughout the optimization progress for specific problems. We propose a deep reinforcement learning-based dynamic algorithm selection framework to accomplish this task. Our approach models the dynamic algorithm selection a Markov decision process, training an agent in a policy gradient manner to select the most suitable algorithm according to the features observed during the optimization process. To empower the agent with the necessary information, our framework incorporates a thoughtful design of landscape and algorithmic features. Meanwhile, we employ a sophisticated deep neural network model to infer the optimal action, ensuring informed algorithm selections. Additionally, an algorithm context restoration mechanism is embedded to facilitate smooth switching among different algorithms. These mechanisms together enable our framework to seamlessly select and switch algorithms in a dynamic online fashion. Notably, the proposed framework is simple and generic, offering potential improvements across a broad spectrum of evolutionary algorithms. As a proof-of-principle study, we apply this framework to a group of differential evolution algorithms. The experimental results showcase the remarkable effectiveness of the proposed framework, not only enhancingthe overall optimization performance but also demonstrating favorable generalization ability across different problem classes.

Recently, Meta-Black-Box Optimization with Reinforcement Learning (MetaBBO-RL) has showcased the power of leveraging RL at the meta-level to mitigate manual fine-tuning of low-level black-box optimizers. However, this field is hindered by the lack of a unified benchmark. To fill this gap, we introduce MetaBox, the first benchmark platform expressly tailored for developing and evaluating MetaBBO-RL methods. MetaBox offers a flexible algorithmic template that allows users to effortlessly implement their unique designs within the platform. Moreover, it provides a broad spectrum of over 300 problem instances, collected from synthetic to realistic scenarios, and an extensive library of 19 baseline methods, including both traditional black-box optimizers and recent MetaBBO-RL methods. Besides, MetaBox introduces three standardized performance metrics, enabling a more thorough assessment of the methods. In a bid to illustrate the utility of MetaBox for facilitating rigorous evaluation and in-depth analysis, we carry out a wide-ranging benchmarking study on existing MetaBBO-RL methods. Our MetaBox is open-source and accessible at: https://github.com/GMC-DRL/MetaBox.

Many mobile games adopt autobattle systems in which the major consideration of players is how to assemble strong teams. The automated team assembly (ATA) becomes a crucial issue from different standpoints, such as assisting the game designers in performing balance analysis and directing the players to configure teams. Since the ATA is generally a combinatorial optimization problem, this article exploits the evolutionary optimizers. However, unlike the traditional problems that the evaluation functions are explicit, in the ATA, we are unable to evaluate the team strengths straightforwardly. To address this issue, we collect data from the server and build an end-to-end deep learning surrogate for estimating the team strengths. The model has a three-layer architecture of a feature embedding layer, a sequential relation layer, and a regression layer, which is able to characterize the complex dependencies between the sparse input features and the team strengths. The evolutionary algorithms are then guided by the constructed surrogate to seek for the strongest teams. Several adjustments are also made on the evolutionary algorithms to adapt it to the ATA problem with multiple constraints. Simulations on the gameRomance of the Three Kingdoms: Strategy Editionvalidate a good performance of the proposed data-driven evolutionary optimizers.

Offline data-driven evolutionary algorithms (DDEAs), which learn problem models from historical data and then perform optimization, have attracted significant attention in the data-driven age. Most existing studies build surrogate models based on regression methods to predict the fitness of each solution, which depends heavily on the quality and quantity of offline data. Considering the evolution trait of evolutionary algorithms (EAs), the absolute fitness of each individual is not essential, instead, the relative strengths of individuals are adequate. This article explores an alternative way to realize DDEAs by establishing a contrastive learning model that performs binary classification to determine the pros and cons between individuals. The task of binary classification is relatively simpler than regression, and meanwhile the training data is inherently augmented to the square of the origin. The proposed contrastive learning model is implemented based on a siamese neural network to measure the differences between solutions. Further, we use the predicted pairwise relationship between individuals to construct a directed graph and propose a topological sort algorithm on the graph to obtain the ranking of the population. During the topological sort, a regression model based on local principle is used to resolve some conflicting issues. Integrating the above components, an offline DDEA named contrastive learning-based DDEA (CL-DDEA) is put forward. Experiments and comparisons with state-of-the-arts validate the powerfulness of CL-DDEA, especially on high-dimensional problems.

Trajectory planning is a crucial task in designing the navigation systems of automatic underwater vehicles (AUVs). Due to the complexity of underwater environments, decision makers may hope to obtain multiple alternative trajectories in order to select the best. This paper focuses on the multiple-trajectory planning (MTP) problem, which is a new topic in this field. First, we establish a comprehensive MTP model for AUVs, by taking into account the complex underwater environments, the efficiency of each trajectory, and the diversity among different trajectories, simultaneously. Then, to solve the MTP, we develop an ant colony-based trajectory optimizer, which is characterized by a niching strategy, a decayed alarm pheromone measure, and a diversified heuristic measure. The niching strategy assists in identifying and maintaining a diverse set of high-quality solutions. The use of decayed alarm pheromone and diversified heuristic further improves the search effectiveness and efficiency of the algorithm. Experimental results on practical datasets show that our proposed algorithm not only provides multiple AUV trajectories for a flexible choice, but it also outperforms the state-of-the-art algorithms in terms of the single trajectory efficiency.

Travel time estimation is a crucial task in practical transportation applications, while providing the reliability of estimation is important in many working scenarios. Most existing studies do not consider the dynamics of traffic status for different road segments in real time, thus yielding unsatisfactory results. To address the problem, we propose to formulate the traffic network as a temporal attributed graph and perform node representation learning on it. The learned representation is capable of jointly exploiting the dynamic traffic conditions and the topology of the road network, which is then fed into a route-based spatio-temporal dependence learning module to estimate the travel time. By incorporating a distribution loss function, our proposed model is able to predict the distribution of travel time. In the meantime, we design an auxiliary local task of predicting the congestion status of each road segment, which further enhances the generalization performance of the representation learning. Extensive experiments on real-world large-scale datasets demonstrated the superiority of our method compared with the state-of-the-arts.

We present an efficient Neural Neighborhood Search (N2S) approach for pickup and delivery problems (PDPs). In specific, we design a powerful Synthesis Attention that allows the vanilla self-attention to synthesize various types of features regarding a route solution. We also exploit two customized decoders that automatically learn to perform removal and reinsertion of a pickup-delivery node pair to tackle the precedence constraint. Additionally, a diversity enhancement scheme is leveraged to further ameliorate the performance. Our N2S is generic, and extensive experiments on two canonical PDP variants show that it can produce state-of-the-art results among existing neural methods. Moreover, it even outstrips the well-known LKH3 solver on the more constrained PDP variant. Our implementation for N2S is available online.

Estimating the time of arrival is a crucial task in intelligent transportation systems. Although considerable efforts have been made to solve this problem, most of them decompose a trajectory into several segments and then compute the travel time by integrating the attributes from all segments. The segment view, though being able to depict the local traffic conditions straightforwardly, is insufficient to embody the intrinsic structure of trajectories on the road network. To overcome the limitation, this study proposes multi-view trajectory representation that comprehensively interprets a trajectory from the segment-, link-, and intersection-views. To fulfill the purpose, we design a hierarchical self-attention network (HierETA) that accurately models the local traffic conditions and the underlying trajectory structure. Specifically, a segment encoder is developed to capture the spatio-temporal dependencies at a fine granularity, within which an adaptive self-attention module is designed to boost performance. Further, a joint link-intersection encoder is developed to characterize the natural trajectory structure consisting of alternatively arranged links and intersections. Afterward, a hierarchy-aware attention decoder is designed to realize a tradeoff between the multi-view spatio-temporal features. The hierarchical encoders and the attentive decoder are simultaneously learned to achieve an overall optimality. Experiments on two large-scale practical datasets show the superiority of HierETA over the state-of-the-arts.

Multimodal optimization problems have multiple satisfactory solutions to identify. Most of the existing works conduct the search based on the information of the current population, which can be inefficient. This article proposes a probabilistic niching evolutionary computation framework that guides the future search based on more sufficient historical information, in order to locate diverse and high-quality solutions. A binary space partition tree is built to structurally organize the space visiting information. Based on the tree, a probabilistic niching strategy is defined to reinforce exploration and exploitation by making full use of the structural historical information. The proposed framework is universal for incorporating various baseline niching algorithms. In this article, we integrate the proposed framework with two niching algorithms: 1) a distance-based differential evolution algorithm and 2) a topology-based particle swarm optimization algorithm. The two new algorithms are evaluated on 20 multimodal optimization test functions. The experimental results show that the proposed framework helps the algorithms obtain competitive performance. They outperform a number of state-of-the-art niching algorithms on most of the test functions.

