As a cornerstone in the Evolutionary Computation (EC) domain, Differential Evolution (DE) is known for its simplicity and effectiveness in handling challenging black-box optimization problems. While the advantages of DE are well-recognized, achieving peak performance heavily depends on its hyperparameters such as the mutation factor, crossover probability, and the selection of specific DE strategies. Traditional approaches to this hyperparameter dilemma have leaned towards parameter tuning or adaptive mechanisms. However, identifying the optimal settings tailored for specific problems remains a persistent challenge. In response, we introduce MetaDE, an approach that evolves DE’s intrinsic hyperparameters and strategies using DE itself at a meta-level. A pivotal aspect of MetaDE is a specialized parameterization technique, which endows it with the capability to dynamically modify DE’s parameters and strategies throughout the evolutionary process. To augment computational efficiency, MetaDE incorporates a design that leverages parallel processing through a GPU-accelerated computing framework. Within such a framework, DE is not just a solver but also an optimizer for its own configurations, thus streamlining the process of hyperparameter optimization and problem-solving into a cohesive and automated workflow. Extensive evaluations on the CEC2022 benchmark suite demonstrate MetaDE’s promising performance. Moreover, when applied to robot control via evolutionary reinforcement learning, MetaDE also demonstrates promising performance. The source code of MetaDE is publicly accessible at: https://github.com/EMI-Group/metade.

Evolutionary multiobjective optimization (EMO) has made significant strides over the past two decades. However, as problem scales and complexities increase, traditional EMO algorithms face substantial performance limitations due to insufficient parallelism and scalability. While most work has focused on algorithm design to address these challenges, little attention has been given to hardware acceleration, thereby leaving a clear gap between EMO algorithms and advanced computing devices, such as GPUs. To bridge the gap, we propose to parallelize EMO algorithms on GPUs via the tensorization methodology. By employing tensorization, the data structures and operations of EMO algorithms are transformed into concise tensor representations, which seamlessly enables automatic utilization of GPU computing. We demonstrate the effectiveness of our approach by applying it to three representative EMO algorithms: NSGA-III, MOEA/D, and HypE. To comprehensively assess our methodology, we introduce a multiobjective robot control benchmark using a GPU-accelerated physics engine. Our experiments show that the tensorized EMO algorithms achieve speedups of up to 1113× compared to their CPU-based counterparts, while maintaining solution quality and effectively scaling population sizes to hundreds of thousands. Furthermore, the tensorized EMO algorithms efficiently tackle complex multiobjective robot control tasks, producing high-quality solutions with diverse behaviors. Source codes are available at https://github.com/EMI-Group/evomo.

The NeuroEvolution of Augmenting Topologies (NEAT) algorithm has received considerable recognition in the field of neuroevolution. Its effectiveness is derived from initiating with simple networks and incrementally evolving both their topologies and weights. Although its capability across various challenges is evident, the algorithm’s computational efficiency remains an impediment, limiting its scalability potential. To address these limitations, this article introduces TensorNEAT, a GPU-accelerated library that applies tensorization to the NEAT algorithm. Tensorization reformulates NEAT’s diverse network topologies and operations into uniformly shaped tensors, enabling efficient parallel execution across entire populations. TensorNEAT is built upon JAX, leveraging automatic function vectorization and hardware acceleration to significantly enhance computational efficiency. In addition to NEAT, the library supports variants such as CPPN and HyperNEAT and integrates with benchmark environments like Gym, Brax, and gymnax. Experimental evaluations across various robotic control environments in Brax demonstrate that TensorNEAT delivers up to 500× speedups compared to existing implementations, such as NEAT-Python. The source code for TensorNEAT is publicly available at: https://github.com/EMI-Group/tensorneat .