The automatic itinerary planning service requires to generate multiple-day schedules automatically under user-specified POIs and constraints. Knowing as an NP-Hard optimization problem, the task is commonly solved by (meta-)heuristic algorithms such as the genetic algorithms (GAs). However, considering the concurrent requests received by a web server in practice, the time efficiency of the existing itinerary planners can be rather unsatisfactory. To address the issue, this paper proposes a computational approach that hybridizing a GA with the reinforcement learning (RL) technology. The benefit is that we no longer need to re-execute the GA for each new request arrived. Instead, the approach keeps the historical solutions in track and maintains a RL agent to sequentially decide how to handle each new request. Experimental results show that the proposed approach is able to stably provide high-quality solutions, while greatly reducing the average time overhead of the web server.

Estimated time of arrival (ETA) is an important task in Intelligent Transportation Systems. Usually, the task involves a large amount of spatial-temporal data and is affected by different factors such as route distance, road capacity, traffic lights, and the real-time traffic condition. Real-time traffic conditions are highly uncertain and dynamic, which makes ETA challenging. For this reason, we propose an ETA model that incorporates the task of traffic condition prediction. Specifically, we introduce a Geo-Attention Network that combines a geo-location encoder and the geo-attentioned graph convolution to predict traffic conditions. Then, we use convolution network and recurrent neural network to capture the spatial and temporal correlations. Finally, we learn to estimate the arrival time and the traffic conditions simultaneously in a multi-task learning component. Extensive experiments have been carried out on the large-scale floating car data provided by GISCUP 2021, and excellent results have been achieved.

In many practical applications, it is crucial to perform automatic data clustering without knowing the number of clusters in advance. The evolutionary computation paradigm is good at dealing with this task, but the existing algorithms encounter several deficiencies, such as the encoding redundancy and the cross-dimension learning error. In this article, we propose a novel elastic differential evolution algorithm to solve automatic data clustering. Unlike traditional methods, the proposed algorithm considers each clustering layout as a whole and adapts the cluster number and cluster centroids inherently through the variable-length encoding and the evolution operators. The encoding scheme contains no redundancy. To enable the individuals of different lengths to exchange information properly, we develop a subspace crossover and a two-phase mutation operator. The operators employ the basic method of differential evolution and, in addition, they consider the spatial information of cluster layouts to generate offspring solutions. Particularly, each dimension of the parameter vector interacts with its correlated dimensions, which not only adapts the cluster number but also avoids the cross-dimension learning error. The experimental results show that our algorithm outperforms the state-of-the-art algorithms that it is able to identify the correct number of clusters and obtain a good cluster validation value.

Sensor activity scheduling is critical for prolonging the lifetime of wireless sensor networks (WSNs). However, most existing methods assume sensors to have one fixed sensing range. Prevalence of sensors with adjustable sensing ranges posts two new challenges to the topic: 1) expanded search space, due to the rise in the number of possible activation modes and 2) more complex energy allocation, as the sensors differ in the energy consumption rate when using different sensing ranges. These two challenges make it hard to directly solve the lifetime maximization problem of WSNs with range-adjustable sensors (LM-RASs). This article proposes a neighborhood-based estimation of distribution algorithm (NEDA) to address it in a recursive manner. In NEDA, each individual represents a coverage scheme in which the sensors are selectively activated to monitor all the targets. A linear programming (LP) model is built to assign activation time to the schemes in the population so that their sum, the network lifetime, can be maximized conditioned on the current population. Using the activation time derived from LP as individual fitness, the NEDA is driven to seek coverage schemes promising for prolonging the network lifetime. The network lifetime is thus optimized by repeating the steps of the coverage scheme evolution and LP model solving. To encourage the search for diverse coverage schemes, a neighborhood sampling strategy is introduced. Besides, a heuristic repair strategy is designed to fine-tune the existing schemes for further improving the search efficiency. Experimental results on WSNs of different scales show that NEDA outperforms state-of-the-art approaches. It is also expected that NEDA can serve as a potential framework for solving other flexible LP problems that share the same structure with LM-RAS.

As the cornerstone for joint dimension reduction and feature extraction, extensive linear projection algorithms were proposed to fit various requirements. When being applied to image data, however, existing methods suffer from representation deficiency since the multi-way structure of the data is (partially) neglected. To solve this problem, we propose a novel Low-Rank Preserving t-Linear Projection (LRP-tP) model that preserves the intrinsic structure of the image data using t-product-based operations. The proposed model advances in four aspects: 1) LRP-tP learns the t-linear projection directly from the tensorial dataset so as to exploit the correlation among the multi-way data structure simultaneously; 2) to cope with the widely spread data errors, e.g., noise and corruptions, the robustness of LRP-tP is enhanced via self-representation learning; 3) LRP-tP is endowed with good discriminative ability by integrating the empirical classification error into the learning procedure; 4) an adaptive graph considering the similarity and locality of the data is jointly learned to precisely portray the data affinity. We devise an efficient algorithm to solve the proposed LRP-tP model using the alternating direction method of multipliers. Extensive experiments on image feature extraction have demonstrated the superiority of LRP-tP compared to the state-of-the-arts.

In multi-view subspace clustering, the low-rankness of the stacked self-representation tensor is widely accepted to capture the high-order cross-view correlation. However, using the nuclear norm as a convex surrogate of the rank function, the self-representation tensor exhibits strong connectivity with dense coefficients. When noise exists in the data, the generated affinity matrix may be unreliable for subspace clustering as it retains the connections across inter-cluster samples due to the lack of sparsity. Since both the connectivity and sparsity of the self-representation coefficients are curial for subspace clustering, we propose a Reliable Multi-View Affinity Learning (RMVAL) method so as to optimize both properties in a single model. Specifically, RMVAL employs the low-rank tensor constraint to yield a well-connected yet dense solution, and purifies the densely connected self-representation tensor by preserving only the connections in local neighborhoods using the$l_1$-norm regularization. This way, the strong connections on the self-representation tensor are retained and the trivial coefficients corresponding to the inter-cluster connections are suppressed, leading to a “clean” self-representation tensor and also a reliable affinity matrix. We propose an efficient algorithm to solve RMVAL using the alternating direction method of multipliers. Extensive experiments on benchmark databases have demonstrated the superiority of RMVAL.

To learn the self-representation matrices/tensor that encodes the intrinsic structure of the data, existing multiview self-representation models consider only the multiview features and, thus, impose equal membership preference across samples. However, this is inappropriate in real scenarios since the prior knowledge, e.g., explicit labels, semantic similarities, and weak-domain cues, can provide useful insights into the underlying relationship of samples. Based on this observation, this article proposes a prior knowledge regularized multiview self-representation (P-MVSR) model, in which the prior knowledge, multiview features, and high-order cross-view correlation are jointly considered to obtain an accurate self-representation tensor. The general concept of "prior knowledge" is defined as the complement of multiview features, and the core of P-MVSR is to take advantage of the membership preference, which is derived from the prior knowledge, to purify and refine the discovered membership of the data. Moreover, P-MVSR adopts the same optimization procedure to handle different prior knowledge and, thus, provides a unified framework for weakly supervised clustering and semisupervised classification. Extensive experiments on real-world databases demonstrate the effectiveness of the proposed P-MVSR model.

Real-time taxi-passenger matching plays a critical role in modern taxi dispatch systems. Currently, the greedy strategy is widely adopted, which limits the quality of the service (QoS) and the profit of the entire system. There are two crucial tasks in this system: 1) the pairwise prioritization and 2) the matching of taxi-passenger pairs. In this paper, we develop a two-stage taxi-passenger matching system to deal with these two tasks. In the first stage, we design a fuzzy controller to assign a priority score to each taxi-passenger pair in real time. To ensure its performance on providing good QoS and profit, the fuzzy controller is optimized by an offline differential evolution algorithm. New individual representation is designed to optimize the membership functions and fuzzy rule base simultaneously. To accelerate the optimization process, the algorithm is implemented in a parallel way. Then, in the second stage, considering the priority scores as weights in the bipartite graph of taxi and passenger sets, we further apply a polynomial Kuhn-Munkres algorithm to find the maximum weight perfect matching in the bipartite graph. Simulated results validate the effectiveness of the proposed algorithm, which is able to enhance the QoS provided by the taxi system and improve the profit gained by the taxi service company.