In the history of knowledge distillation (KD), the focus has once shifted over time from logit-based to feature-based approaches. However, this transition has been revisited with the advent of decoupled KD (DKD), which reemphasizes the importance of logit knowledge through advanced decoupling and weighting strategies. While DKD marks a significant advancement, its underlying mechanisms merit deeper exploration. As a response, we rethink DKD from a predictive distribution perspective. First, we introduce an enhanced version, the generalized DKD (GDKD) loss, which offers a more versatile method for decoupling logits. Then, we pay particular attention to the teacher model's predictive distribution and its impact on the gradients of GDKD loss, uncovering two critical insights often overlooked: 1) the partitioning by the top logit considerably improves the interrelationship of nontop logits and 2) amplifying the focus on the distillation loss of nontop logits enhances the knowledge extraction among them. Utilizing these insights, we further propose a streamlined GDKD algorithm with an efficient partition strategy to handle the multimodality of teacher models' predictive distribution. Our comprehensive experiments conducted on a variety of benchmarks, including CIFAR-100, ImageNet, Tiny-ImageNet, CUB-200-2011, and Cityscapes, demonstrate GDKD's superior performance over both the original DKD and other leading KD methods. The code is available at https://github.com/ZaberKo/GDKD.

NSGA-III is one of the most widely adopted algorithms for tackling many-objective optimization problems. However, its CPU-based design severely limits scalability and computational efficiency. To address the limitations, we propose TensorNSGA-III, a fully tensorized implementation of NSGA-III that leverages GPU parallelism for large-scale many-objective optimization. Unlike conventional GPU-accelerated evolutionary algorithms that rely on heuristic approximations to improve efficiency, TensorNSGA-III maintains the exact selection and variation mechanisms of NSGA-III while achieving significant acceleration. By reformulating the selection process with tensorized data structures and an optimized caching strategy, our approach effectively eliminates computational bottlenecks inherent in traditional CPU-based and naïve GPU implementations. Experimental results on widely used numerical benchmarks show that TensorNSGA-III achieves speedups of up to 3629× over the CPU version of NSGA-III. Additionally, we validate its effectiveness in multiobjective robotic control tasks, where it discovers diverse and high-quality behavioral solutions. Furthermore, we investigate the critical role of large population sizes in many-objective optimization and demonstrate the scalability of TensorNSGA-III in such scenarios. The source code is available at https://github.com/EMI-Group/evomo.

The reasoning capabilities of large language models (LLMs) have advanced rapidly, particularly following the release of DeepSeek-R1, which has inspired a surge of research into data quality and reinforcement learning (RL) algorithms. Despite the pivotal role diversity plays in RL, its influence on LLM reasoning remains largely underexplored. To bridge this gap, this work presents a systematic investigation into the impact of diversity in RL-based training for LLM reasoning, and proposes a novel diversity-aware policy optimization method. Across evaluations on 12 LLMs, we observe a strong positive correlation between the solution diversity and potential@k (a novel metric quantifying an LLM’s reasoning potential) in high-performing models. This finding motivates our method to explicitly promote diversity during RL training. Specifically, we design a token-level diversity and reformulate it into a practical objective, then we selectively apply it to positive samples. Integrated into the R1-zero training framework, our method achieves a 3.5\% average improvement across four mathematical reasoning benchmarks, while generating more diverse and robust solutions.

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

Advancements in adapting deep convolution architectures for spiking neural networks (SNNs) have significantly enhanced image classification performance and reduced computational burdens. However, the inability of multiplication-free inference (MFI) to align with attention and transformer mechanisms, which are critical to superior performance on high-resolution vision tasks, imposes limitations on these gains. To address this, our research explores a new pathway, drawing inspiration from the progress made in multilayer perceptrons (MLPs). We propose an innovative spiking MLP architecture that uses batch normalization (BN) to retain MFI compatibility and introduce a spiking patch encoding (SPE) layer to enhance local feature extraction capabilities. As a result, we establish an efficient multistage spiking MLP network that blends effectively global receptive fields with local feature extraction for comprehensive spike-based computation. Without relying on pretraining or sophisticated SNN training techniques, our network secures a top-one accuracy of 66.39% on the ImageNet-1K dataset, surpassing the directly trained spiking ResNet-34 by 2.67%. Furthermore, we curtail computational costs, model parameters, and simulation steps. An expanded version of our network compares with the performance of the spiking VGG-16 network with a 71.64% top-one accuracy, all while operating with a model capacity 2.1 times smaller. Our findings highlight the potential of our deep SNN architecture in effectively integrating global and local learning abilities. Interestingly, the trained receptive field in our network mirrors the activity patterns of cortical cells.

Spiking neural networks (SNNs), known for their low-power, event-driven computation, and intrinsic temporal dynamics, are emerging as promising solutions for processing dynamic, asynchronous signals from event-based sensors. Despite their potential, SNNs face challenges in training and architectural design, resulting in limited performance in challenging event-based dense prediction tasks compared with artificial neural networks (ANNs). In this work, we develop an efficient spiking encoder-decoder network (SpikingEDN) for large-scale event-based semantic segmentation (EbSS) tasks. To enhance the learning efficiency from dynamic event streams, we harness the adaptive threshold which improves network accuracy, sparsity, and robustness in streaming inference. Moreover, we develop a dual-path spiking spatially adaptive modulation (SSAM) module, which is specifically tailored to enhance the representation of sparse events and multimodal inputs, thereby considerably improving network performance. Our SpikingEDN attains a mean intersection over union (MIoU) of 72.57% on the DDD17 dataset and 58.32% on the larger DSEC-Semantic dataset, showing competitive results to the state-of-the-art ANNs while requiring substantially fewer computational resources. Our results shed light on the untapped potential of SNNs in event-based vision applications. The source codes are publicly available at https://github.com/EMI-Group/spikingedn.

Multi-objective evolutionary algorithms (MOEAs) have emerged as powerful tools for solving complex optimization problems characterized by multiple, often conflicting, objectives. While advancements have been made in computational efficiency as well as diversity and convergence of solutions, a critical challenge persists: the internal evolutionary mechanisms are opaque to human users. Drawing upon the successes of explainable AI in explaining complex algorithms and models, we argue that the need to understand the underlying evolutionary operators and population dynamics within MOEAs aligns well with a visual analytics paradigm. This paper introduces ParetoTracker, a visual analytics framework designed to support the comprehension and inspection of population dynamics in the evolutionary processes of MOEAs. Informed by preliminary literature review and expert interviews, the framework establishes a multi-level analysis scheme, which caters to user engagement and exploration ranging from examining overall trends in performance metrics to conducting fine-grained inspections of evolutionary operations. In contrast to conventional practices that require manual plotting of solutions for each generation, ParetoTracker facilitates the examination of temporal trends and dynamics across consecutive generations in an integrated visual interface. The effectiveness of the framework is demonstrated through case studies and expert interviews focused on widely adopted benchmark optimization problems.

Evolutionary multiobjective optimization has witnessed remarkable progress during the past decades. However, existing algorithms often encounter computational challenges in large-scale scenarios, primarily attributed to the absence of hardware acceleration. In response, we introduce a Tensorized Reference Vector Guided Evolutionary Algorithm (TensorRVEA) for harnessing the advancements of GPU acceleration. In TensorRVEA, the key data structures and operators are fully transformed into tensor forms for leveraging GPU-based parallel computing. In numerical benchmark tests involving large-scale populations and problem dimensions, TensorRVEA consistently demonstrates high computational performance, achieving up to over 1000× speedups. Then, we applied TensorRVEA to the domain of multiobjective neuroevolution for addressing complex challenges in robotic control tasks. Furthermore, we assessed TensorRVEA's extensibility by altering several tensorized reproduction operators. Experimental results demonstrate promising scalability and robustness of TensorRVEA. Source codes are available at https://github.com/EMI-Group/tensorrvea.

The NeuroEvolution of Augmenting Topologies (NEAT) algorithm has received considerable recognition in the field of neuroevolution. Its effectiveness is derived from initiating with simple networks and incrementally evolving both their topologies and weights. Although its capability across various challenges is evident, the algorithm's computational efficiency remains an impediment, limiting its scalability potential. In response, this paper introduces a tensorization method for the NEAT algorithm, enabling the transformation of its diverse network topologies and associated operations into uniformly shaped tensors for computation. This advancement facilitates the execution of the NEAT algorithm in a parallelized manner across the entire population. Furthermore, we develop TensorNEAT, a library that implements the tensorized NEAT algorithm and its variants, such as CPPN and HyperNEAT. Building upon JAX, TensorNEAT promotes efficient parallel computations via automated function vectorization and hardware acceleration. Moreover, the TensorNEAT library supports various benchmark environments including Gym, Brax, and gymnax. Through evaluations across a spectrum of robotics control environments in Brax, TensorNEAT achieves up to 500x speedups compared to the existing implementations such as NEAT-Python. Source codes are available at: https://github.com/EMI-Group/tensorneat.