Multi-solution traveling salesman problem has diverse optimal routes. To obtain the different optimal solutions, current researches incorporate evolutionary algorithms with niching techniques. However, without knowing the problem characteristics in advance, the algorithms suffer from difficulties in setting the niching parameters. To address this issue, we utilize a graph neural network to predict a prior knowledge about the optimal tour length. Then, with the prior estimate, the niche radius can be adjusted for a specific problem. We develop a niching evolutionary algorithm that utilizes the calculated niche radius to identify diverse niches. Besides, a selective local search strategy is embedded into the algorithm to enhance the search capability. The experimental results show that the proposed algorithm has a competitive performance over the comparison algorithms on the benchmark suite.

As a global optimization technique, the evolutionary algorithms provide powerful solvers to the data clustering problem. However, the individual representations in evolutionary clustering algorithms exist redundancy and inconsistency problems, which not only wastes the search efforts but also disorders the mutual learning process between individuals. To address the problems, in this paper, we propose a genetic sequence resorting method. This method first identifies a reference parameter vector and then resorts the order of the genetic sequences in each individual according to their distance to the reference vector. In this way, the solutions represented by individuals are unified, which removes redundancy and enhances the efficiency of the mutual learning in the algorithm. Incorporating the above method, a new and generic evolutionary clustering framework is developed. Under this framework, we specifically design two algorithms: one for distance-based convex clustering and the other for density-based nonconvex clustering. Experiments show that our method can effectively improve the performance of evolutionary clustering algorithms on various datasets with both convex and nonconvex cluster shapes.

Recent years have witnessed the success of deep learning in many fields. Commonly, the deep neural networks are trained by gradient-based methods, which is however ineffective in some cases when the optimization landscapes contain many local optima. In this study, we propose a novel optimization approach that combines neuroevolution with gradient-based method, which possesses the advantages of global search and fast convergence. The main challenge is the high expense of network training, especially when the network structure becomes deeper. This motivates us to utilize the concept of transfer learning which borrows knowledge from a source domain to enhance the learning ability in a target domain. Unfortunately, the design of transfer learning strategies for specific scenarios usually requires external expert knowledge. We therefore propose an adaptive transfer system (ATS) based on dataset similarity, which adaptively adjusts the transferring and retraining modules according to the similarity of the source and target tasks. Empirical studies on image classification problems demonstrate the effectiveness of the proposed algorithm. We are the first attempt to show that the neuroevolution can be successfully applied to deep transfer learning.

Multi-solution problems extensively exist in practice. Particularly, the traveling salesman problem (TSP) may possess multiple shortest tours, from which travelers can choose one according to their specific requirements. However, very few efforts have been devoted to the multi-solution problems in the discrete domain. In order to fill this research gap and to effectively tackle the multi-solution TSP, we propose a niching memetic algorithm in this article. The proposed algorithm is characterized by a niche preservation technique to enable the parallel search of multiple optimal solutions; an adaptive neighborhood strategy to balance the exploration and exploitation; a critical edge-aware method to provide effective guidance to the reproduction; and a selective local search strategy to improve the search efficiency. To evaluate the performance of the proposed algorithm, we conduct comprehensive experiments on a recently published multi-solution optimization test suite. The experimental results show that our algorithm outperforms other compared algorithms. Furthermore, the proposed algorithm is adopted to tackle problems from the well-known TSPLIB library to obtain a set of distinct but good solutions.

The subgraph isomorphism problems, which aim to map subgraphs to a given graph, are widely seen in many applications and are usually nondeterministic polynomial-time complete (NP-complete). As a representative extension of the subgraph isomorphism problem, virtual network embedding (VNE) is a key problem in datacenter scheduling and network virtualization. Existing metaheuristic approaches to VNE problems tend to schedule networks as a whole. But when the problem scale grows, the performance of these approaches may degenerate due to the curse of dimensionality. In this article, we intend to propose a divide-and-conquer evolutionary algorithm with overlapping decomposition (ODEA) to solve large-scale VNE problems. First, realizing the fact that the decision variables in graph-based optimization problems like VNE are usually nonseparable, an overlapping decomposition method is introduced by investigating the characteristic of the network structure. In this method, the critical elements which have tight connections to many other nodes can belong to multiple subcomponents. As a result, the decision variables with tight connections can always be evolved together in multiple subcomponents. Second, to combine the subsolutions into a complete feasible solution, a competitive strategy is devised. Through the competition among critical elements, the optimizing information is shared among subcomponents, which can further improve the effectiveness of ODEA. The proposed ODEA can adopt different metaheuristics as the optimizer, and we conduct experiments on both the scenarios with a single virtual network and with a series of online networks. The experimental results verify that ODEA can significantly improve the performance of different metaheuristics in large-scale VNE problems.

Neighborhood information plays an important role in improving the performance of evolutionary computation in various optimization scenarios, particularly in the context of multimodal optimization. Several neighborhood concepts, i.e., index-based neighborhood, nearest neighborhood, and fuzzy neighborhood, have been studied and engaged in the design of niching methods. However, the use of these neighborhood concepts requires the specification of some problem-related parameters, which is difficult to determine without a prior knowledge. In this paper, we introduce a new neighborhood concept based on a geometrical construction called Voronoi diagram. The new concept offers two advantages at the expense of increasing the computational complexity to a higher level. It eliminates the need of additional parameters and it is more informative than the existing ones. The information provided by the Voronoi neighbors of an individual can be exploited to estimate the evolutionary state. Based on the information, we divide the population into three groups and assign each group a different reproduction strategy to support the exploration and exploitation of the search space. We show the use of the concept in the design of an effective evolutionary algorithm for multimodal optimization. The experiments have been conducted to investigate the performance of the algorithm. The results reveal that the proposed algorithm compare favorably with the state-of-the-art algorithms designed based on other types of neighborhood concepts.

Linear discriminant analysis has been incorporated with various representations and measurements for dimension reduction and feature extraction. In this paper, we propose two-dimensional quaternion sparse discriminant analysis (2D-QSDA) that meets the requirements of representing RGB and RGB-D images. 2D-QSDA advances in three aspects: 1) including sparse regularization, 2D-QSDA relies only on the important variables, and thus shows good generalization ability to the out-of-sample data which are unseen during the training phase; 2) benefited from quaternion representation, 2D-QSDA well preserves the high order correlation among different image channels and provides a unified approach to extract features from RGB and RGB-D images; 3) the spatial structure of the input images is retained via the matrix-based processing. We tackle the constrained trace ratio problem of 2D-QSDA by solving a corresponding constrained trace difference problem, which is then transformed into a quaternion sparse regression (QSR) model. Afterward, we reformulate the QSR model to an equivalent complex form to avoid the processing of the complicated structure of quaternions. A nested iterative algorithm is designed to learn the solution of 2D-QSDA in the complex space and then we convert this solution back to the quaternion domain. To improve the separability of 2D-QSDA, we further propose 2D-QSDAw using the weighted pairwise between-class distances. Extensive experiments on RGB and RGB-D databases demonstrate the effectiveness of 2D-QSDA and 2D-QSDAw compared with peer competitors.

Automatic itinerary planning is a crucial and challenging issue in tourism. This paper proposes a novel automatic planning method to suggest multiple itineraries that satisfy the specific demands of tourists. First, a multiple-itinerary planning model is developed, which provides three customized goals for a tourist to choose and supports generating multiple D -day trips. The model makes fewer assumptions than the literature works did, while it provides more flexibility to the tourists. Then, based on the multiple-itinerary planning model, we design a niching genetic evolution approach to accomplish the automatic itinerary planning task. The genetic evolution approach guarantees a high search efficiency, while the niching strategy facilitates maintaining the population diversity. Consequently, the resultant algorithm can finally provide a number of diverse and superior solutions. Experimental results on real-world datasets show that our proposed algorithm not only outperforms state-of-the-art methods in considering different user-specified goals, but it is also capable of generating a set of diverse itineraries for the tourist to select. Additional experiments further verify the scalability of the proposed algorithm in terms of the problem size and the optimization objective.

The increasing popularity of battery-limited electric vehicles puts forward an important issue of how to charge the vehicles effectively. This problem, commonly referred to as Electric Vehicle Charging Scheduling (EVCS), has been proven to be NP-hard. Most of the existing works formulate the EVCS problem simply as a constrained shortest path finding problem and treat it by discrete optimization. However, other variables such as the charging amount of energy and the charging option at a station need to be considered in practical use. This paper hence formulates the EVCS problem as a hierarchical mixed-variable optimization problem, considering the dependency among the station selection, the charging option at each station and the charging amount settings. To adapt to the new problem model, we specifically design a Mixed-Variable Differentiate Evolution (MVDE) as the scheduling algorithm for our proposed EVCS system. The MVDE contains several specific operators, including a charging station route construction, a hierarchical mixed-variable mutation operator and a constraint-aware evaluation operator. Experimental results validate the effectiveness of our proposed MVDE-based system on both synthetic and real-world transportation networks.