Neural Architecture Search (NAS) has emerged as a key tool in identifying optimal configurations of deep neural networks tailored to specific tasks. However, training and assessing numerous architectures introduces considerable computational overhead. One method to mitigating this is through performance predictors, which offer a means to estimate the potential of an architecture without exhaustive training. Given that neural architectures fundamentally resemble Directed Acyclic Graphs (DAGs), Graph Neural Networks (GNNs) become an apparent choice for such predictive tasks. Nevertheless, the scarcity of training data can impact the precision of GNN-based predictors. To address this, we introduce a novel GNN predictor for NAS. This predictor renders neural architectures into vector representations by combining both the conventional and inverse graph views. Additionally, we incorporate a customized training loss within the GNN predictor to ensure efficient utilization of both types of representations. We subsequently assessed our method through experiments on benchmark datasets including NAS-Bench-101, NAS-Bench-201, and the DARTS search space, with a training dataset ranging from 50 to 400 samples. Benchmarked against leading GNN predictors, the experimental results showcase a significant improvement in prediction accuracy, with a 3%–16% increase in Kendall-tau correlation. Source codes are available at https://github.com/EMI-Group/fr-nas.

Despite the emerging progress of integrating evolutionary computation into reinforcement learning, the absence of a high-performance platform endowing composability and massive parallelism causes nontrivial difficulties for research and applications related to asynchronous commercial games. Here, we introduce Lamarckian1—an open-source platform featuring support for evolutionary reinforcement learning scalable to distributed computing resources. To improve the training speed and data efficiency, Lamarckian adopts optimized communication methods and an asynchronous evolutionary reinforcement learning workflow. To meet the demand for an asynchronous interface by commercial games and various methods, Lamarckian tailors an asynchronous Markov Decision Process interface and designs an object-oriented software architecture with decoupled modules. In comparison with the state-of-the-art RLlib, we empirically demonstrate the unique advantages of Lamarckian on benchmark tests with up to 6000 CPU cores: 1) both the sampling efficiency and training speed are doubled when running proximal policy optimization (PPO) on Google football game; 2) the training speed is 13 times faster when running PBT+PPO onPonggame. Moreover, we also present two use cases: 1) how Lamarckian is applied to generating behavior-diverse game AI; 2) how Lamarckian is applied to game balancing tests for an asynchronous commercial game.

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

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

Sparse large-scale evolutionary multiobjective optimization has garnered substantial interest over the past years due to its significant practical implications. These optimization problems are characterized by a predominance of zero-valued decision variables in the Pareto optimal solutions. Most existing algorithms focus on exploiting the sparsity of solutions by starting with initializing all decision variables with a nonzero value. Opposite to the existing approaches, we propose to initialize all decision variables to zero, then progressively identify and optimize the nonzero ones. The proposed framework consists of two stages. In the first stage of evolutionary optimization, a clustering method is applied at a predefined period of generations to identify nonzero decision variables according to the statistics of each variable’s current and historical values. Once a new nonzero decision variable is identified, it is randomly initialized within one of the two intervals, one defined by its lower quartile and lower bound, and the other by its upper quartile and upper bound. In the second stage, the clustering method is also periodically employed to distinguish between zero and nonzero decision variables. Different to the first stage, the zero decision variables will be set to zero straight, and the nonzero decision variables will be mutated at a higher probability. The performance of the proposed framework is empirically examined against state-of-the-art evolutionary algorithms on both sparse and nonsparse benchmarks and real-world problems, demonstrating its superior performance on different classes of problems.

Evolutionary multi-objective optimization (EMO) algorithms have been demonstrated to be effective in solving multi-criteria decision-making problems. In real-world applications, analysts often employ several algorithms concurrently and compare their solution sets to gain insight into the characteristics of different algorithms and explore a broader range of feasible solutions. However, EMO algorithms are typically treated as black boxes, leading to difficulties in performing detailed analysis and comparisons between the internal evolutionary processes. Inspired by the successful application of visual analytics tools in explainable AI, we argue that interactive visualization can significantly enhance the comparative analysis between multiple EMO algorithms. In this paper, we present a visual analytics framework that enables the exploration and comparison of evolutionary processes in EMO algorithms. Guided by a literature review and expert interviews, the proposed framework addresses various analytical tasks and establishes a multi-faceted visualization design to support the comparative analysis of intermediate generations in the evolution as well as solution sets. We demonstrate the effectiveness of our framework through case studies on benchmarking and real-world multi-objective optimization problems to elucidate how analysts can leverage our framework to inspect and compare diverse algorithms.

Multi-task learning (MTL) seeks to learn a single model to accomplish multiple tasks by leveraging shared information among the tasks. Existing MTL models, however, have been known to suffer from negative interference among tasks. Efforts to mitigate task interference have focused on either loss/gradient balancing or implicit parameter partitioning with partial overlaps among the tasks. In this paper, we propose ETR-NLP to mitigate task interference through a synergistic combination of non-learnable primitives (NLPs) and explicit task routing (ETR). Our key idea is to employ non-learnable primitives to extract a diverse set of task-agnostic features and recombine them into a shared branch common to all tasks and explicit task-specific branches reserved for each task. The non-learnable primitives and the explicit decoupling of learnable parameters into shared and task-specific ones afford the flexibility needed for minimizing task interference. We evaluate the efficacy of ETR-NLP networks for both image-level classification and pixel-level dense prediction MTL problems. Experimental results indicate that ETR-NLP significantly outperforms state-of-the-art baselines with fewer learnable parameters and similar FLOPs across all datasets. Code is available at this URL.

The state of the arts in vision-language pretraining (VLP) achieves exemplary performance but suffers from high training costs resulting from slow convergence and long training time, especially on large-scale web datasets. An essential obstacle to training efficiency lies in the entangled prediction rate (percentage of tokens for reconstruction) and corruption rate (percentage of corrupted tokens) in masked language modeling (MLM), that is, a proper corruption rate is achieved at the cost of a large portion of output tokens being excluded from prediction loss. To accelerate the convergence of VLP, we propose a new pretraining task, namely, free language modeling (FLM), that enables a 100% prediction rate with arbitrary corruption rates. FLM successfully frees the prediction rate from the tie-up with the corruption rate while allowing the corruption spans to be customized for each token to be predicted. FLM-trained models are encouraged to learn better and faster given the same GPU time by exploiting bidirectional contexts more flexibly. Extensive experiments show FLM could achieve an impressive 2.5 × pretraining time reduction in comparison to the MLM-based methods, while keeping competitive performance on both vision-language understanding and generation tasks. Code will be public at https://github.com/TencentARC/FLM.

While off-policy reinforcement learning (RL) algorithms are sample efficient due to gradient-based updates and data reuse in the replay buffer, they struggle with convergence to local optima due to limited exploration. On the other hand, population-based algorithms offer a natural exploration strategy, but their heuristic black-box operators are inefficient. Recent algorithms have integrated these two methods, connecting them through a shared replay buffer. However, the effect of using diverse data from population optimization iterations on off-policy RL algorithms has not been thoroughly investigated. In this paper, we first analyze the use of off-policy RL algorithms in combination with population-based algorithms, showing that the use of population data could introduce an overlooked error and harm performance. To test this, we propose a uniform and scalable training design and conduct experiments on our tailored framework in robot locomotion tasks from the OpenAI gym. Our results substantiate that using population data in off-policy RL can cause instability during training and even degrade performance. To remedy this issue, we further propose a double replay buffer design that provides more on-policy data and show its effectiveness through experiments. Our results offer practical insights for training these hybrid methods.

Deploying high-performance convolutional neural network (CNN) models on low-earth orbit (LEO) satellites for rapid remote sensing image processing has attracted significant interest from industry and academia. However, the limited resources available on LEO satellites contrast with the demands of resource-intensive CNN models, necessitating the adoption of ground-station server assistance for training and updating these models. Existing approaches often require large floating-point operations (FLOPs) and substantial model parameter transmissions, presenting considerable challenges. To address these issues, this paper introduces a ground-station server-assisted framework. With the proposed framework, each layer of the CNN model contains only one learnable feature map (called the seed feature map) from which other feature maps are generated based on specific rules. The hyperparameters of these rules are randomly generated instead of being trained, thus enabling the generation of multiple feature maps from the seed feature map and significantly reducing FLOPs. Furthermore, since the random hyperparameters can be saved using a few random seeds, the ground station server assistance can be facilitated in updating the CNN model deployed on the LEO satellite. Experimental results on the ISPRS Vaihingen, ISPRS Potsdam, UAVid, and LoveDA datasets for semantic segmentation services demonstrate that the proposed framework outperforms existing state-of-the-art approaches. In particular, the SineFM-based model achieves a higher mIoU than the UNetFormer on the UAVid dataset, with 3.3 × fewer parameters and 2.2 × fewer FLOPs.