The Reversible lanes optimization problem (RLOP) is a complex optimization problem in traffic management. The objective of this problem is to find an optimal direction assignment of lanes in an urban traffic network, so that the traffic capacity of urban streets could get the utmost promotion. To solve this problem efficiently, we particularly devise a histogram-based estimation of distribution algorithm (HEDA) in this paper. Specifically, during the estimation of the distribution, this algorithm considers different individuals differently based on their contributions. Besides, HEDA also combines both the current and historical population distribution information to generate offspring. Experiments conducted on ten different traffic network instances substantiate that HEDA achieves better performance than the compared method on most instances, especially on large-scale network instances.

Mobile crowdsourcing is an emerging crowdsourcing paradigm, which generates large-scale sensing tasks and sensing data. One of the major issues in mobile crowdsourcing is how to maximize social welfare through selecting appropriate sensing tasks for crowd workers and selecting appropriate workers for sensing tasks such that it can improve the effectiveness and efficiency of mobile crowdsourcing. This paper proposes an incentive mechanism to maximize social welfare for mobile crowdsourcing and, respectively, investigates worker-centric task selection and platform-centric worker selection. This paper applies an optimization algorithm in task selection for mobile crowdsourcing systems. A discrete particle swarm optimization (DPSO) algorithm for worker-centric task selection is designed to maximize the utilities of workers. In addition, a platform-centric worker selection method, which integrates multiattribute auction and two-stage auction, is proposed to maximize the utility of the platform. The performance of the proposed incentive mechanism is evaluated through experiments. The experimental results show that the proposed incentive mechanism can improve the efficiency and truthfulness of mobile crowdsourcing effectively.

Cloud workflow scheduling is significantly challenging due to not only the large scale of workflow but also the elasticity and heterogeneity of cloud resources. Moreover, the pricing model of clouds makes the execution time and execution cost two critical issues in the scheduling. This paper models the cloud workflow scheduling as a multiobjective optimization problem that optimizes both execution time and execution cost. A novel multiobjective ant colony system based on a co-evolutionary multiple populations for multiple objectives framework is proposed, which adopts two colonies to deal with these two objectives, respectively. Moreover, the proposed approach incorporates with the following three novel designs to efficiently deal with the multiobjective challenges: 1) a new pheromone update rule based on a set of nondominated solutions from a global archive to guide each colony to search its optimization objective sufficiently; 2) a complementary heuristic strategy to avoid a colony only focusing on its corresponding single optimization objective, cooperating with the pheromone update rule to balance the search of both objectives; and 3) an elite study strategy to improve the solution quality of the global archive to help further approach the global Pareto front. Experimental simulations are conducted on five types of real-world scientific workflows and consider the properties of Amazon EC2 cloud platform. The experimental results show that the proposed algorithm performs better than both some state-of-the-art multiobjective optimization approaches and the constrained optimization approaches.

Parallel test assembly has long been an important yet challenging topic in educational assessment. Cognitive diagnosis models (CDMs) are a new class of assessment models and have drawn increasing attention for being able to measure examinees' ability in detail. However, few studies have been devoted to the parallel test assembly problem in CDMs (CDM-PTA). To fill the gap, this paper models CDM-PTA as a subset-based bi-objective combinatorial optimization problem. Given an item bank, it aims to find a required number of tests that achieve optimal but balanced diagnostic performance, while satisfying important practical requests in the aspects of test length, item type distribution, and overlapping proportion. A set-based multiobjective particle swarm optimizer based on decomposition (S-MOPSO/D) is proposed to solve the problem. To coordinate with the property of CDM-PTA, S-MOPSO/D utilizes an assignment-based representation scheme and a constructive learning strategy. Through this, promising solutions can be built efficiently based on useful assignment patterns learned from personal and collective search experience on neighboring scalar problems. A heuristic constraint handling strategy is also developed to further enhance the search efficiency. Experimental results in comparison with three representative approaches validate that the proposed algorithm is effective and efficient.

This paper develops a decomposition-based coevolutionary algorithm for many-objective optimization, which evolves a number of subpopulations in parallel for approaching the set of Pareto optimal solutions. The many-objective problem is decomposed into a number of subproblems using a set of well-distributed weight vectors. Accordingly, each subpopulation of the algorithm is associated with a weight vector and is responsible for solving the corresponding subproblem. The exploration ability of the algorithm is improved by using a mating pool that collects elite individuals from the cooperative subpopulations for breeding the offspring. In the subsequent environmental selection, the top-ranked individuals in each subpopulation, which are appraised by aggregation functions, survive for the next iteration. Two new aggregation functions with distinct characteristics are designed in this paper to enhance the population diversity and accelerate the convergence speed. The proposed algorithm is compared with several state-of-the-art many-objective evolutionary algorithms on a large number of benchmark instances, as well as on a real-world design problem. Experimental results show that the proposed algorithm is very competitive.

The cooperative coevolution (CC) framework achieves a promising performance in solving large scale global optimization problems. The framework encounters difficulties on nonseparable problems, where variables interact with each other. Using the static grouping methods, variables will be theoretically grouped into one big subcomponent, whereas the random grouping strategy endures low efficiency. In this paper, a dynamic CC framework is proposed to tackle the challenge. The proposed framework works in a computationally efficient manner, in which the computational resources are allocated to a series of elitist subcomponents consisting of superior variables. First, a novel estimation method is proposed to evaluate the contribution of variables using the historical information of the best overall fitness. Based on the contribution and the interaction information, a dynamic grouping strategy is conducted to construct the dynamic subcomponent that evolves in the next evolutionary period. The constructed subcomponents are different from each other, and therefore the required parameters to control the optimization of each subcomponent vary a lot in each evolutionary period. A stage-by-stage parameter adaptation strategy is proposed to adapt the optimizer to the dynamic optimization environment. Experimental results indicate that the proposed framework achieves competitive results compared with the state-of-the-art CC frameworks.

Recent studies have shown the effectiveness of using depth information in salient object detection. However, the most commonly seen images so far are still RGB images that do not contain the depth data. Meanwhile, the human brain can extract the geometric model of a scene from an RGB-only image and hence provides a 3D perception of the scene. Inspired by this observation, we propose a new concept named RGB-'D' saliency detection, which derives pseudo depth from the RGB images and then performs 3D saliency detection. The pseudo depth can be utilized as image features, prior knowledge, an additional image channel, or independent depth-induced models to boost the performance of traditional RGB saliency models. As an illustration, we develop a new salient object detection algorithm that uses the pseudo depth to derive a depth-driven background prior and a depth contrast feature. Extensive experiments on several standard databases validate the promising performance of the proposed algorithm. In addition, we also adapt two supervised RGB saliency models to our RGB-'D' saliency framework for performance enhancement. The results further demonstrate the generalization ability of the proposed RGB-'D' saliency framework.

Cross-docks serve as distribution centers where shipments from different vendors are first consolidated according to their destinations, and then delivered to the retailers directly, with little or no storage in between. A critical problem encountered in the operation of cross-docks is the assignment of receiving and shipping doors, which greatly influences the labor or machinery cost of transferring the shipments between inbound and outbound transports. We show that the cross-dock door assignment problem (CDAP) is strictly non-deterministic polynomial-time complete. Although some deterministic algorithms have been reported to handle small-scale problems, the solutions to the middle- and large-scale CDAPs progressed at a slow pace. In this paper, we develop a nature-inspired dual-colony ant algorithm for CDAP, in which the two colonies of ants cooperatively search the optimal assignments of receiving and shipping doors to minimize the transferring costs of shipments. A collaborative local search strategy is designed and incorporated into the algorithm to enhance the search efficiency. Experiments have been conducted on a number of problem instances with different cross-dock sizes and freight flow patterns. The results show that the proposed algorithm is very competitive and can provide better solutions than the state-of-the-art heuristic algorithms.

As the mutation strategy and algorithmic parameters in differential evolution (DE) are sensitive to the problems being solved, a hot research topic is to adaptively control the strategy and parameters according to the requirements of the problem. In the literature, most adaptive DE use either historical experiences of the population or heuristic information of the individuals to promote adaptation. In this paper, we develop a novel variant of adaptive DE, utilizing both the historical experience and heuristic information for the adaptation. In this novel historical and heuristic DE (HHDE), each individual dynamically adjusts its mutation strategy and associated parameters not only by learning from previous successful experience of the whole population, but also according to heuristic information related with its own current state. These help the algorithm select a more suitable mutation strategy and determinate better parameters for each individual in different evolutionary stages. The performance of the proposed HHDE is extensively evaluated on 30 benchmark functions with different dimensions. Experimental results confirm the competitiveness of the proposed algorithm to a number of DE variants.