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

Complex optimization problems with hundreds or even thousands of decision variables and dozens of conflicting objectives are not uncommon in the real world. In the past five years, increased research efforts have been dedicated to large-scale multiobjective optimization problems (LSMOPs) by using a variety of search strategies, including variable grouping, variable analysis, problem transformation, dimensionality reduction, and novel recombination operators. Despite the success of these efforts in solving some general LSMOPs, there still remains a big gap between the LSMOPs that have been addressed and those encountered in real life, such as sparse, highly constrained, dynamic, and expensive LMOPs, as well as very large-scale and many-objective optimization problems that are widely seen and of paramount importance for solving scientific and engineering problems. Due to the significant practical importance of large-scale multiobjective optimization, there is a high demand for computationally efficient and effective evolutionary algorithms for solving LSMOPs.

Existing vision-language pre-training (VLP) methods primarily rely on paired image-text datasets, which are either annotated by enormous human labors or crawled from the internet followed by elaborate data cleaning techniques. To reduce the dependency on well-aligned image-text pairs, it is promising to directly leverage the large-scale text-only and image-only corpora. This paper proposes a data augmentation method, namely cross-modal CutMix (CMC), for implicit cross-modal alignment learning in unpaired VLP. Specifically, CMC transforms natural sentences in the textual view into a multi-modal view, where visually-grounded words in a sentence are randomly replaced by diverse image patches with similar semantics. There are several appealing proprieties of the proposed CMC. First, it enhances the data diversity while keeping the semantic meaning intact for tackling problems where the aligned data are scarce; Second, by attaching cross-modal noise on uni-modal data, it guides models to learn token-level interactions across modalities for better denoising. Furthermore, we present a new unpaired VLP method, dubbed as VLMixer, that integrates CMC with contrastive learning to pull together the uni-modal and multi-modal views for better instance-level alignments among different modalities. Extensive experiments on five downstream tasks show that VLMixer could surpass previous state-of-the-art unpaired VLP methods.

Multipopulation methods are highly effective in solving dynamic optimization problems. Three factors affect this significantly: 1) the exclusion mechanisms to avoid the convergence to the same peak by multiple subpopulations; 2) the resource allocation mechanism that assigns the computational resources to the subpopulations; and 3) the control mechanisms to adaptively adjust the number of subpopulations by considering the number of optima and available computational resources. In the existing exclusion mechanisms, when the distance (i.e., the distance between their best found positions) between two subpopulations becomes less than a predefined threshold, the inferior one will be removed/reinitialized. However, this leads to incapability of algorithms in covering peaks/optima that are closer than the threshold. Moreover, despite the importance of resource allocation due to the limited available computational resources between environmental changes, it has not been well studied in the literature. Finally, the number of subpopulations should be adapted to the number of optima. However, in most existing adaptive multipopulation methods, there is no predefined upper bound for generating subpopulations. Consequently, in problems with large numbers of peaks, they can generate too many subpopulations sharing limited computational resources. In this article, a multipopulation framework is proposed to address the aforementioned issues by using three adaptive approaches: 1) subpopulation generation; 2) double-layer exclusion; and 3) computational resource allocation. The experimental results demonstrate the superiority of the proposed framework over several peer approaches in solving various benchmark problems.

Dynamic changes are an important and inescapable aspect of many real-world optimization problems. Designing algorithms to find and track desirable solutions while facing challenges of dynamic optimization problems is an active research topic in the field of swarm and evolutionary computation. To evaluate and compare the performance of algorithms, it is imperative to use a suitable benchmark that generates problem instances with different controllable characteristics. In this article, we give a comprehensive review of existing benchmarks and investigate their shortcomings in capturing different problem features. We then propose a highly configurable benchmark suite, the generalized moving peaks benchmark, capable of generating problem instances whose components have a variety of properties, such as different levels of ill-conditioning, variable interactions, shape, and complexity. Moreover, components generated by the proposed benchmark can be highly dynamic with respect to the gradients, heights, optimum locations, condition numbers, shapes, complexities, and variable interactions. Finally, several well-known optimizers and dynamic optimization algorithms are chosen to solve generated problems by the proposed benchmark. The experimental results show the poor performance of the existing methods in facing new challenges posed by the addition of new properties.