Nowadays, large-scale optimization problems are ubiquitous in many research fields. To deal with such problems efficiently, this paper proposes a distributed differential evolution with adaptive mergence and split (DDE-AMS) on subpopulations. The novel mergence and split operators are designed to make full use of limited population resource, which is important for large-scale optimization. They are adaptively performed based on the performance of the subpopulations. During the evolution, once a subpopulation finds a promising region, the current worst performing subpopulation will merge into it. If the merged subpopulation could not continuously provide competitive solutions, it will be split in half. In this way, the number of subpopulations is adaptively adjusted and better performing subpopulations obtain more individuals. Thus, population resource can be adaptively arranged for subpopulations during the evolution. Moreover, the proposed algorithm is implemented with a parallel master-slave manner. Extensive experiments are conducted on 20 widely used large-scale benchmark functions. Experimental results demonstrate that the proposed DDE-AMS could achieve competitive or even better performance compared with several state-of-the-art algorithms. The effects of DDE-AMS components, adaptive behavior, scalability, and parameter sensitivity are also studied. Finally, we investigate the speedup ratios of DDE-AMS with different computation resources.

Superpixel segmentation has been of increasing importance in many computer vision applications recently. To handle the problem, most state-of-the-art algorithms either adopt a local color variance model or a local optimization algorithm. This paper develops a new approach, named differential evolutionary superpixels, which is able to optimize the global properties of segmentation by means of a global optimizer. We design a comprehensive objective function aggregating within-superpixel error, boundary gradient, and a regularization term. Minimizing the within-superpixel error enforces the homogeneity of superpixels. In addition, the introduction of boundary gradient drives the superpixel boundaries to capture the natural image boundaries, so as to make each superpixel overlaps with a single object. The regularizer further encourages producing similarly sized superpixels that are friendly to human vision. The optimization is then accomplished by a powerful global optimizer-differential evolution. The algorithm constantly evolves the superpixels by mimicking the process of natural evolution, while using a linear complexity to the image size. Experimental results and comparisons with eleven state-of-the-art peer algorithms verify the promising performance of our algorithm.

Superpixel segmentation targets at grouping pixels in an image into atomic regions whose boundaries align well with the natural object boundaries. This paper first proposes a new feature representation for superpixel segmentation that holistically embraces color, contour, texture, and spatial features. Then, we introduce a clustering-based discriminability measure to iteratively evaluate the importance of different features. Integrating the feature representation and the discriminability measure, we propose a novel content-adaptive superpixel (CAS) segmentation algorithm. CAS is able to automatically and iteratively adjust the weights of different features to fit various properties of image instances. Experiments on several challenging datasets demonstrate that the proposed CAS outperforms the state-of-the-art methods and has a low computational cost.

Many trajectory-based applications require an essential step of mapping raw GPS trajectories onto the digital road network accurately. This task, commonly referred to as map matching, is challenging due to the measurement error of GPS devices in critical environment and the sampling error caused by long sampling intervals. Traditional algorithms focus on either a local or a global perspective to deal with the problem. To further improve the performance, this paper develops a novel map matching model that considers local geometric/topological information and a global similarity measure simultaneously. To accomplish the optimization goal in this complex model, we adopt an ant colony optimization algorithm that mimics the path finding process of ants transporting food in nature. The algorithm utilizes both local heuristic and global fitness to search the global optimum of the model. Experimental results verify that the proposed algorithm is able to provide accurate map matching results within a relatively short execution time.

Most learning methods contain optimization as a substep, where the nondifferentiability and multimodality of objectives push forward the interplay of evolutionary optimization algorithms and machine learning models. The recently emerged evolutionary multimodal optimization (MMOP) technique enables the learning of diverse sets of effective parameters for the models simultaneously, providing new opportunities to the applications requiring both accuracy and diversity, such as ensemble, interactive, and interpretive learning. Targeting at locating multiple optima simultaneously in the multimodal landscape, this paper develops an efficient neighborhood-based niching algorithm. Bare-bones differential evolution is used as the baseline. Further, using Gaussian mutation with local mean and standard deviations, the neighborhoods capture niches that match well with the contours of peaks in the landscape. To increase diversity and enhance global exploration, the proposed algorithm embeds a diversity preserving operator to reinitialize converged or overlapped neighborhoods. The experimental results verify that the proposed algorithm has superior and consistent performance for a wide range of MMOP problems. Further, the algorithm has been successfully applied to train neural network ensembles, which validates its effectiveness and benefits of learning multimodal parameters.

Taxi dispatch is a critical issue for taxi company to consider in modern life. This paper formulates the problem into a taxi-passenger matching model and proposes a parallel ant colony optimization algorithm to optimize the model. As the search space is large, we develop a region-dependent decomposition strategy to divide and conquer the problem. To keep the global performance, a critical region is defined to deal with the communications and interactions between the subregions. The experimental results verify that the proposed algorithm is effective, efficient, and extensible, which outperforms the traditional global perspective greedy algorithm in terms of both accuracy and efficiency.

Virtual network embedding (VNE), which is a significant problem in cloud computing, has gained much attention among many researchers recently. Due to the NP-hardness of VNE, the existing solvers are either inefficient or inaccurate. This paper develops a novel algorithm based on the ant colony system (ACS). To solve the VNE problem, the algorithm structure concentrates on the link mapping from virtual network to substrate network. Particularly, for a specific virtual network request, we first sort the embedding sequence of virtual nodes according to their link resources. Then, ACS is used to embed the virtual nodes onto substrate nodes according the sorted sequence, while the virtual links are mapped via a shortest path strategy for the embedded nodes. For the first time, we propose a link resource heuristic information and incorporate it into the search process of ACS. The link resource heuristic information has two significant effects, one is to make virtual nodes tend to be embedded on the substrate nodes that cost less bandwidth, and the other is to confirm the connectivity of the substrate nodes that embed the virtual nodes. The proposed algorithm improves the optimization performance of VNE when compared with a few existing algorithms, while it substantially reduces the cost of time.

Superpixel segmentation targets at grouping pixels in an image into atomic regions that align well with the natural object boundaries. In this paper, we propose a novel superpixel segmentation method based on an iterative and adaptive clustering algorithm that embraces color, contour, texture, and spatial features together. The algorithm adjusts the weights of different features automatically in a content-aware way, so as to fit the requirements of various image instances. More specifically, in each iteration, the weights in the aggregation function are adjusted according to the discriminabilities of features in the current working scenario. This way, the algorithm not only possesses improved robustness but also relieves the burden of setting the parameters manually. Experimental verification shows that the algorithm outperforms existing peer algorithms in terms of commonly used evaluation metrics, while using a low computational cost.

The cooperative co-evolution (CC) framework is one of the most efficient methods to solve large scale optimization problems. The traditional CC framework divides decision variables into several mutually-exclusive groups. In this paper, we propose the overlapped cooperative co-evolution (OCC) framework for large scale optimization problems. In OCC framework, the decision variables that have strong impacts on the optimization are overlapped by different groups. First, we devise the delta-disturbance strategy to detect the influential variables. Then the overlapped grouping strategy is proposed to overlap the influential variables. Finally, the OCC framework is proposed to allocate more computation resources to the influential decision variables. To compare the performance of CC and OCC, we combine two frameworks with the random grouping strategy and the differential grouping strategy, and the comparative experiments are conducted on the CEC2010 benchmark functions. The experimental results verify that the proposed OCC framework is promising through comparing with the CC framework.

Niching techniques have recently been incorporated into evolutionary algorithms (EAs) for multisolution optimization in multimodal landscape. However, existing niching techniques inevitably increase the time complexity of basic EAs due to the computation of the distance matrix of individuals. In this paper, we propose a fast niching technique. The technique avoids pairwise distance calculations by introducing the locality sensitive hashing, an efficient algorithm for approximately retrieving nearest neighbors. Individuals are projected to a number of buckets by hash functions. The similar individuals possess a higher probability of being hashed into the same bucket than the dissimilar ones. Then, interactions between individuals are limited to the candidates that fall in the same bucket to achieve local evolution. It is proved that the complexity of the proposed fast niching is linear to the population size. In addition, this mechanism induces stable niching behavior and it inherently keeps a balance between the exploration and exploitation of multiple optima. The theoretical analysis conducted in this paper suggests that the proposed technique is able to provide bounds for the exploration and exploitation probabilities. Experimental results show that the fast niching versions of the multimodal algorithms can exhibit similar or even better performance than their original ones. More importantly, the execution time of the algorithms is significantly reduced.

Many-objective optimization has posed great challenges to existing evolutionary algorithms that are designed for solving two- or three-objective problems. Most of the algorithms do not scale well with the number of objectives due to the expansion of the objective space. In this paper, a hybrid evolutionary algorithm with dual populations (HEA-DP) is proposed to tackle many-objective problems. The algorithm combines the advantages of decomposition-based and indicator-based approaches by maintaining two populations. The fitness values of individuals in the first population are determined by an aggregation function, while individuals in the second population are evaluated according to an efficient performance indicator. The information about the objective space is shared by employing a reproduction strategy that chooses parents from both populations. In this way, the algorithm can explore the objective space more thoroughly and can have more stable performance. Several state-of-the-art many-objective algorithms are adopted as peer algorithms to validate the proposed algorithm. We test the algorithms on two commonly used many-objective problem suites using different numbers of objectives. Numerical results indicate that HEA-DP is highly competitive in most of the problem instances.

This paper deals with the superpixel segmentation problem using a powerful global optimization technique: Differential Evolution. The algorithm mimics the process of nature evolution to realize efficient optimization, and it poses no restrictions on the form of objective functions. This way, we develop a novel and comprehensive objective function considering both local and global costs in the segmentation, including within-superpixel error, boundary gradient, a regularization term. The proposed method can produce superpixels in a computational time linear to the image size. Experimental results validate the competitive performance of our algorithm in terms of boundary adherence and segmentation capability.

Social learning in particle swarm optimization (PSO) helps collective efficiency, whereas individual reproduction in genetic algorithm (GA) facilitates global effectiveness. This observation recently leads to hybridizing PSO with GA for performance enhancement. However, existing work uses a mechanistic parallel superposition and research has shown that construction of superior exemplars in PSO is more effective. Hence, this paper first develops a new framework so as to organically hybridize PSO with another optimization technique for "learning." This leads to a generalized "learning PSO" paradigm, the *L-PSO. The paradigm is composed of two cascading layers, the first for exemplar generation and the second for particle updates as per a normal PSO algorithm. Using genetic evolution to breed promising exemplars for PSO, a specific novel *L-PSO algorithm is proposed in the paper, termed genetic learning PSO (GL-PSO). In particular, genetic operators are used to generate exemplars from which particles learn and, in turn, historical search information of particles provides guidance to the evolution of the exemplars. By performing crossover, mutation, and selection on the historical information of particles, the constructed exemplars are not only well diversified, but also high qualified. Under such guidance, the global search ability and search efficiency of PSO are both enhanced. The proposed GL-PSO is tested on 42 benchmark functions widely adopted in the literature. Experimental results verify the effectiveness, efficiency, robustness, and scalability of the GL-PSO.

This paper studies the optimization problem of topological active net (TAN), which is often seen in image segmentation and shape modeling. A TAN is a topological structure containing many nodes, whose positions must be optimized while a predefined topology needs to be maintained. TAN optimization is often time-consuming and even constructing a single solution is hard to do. Such a problem is usually approached by a "best improvement local search" (BILS) algorithm based on deterministic search (DS), which is inefficient because it spends too much efforts in nonpromising probing. In this paper, we propose the use of micro-differential evolution (DE) to replace DS in BILS for improved directional guidance. The resultant algorithm is termed deBILS. Its micro-population efficiently utilizes historical information for potentially promising search directions and hence improves efficiency in probing. Results show that deBILS can probe promising neighborhoods for each node of a TAN. Experimental tests verify that deBILS offers substantially higher search speed and solution quality not only than ordinary BILS, but also the genetic algorithm and scatter search algorithm.

Operating mode scheduling is crucial for the lifetime of wireless sensor networks (WSNs). However, the growing scale of networks has made such a scheduling problem more challenging, as existing set cover and evolutionary algorithms become unable to provide satisfactory efficiency due to the curse of dimensionality. In this paper, a Kuhn–Munkres (KM) parallel genetic algorithm is developed to solve the set cover problem and is applied to the lifetime maximization of large-scale WSNs. The proposed algorithm schedules the sensors into a number of disjoint complete cover sets and activates them in batch for energy conservation. It uses a divide-and-conquer strategy of dimensionality reduction, and the polynomial KM algorithm a are hence adopted to splice the feasible solutions obtained in each subarea to enhance the search efficiency substantially. To further improve global efficiency, a redundant-trend sensor schedule strategy was developed. Additionally, we meliorate the evaluation function through penalizing incomplete cover sets, which speeds up convergence. Eight types of experiments are conducted on a distributed platform to test and inform the effectiveness of the proposed algorithm. The results show that it offers promising performance in terms of the convergence rate, solution quality, and success rate.

Destination prediction is very important in location-based services such as recommendation of targeted advertising location. Most current approaches always predict destination according to existing trip based on history trajectories. However, no existing work has considered the difference between the effects of passing-by locations and the destination in history trajectories, which seriously impacts the accuracy of predicted results as the destination can indicate the purpose of traveling. Meanwhile, the temporal information of history trajectories in destination prediction plays an important role. On one hand, the history trajectories in different periods also differ in the influence, e.g., the history trajectories from last week can reflect the status quo more accurately than the history trajectories two years ago. On the other hand, the history trajectories in different time slots reflect different facts of traffic and moving habits of people, e.g., visiting a restaurant in the daytime and visiting a bar at night. Although a huge amount of history trajectories can be achieved in the era of big data, it is still far from covering all the query trajectories since a road network is widely distributed and trajectory data is sparse. The temporal sensitivity of history trajectories highlights the sparsity problem even more. Therefore, we propose a novel model T-DesP to solve the aforementioned problems. The model is comprised of two modules: trajectory learning and destination prediction. In the module of trajectory learning, a novel method called the mirror absorbing Markov chain model is proposed for modeling the trajectories for isolating the destination. We build a transition tensor to deduce the transition probability between each location pair in a particular time slot. To address the data sparsity problem, we fill the missing values in transition tensor through a context-aware tensor decomposition approach. In the module of destination prediction, an absorbing tensor is derived from the filled transition tensor, and the theoretical model is established for destination prediction. The experiments prove the effectiveness and efficiency of T-DesP.

The aim of multimodal optimization is to locate multiple optima of a given problem. Evolutionary algorithms (EAs) are one of the most promising candidates for multimodal optimization. However, due to the use of greedy selection operators, the population of an EA will generally converge to one region of attraction. By incorporating a well-designed selection operator that can facilitate the formation of different species, EAs will be able to allow multiple convergence. Following this research avenue, we propose a novel selection operator, namely, queueing selection (QS) and integrate it with one of the most promising DE variants, called composite differential evolution (CoDE). The integrated algorithm (denoted by CoDE-QS) inherits the strong global search ability of CoDE and is capable of finding and maintaining multiple optima. It has been tested on the CEC2013 benchmark functions. Experimental results show that CoDE-QS is very competitive.

In this work we focus on reconstruction of cross-cut shredded text documents (RCCSTD), which is of high interest in the fields of forensics and archeology. A novel genetic algorithm, with splicing-driven crossover, four mutation operators, and a row-oriented elitism strategy, is proposed to improve the capability of solving RCCSTD in complex space. We also design a novel and comprehensive objective function based on both edge and empty vector-based splicing error to guarantee that the correct reconstruction always has the lowest cost value. Experiments are conducted on six RCCSTD scenarios, with experimental results showing that the proposed algorithm significantly outperforms the previous best-known algorithms for this problem.

Existing multiobjective evolutionary algorithms (MOEAs) tackle a multiobjective problem either as a whole or as several decomposed single-objective sub-problems. Though the problem decomposition approach generally converges faster through optimizing all the sub-problems simultaneously, there are two issues not fully addressed, i.e., distribution of solutions often depends on a priori problem decomposition, and the lack of population diversity among sub-problems. In this paper, a MOEA with double-level archives is developed. The algorithm takes advantages of both the multiobjective-problem-level and the sub-problem-level approaches by introducing two types of archives, i.e., the global archive and the sub-archive. In each generation, self-reproduction with the global archive and cross-reproduction between the global archive and sub-archives both breed new individuals. The global archive and sub-archives communicate through cross-reproduction, and are updated using the reproduced individuals. Such a framework thus retains fast convergence, and at the same time handles solution distribution along Pareto front (PF) with scalability. To test the performance of the proposed algorithm, experiments are conducted on both the widely used benchmarks and a set of truly disconnected problems. The results verify that, compared with state-of-the-art MOEAs, the proposed algorithm offers competitive advantages in distance to the PF, solution coverage, and search speed.

Utilizing cumulative correlation information already existing in an evolutionary process, this paper proposes a predictive approach to the reproduction mechanism of new individuals for differential evolution (DE) algorithms. DE uses a distributed model (DM) to generate new individuals, which is relatively explorative, whilst evolution strategy (ES) uses a centralized model (CM) to generate offspring, which through adaptation retains a convergence momentum. This paper adopts a key feature in the CM of a covariance matrix adaptation ES, the cumulatively learned evolution path (EP), to formulate a new evolutionary algorithm (EA) framework, termed DEEP, standing for DE with an EP. Without mechanistically combining two CM and DM based algorithms together, the DEEP framework offers advantages of both a DM and a CM and hence substantially enhances performance. Under this architecture, a self-adaptation mechanism can be built inherently in a DEEP algorithm, easing the task of predetermining algorithm control parameters. Two DEEP variants are developed and illustrated in the paper. Experiments on the CEC'13 test suites and two practical problems demonstrate that the DEEP algorithms offer promising results, compared with the original DEs and other relevant state-of-the-art EAs.

This paper proposes a path planner for autonomous underwater vehicles (AUVs) in 3-D underwater space. We simulate an underwater space with rugged seabed and suspending obstacles, which is close to real world. In the proposed representation scheme, the problem space is decomposed into parallel subspaces and each subspace is described by a grid method. The paths of AUVs are simplified as a set of successive points in the problem space. By jointing these waypoints, the entire path of the AUV is obtained. A cost function with penalty method takes into account the length, energy consumption, safety and curvature constraints of AUVs. It is applied to evaluate the quality of paths. Differential evolution (DE) algorithm is used as a black-box optimization tool to provide optimal solutions for the path planning. In addition, we adaptively adjust the parameters of DE according to population distribution and the blockage of parallel subspaces so as to improve its performance. Experiments are conducted on 6 different scenarios. The results validate that the proposed algorithm is effective for improving solution quality and avoiding premature convergence.

Traditionally, the Evolutionary Computation (EC) paradigm is inspired by Darwinian evolution or the swarm intelligence of animals. Bandura's Social Learning Theory pointed out that the social learning behavior of humans indicates a high level of intelligence in nature. We found that such intelligence of human society can be implemented by numerical computing and be utilized in computational algorithms for solving optimization problems. In this paper, we design a novel and generic optimization approach that mimics the social learning process of humans. Emulating the observational learning and reinforcement behaviors, a virtual society deployed in the algorithm seeks the strongest behavioral patterns with the best outcome. This corresponds to searching for the best solution in solving optimization problems. Experimental studies in this paper showed the appealing search behavior of this human intelligence-inspired approach, which can reach the global optimum even in ill conditions. The effectiveness and high efficiency of the proposed algorithm has further been verified by comparing to some representative EC algorithms and variants on a set of benchmarks.

The performance of a multimodal evolutionary algorithm is highly sensitive to the setting of population size. This paper introduces a generic archive technique to reduce the importance of properly setting the population size parameter. The proposed archive technique contains two components: subpopulation identification and convergence detection. The first component is used to identify subpopulations in a number of individuals while the second one is used to determine whether a subpopulation is converged. By using the two components, converged subpopulations are identified, and then, individuals in the converged subpopulations are stored in an external archive and re-initialized to search for other optima. We integrate the archive technique with several state-of-the-art PSO-based multimodal algorithms. Experiments are carried out on a recently proposed multimodal problem set to investigate the effect of the archive technique. The experimental results show that the proposed method can reduce the influence of the population size parameter and improve the performance of multimodal algorithms.

The performance of differential evolution (DE) largely depends on its mutation strategy and control parameters. In this paper, we propose an adaptive DE (ADE) algorithm with a new mutation strategy DE/lbest/1 and a two-level adaptive parameter control scheme. The DE/lbest/1 strategy is a variant of the greedy DE/best/1 strategy. However, the population is mutated under the guide of multiple locally best individuals in DE/lbest/1 instead of one globally best individual in DE/best/1. This strategy is beneficial to the balance between fast convergence and population diversity. The two-level adaptive parameter control scheme is implemented mainly in two steps. In the first step, the population-level parameters Fp and CRp for the whole population are adaptively controlled according to the optimization states, namely, the exploration state and the exploitation state in each generation. These optimization states are estimated by measuring the population distribution. Then, the individual-level parameters Fi and CRi for each individual are generated by adjusting the population-level parameters. The adjustment is based on considering the individual's fitness value and its distance from the globally best individual. This way, the parameters can be adapted to not only the overall state of the population but also the characteristics of different individuals. The performance of the proposed ADE is evaluated on a suite of benchmark functions. Experimental results show that ADE generally outperforms four state-of-the-art DE variants on different kinds of optimization problems. The effects of ADE components, parameter properties of ADE, search behavior of ADE, and parameter sensitivity of ADE are also studied. Finally, we investigate the capability of ADE for solving three real-world optimization problems.

Traditional particle swarm optimization (PSO) algorithms adopt completely regular network as topologies, which may encounter the problems of premature convergence and insufficient efficiency. In order to improve the performance of PSO, this paper proposes a novel topology based on small-world network. Each particle in the swarm interacts with its cohesive neighbors and by chance to communicate with some distant particles via small-world randomization. In order to improve search diversity, each dimension of the swarm is assigned with a specific network, and the particle is allowed to follow the historical information of different neighbors on different dimensions. Moreover, in the proposed small-world topology, the neighborhood size and the randomization probability are adaptively adjusted based on the convergence state of the swarm. By applying the topology adaptation mechanism, the particle swarm is able to balance its exploitation and exploration abilities during the search process. Experiments were conducted on a set of classical benchmark functions. The results verify the effectiveness and high efficiency of the proposed PSO algorithm with adaptive small-world topology when compared with some other PSO variants.

The TSP problem is considered as classical discrete optimization grouping problem, which is widely used in practice, but it is real a difficult NP problem. Simultaneously differential evolution (DE) algorithm has been proven to be a powerful optimization algorithm. Since the mutation process of DE contains a series of arithmetic operators operating on continuous space, few algorithms based on DE solve this problem nicely and the advantages of DE in continuous space cannot be used to solve TSP. To take full advantages of the strengths of DE, this paper proposes a set-based DE (S-DE) which completely follows the procedure of the original DE. We present a representation scheme to characterize the discrete problem space and by redefining its basic concept and all related operators in mutation, DE can operate directly on the original set space of the discrete optimization problems instead of performing a space transformation. In that way, the searching features of DE in continuous space is kept. In experiment, we test the performance of our proposed S-DE and the results show it is very promising.

Human being is the most intelligent organism in the world and the brainstorming process popularly used by them has been demonstrated to be a significant and promising way to create great ideas for problem solving. Brain storm optimization (BSO) is a new kind of swarm intelligence algorithm inspired by human being creative problem solving process. BSO transplants the brainstorming process in human being into optimization algorithm design and gains successes. BSO generally uses the grouping, replacing, and creating operators to produce ideas as many as possible to approach the problem solution generation by generation. In these operators, BSO involves mainly three control parameters named: (1) p_replce to control the replacing operator; (2) p_one to control the creating operator to create new ideas between one cluster and two clusters; and (3) p_center (p_one_center and p_two_center) to control using cluster center or random idea to create new idea. In this paper, we make investigations on these parameters to see how they affect the performance of BSO. More importantly, a new BSO variant designed according to the investigation results is proposed and its performance is evaluated.

Developing traffic signal control methods is considered as the most important way to improve the traffic efficiency of modern roundabouts. This paper applies a traffic signal controller with two fuzzy layers for signalizing roundabouts. The outer layer of the controller computes urgency degrees of all the phase subsets and then activates the most urgent subset. This mechanism helps to instantly respond to the current traffic condition of the roundabout so as to improve real-timeness. The inner layer computes extension time of the current phase and decides whether to turn to the next phase in the running phase subset. As the phase sequences are well-designed, the inner layer smoothes the traffic flows which helps to avoid traffic jam. An offline particle swarm optimization (PSO) algorithm is developed to optimize the membership functions adopted in the proposed controller. In this way, the membership functions in the controller are no longer given by human experience, but provided by the intelligent algorithm. Simulation results demonstrate that the proposed controller outperforms previous traffic signal controllers in terms of improving traffic efficiency of modern roundabouts.

Developing techniques for optimal allocation of limited resources to a set of activities has received increasing attention in recent years. In this paper, an efficient resource allocation scheme based on particle swarm optimization (PSO) is developed. Different from many existing evolutionary algorithms for solving resource allocation problems (RAPs), this PSO algorithm incorporates a novel representation of each particle in the population and a comprehensive learning strategy for the PSO search process. The novelty of this representation lies in that the position of each particle is represented by a pair of points, one on each side of the constraint hyper-plane in the problem space. The line joining these two points intersects the constraint hyper-plane and their intersection point indicates a feasible solution. With the evaluation value of the feasible solution used as the fitness value of the particle, such a representation provides an effective way to ensure the equality resource constraints in RAPs are met. Without the distraction of infeasible solutions, the particle thus searches the space smoothly. In addition, particles search for optimal solutions by learning from themselves and their neighborhood using the comprehensive learning strategy, helping prevent premature convergence and improve the solution quality for multimodal problems. This new algorithm is shown to be applicable to both single-objective and multiobjective RAPs, with performance validated by a number of benchmarks and by a real-world bed capacity planning problem. Experimental results verify the effectiveness and efficiency of the proposed algorithm.

The rapid development of radio frequency identification (RFID) technology creates the challenge of optimal deployment of an RFID network. The RFID network planning (RNP) problem involves many constraints and objectives and has been proven to be NP-hard. The use of evolutionary computation (EC) and swarm intelligence (SI) for solving RNP has gained significant attention in the literature, but the algorithms proposed have seen difficulties in adjusting the number of readers deployed in the network. However, the number of deployed readers has an enormous impact on the network complexity and cost. In this paper, we develop a novel particle swarm optimization (PSO) algorithm with a tentative reader elimination (TRE) operator to deal with RNP. The TRE operator tentatively deletes readers during the search process of PSO and is able to recover the deleted readers after a few generations if the deletion lowers tag coverage. By using TRE, the proposed algorithm is capable of adaptively adjusting the number of readers used in order to improve the overall performance of RFID network. Moreover, a mutation operator is embedded into the algorithm to improve the success rate of TRE. In the experiment, six RNP benchmarks and a real-world RFID working scenario are tested and four algorithms are implemented and compared. Experimental results show that the proposed algorithm is capable of achieving higher coverage and using fewer readers than the other algorithms.

Vehicle routing problem with time windows (VRPTW) is a well-known NP-hard combinatorial optimization problem that is crucial for transportation and logistics systems. Even though the particle swarm optimization (PSO) algorithm is originally designed to solve continuous optimization problems, in this paper, we propose a set-based PSO to solve the discrete combinatorial optimization problem VRPTW (S-PSO-VRPTW). The general method of the S-PSO-VRPTW is to select an optimal subset out of the universal set by the use of the PSO framework. As the VRPTW can be defined as selecting an optimal subgraph out of the complete graph, the problem can be naturally solved by the proposed algorithm. The proposed S-PSO-VRPTW treats the discrete search space as an arc set of the complete graph that is defined by the nodes in the VRPTW and regards the candidate solution as a subset of arcs. Accordingly, the operators in the algorithm are defined on the set instead of the arithmetic operators in the original PSO algorithm. Besides, the process of position updating in the algorithm is constructive, during which the constraints of the VRPTW are considered and a time-oriented, nearest neighbor heuristic is used. A normalization method is introduced to handle the primary and secondary objectives of the VRPTW. The proposed S-PSO-VRPTW is tested on Solomon's benchmarks. Simulation results and comparisons illustrate the effectiveness and efficiency of the algorithm.

Traffic signal control is a challenging task for traffic systems. As fuzzy logic is proved to be well suited to control some complex systems with uncertainties and human perception, it has been widely used to control the traffic signal in recent years. This paper proposes a novel fuzzy logic controller for signalizing modern roundabouts. Different from existing fuzzy traffic-signal controllers, the proposed controller consists of two fuzzy layers each of which has its own duty. According to the current traffic condition, one layer of the controller controls the phase sequence while the other layer determines the signal timing. By the cooperation of the two layers, the proposed controller is capable of immediately responding to the current traffic condition so as to reduce the vehicle delay or the queue length of waiting vehicles, as well as smoothing the traffic flows in order to reduce the risk of traffic jams. Simulation results prove the effectiveness of the proposed controller, for it can improve the traffic efficiency of the roundabout when compared with several existing controllers.

Real coded genetic algorithms (RCGAs) have been widely studied and applied to deal with continuous optimization problems for years. However, how to improve the degree of accuracy so as to produce high quality solutions is still one of the main difficulties that RCGAs face with. This paper proposes a novel mutation scheme for RCGAs. The mutation operator is defined as a linear map in the space of chromosomes (in RCGAs each chromosome is a floating point vector). It operates on a whole chromosome instead of several single genes to produce the new chromosome. The linear map is represented by a randomly generated mapping matrix which satisfies some predefined constraints. By this way, the constraints restrict the mutations of genes on a same chromosome as a whole. RCGA with the proposed mutation scheme is tested on 16 benchmark functions. Results demonstrate that the proposed scheme not only improves the solution accuracy that RCGA can obtain, but also presents a very fast convergence speed. The linear map-based mutation scheme has a bright future to improve RCGAs.

Bed allocation is a crucial issue in hospital management. This paper proposes a multi-objective comprehensive learning particle swarm optimization with a representation scheme based on binary search (BS-MOCLPSO) to deal with this problem in general hospital. The bed allocation problem (BAP) is first modeled as an M/PH/c queue. Based on the queuing theory, the mathematical forms of admission rates and bed occupancy rate is deduced for each department of the hospital. Taking the maximization of both rates as objectives, the BS-MOCLPSO generates a set of non-dominated optimal allocation decisions for the hospital manager to select. The proposed algorithm introduces a novel binary search-based representation scheme, which transforms a particle's position into a feasible allocation scheme through binary search. Simulation results on real hospital data show that the proposed algorithm can offer allocation decisions that lead to higher service level and better resource utilization.

This paper proposes a PSO-FFPP algorithm based on the particle swarm optimization (PSO) framework to solve the flight frequency programming problem (FFPP). The FFPP is to determine the flight frequency for each type of aircraft on each flight route. This problem is fundamental to an airline's operational planning because it affects the airline's profit and market share greatly. The FFPP can be formulated as an integer programming problem with constraints that is very suitable to be solved by the PSO algorithm. The proposed PSO-FFPP algorithm codes the decision variables of the FFPP with real number to represent the potential solutions and defines the optimization objective as a maximization problem for the airlines profit. A constraints handling method that combines the ideas of feasible solution preserving and infeasible solution rejection is developed. This method avoids the expense of infeasibility repair or penalty, making the algorithm simple to use and easy to extend. An integer handing process is also devised to round the real number to the nearest valid integer before feasibility check and function evaluation. This process maintains the search tendency of the PSO algorithm and can help to search in a promising region for the global optimum. The feasibility of the proposed algorithm is demonstrated and compared with the Monte Carlo method and the enumeration method on a simulation case with promising results. Experiments are also conducted to investigate the factors that affect the solution quality and computational time.

The aircraft arrival sequencing and scheduling (ASS) problem is one of the most significant problems in the air traffic control (ATC). This paper makes the first attempt to design an ant colony system (ACS) based approach to solve this NP-hard problem. In order to reduce the computational effort of the optimization process, the receding horizon control (RHC) strategy is integrated into the ACS to divide the optimization process into several sub-processes and solve them one by one. This strategy can reduce the problem scale in each sub-optimization process, resulting in lighter computational effort and higher quality solution for the whole problem. Experiments are conducted to demonstrate the effectiveness and efficiency of the proposed RHC based ACS algorithm for the ASS problem (RHC-ACS-ASS). Simulation results show that the RHC-ACS-ASS not only outperforms the GA based approaches, but also the ACS based approach without using the RHC strategy.

Ant colony optimization (ACO) has been widely and successfully applied to NP-hard combinatorial optimization problems for its strong searching ability and robustness. Recently, several extended ACO algorithms have also been proposed to deal with continuous optimization problems. However, the ACO algorithms always have slow convergence speed and encounter premature convergence in engineering applications. This paper proposes a novel adaptive parameter control method for continuous ACO algorithms. Clustering analysis is used to judge the optimization state of the algorithm and the flexible adjustment of the parameters is based on these optimization states during the training process. As an example, the adaptive control method is used to improve the performance of the continuous orthogonal ant colony (COAC). Experimental results demonstrate that the clustering-based adaptive parameters control scheme contributes to both faster convergence speed and higher solution accuracy. The proposed adaptive control method has great practical value and bright prospect.