Learning over massive data stored in different locations is essential in many real-world applications. However, sharing data is full of challenges due to the increasing demands of privacy and security with the growing use of smart mobile devices and Internet of thing (IoT) devices. Federated learning provides a potential solution to privacy-preserving and secure machine learning, by means of jointly training a global model without uploading data distributed on multiple devices to a central server. However, most existing work on federated learning adopts machine learning models with full-precision weights, and almost all these models contain a large number of redundant parameters that do not need to be transmitted to the server, consuming an excessive amount of communication costs. To address this issue, we propose a federated trained ternary quantization (FTTQ) algorithm, which optimizes the quantized networks on the clients through a self-learning quantization factor. Theoretical proofs of the convergence of quantization factors, unbiasedness of FTTQ, as well as a reduced weight divergence are given. On the basis of FTTQ, we propose a ternary federated averaging protocol (T-FedAvg) to reduce the upstream and downstream communication of federated learning systems. Empirical experiments are conducted to train widely used deep learning models on publicly available data sets, and our results demonstrate that the proposed T-FedAvg is effective in reducing communication costs and can even achieve slightly better performance on non-IID data in contrast to the canonical federated learning algorithms.

Offspring generation plays an important role in evolutionary multiobjective optimization. However, generating promising candidate solutions effectively in high-dimensional spaces is particularly challenging. To address this issue, we propose an adaptive offspring generation method for large-scale multiobjective optimization. First, a preselection strategy is proposed to select a balanced parent population, and then these parent solutions are used to construct direction vectors in the decision spaces for reproducing promising offspring solutions. Specifically, two kinds of direction vectors are adaptively used to generate offspring solutions. The first kind takes advantage of the dominated solutions to generate offspring solutions toward the Pareto optimal set (PS) for convergence enhancement, while the other kind uses those nondominated solutions to spread the solutions over the PS for diversity maintenance. The proposed offspring generation method can be embedded in many existing multiobjective evolutionary algorithms (EAs) for large-scale multiobjective optimization. Experiments are conducted to reveal the mechanism of our proposed adaptive reproduction strategy and validate its effectiveness. Experimental results on some large-scale multiobjective optimization problems have demonstrated the competitive performance of our proposed algorithm in comparison with five state-of-the-art large-scale EAs.

Acquisition functions for surrogate-assisted many-objective optimization require a delicate balance between convergence and diversity. However, the conflicting nature between many objectives may lead to an imbalance between exploration and exploitation, resulting in a low efficiency in search for a set of optimal solutions that can well balance convergence and diversity. To meet this challenge, we propose an adaptive model management strategy assisted by two sets of reference vectors, one set of adaptive reference vectors accounting for convergence while the other set of fixed reference vectors for diversity. Specifically, we first propose a new acquisition function that calculates an amplified upper confidence bound (AUCB). Two optimization processes are performed in parallel to optimize the acquisition function, each based on one of the two sets of reference vectors. Then, we select one promising candidate solution according to diversity or convergence from the nondominated solutions obtained by the two optimization processes. The experimental results on four suites of test functions as well as six real-world application problems demonstrate the competitive performance of the proposed reference vector-assisted adaptive model management strategy, in comparison with seven state-of-the-art surrogate-assisted evolutionary algorithms (SAEAs).

Large-scale multiobjective optimization problems (LSMOPs) are challenging for existing approaches due to the complexity of objective functions and the massive volume of decision space. Some large-scale multiobjective evolutionary algorithms (LSMOEAs) have recently been proposed, which have shown their effectiveness in solving some benchmarks and real-world applications. They merely focus on handling the massive volume of decision space and ignore the complexity of LSMOPs in terms of objective functions. The complexity issue is also important since the complexity grows along with the increment in the number of decision variables. Our previous study proposed a framework to accelerate evolutionary large-scale multiobjective optimization via problem reformulation for handling large-scale decision variables. Here, we investigate the effectiveness of LSMOF combined with decomposition-based MOEA (MOEA/D), aiming to handle the complexity of LSMOPs in both the decision and objective spaces. Specifically, MOEA/D is embedded in LSMOF via two different strategies, and the proposed algorithm is tested on various benchmark LSMOPs. Experimental results indicate the encouraging performance improvement benefited from the solution of the complexity issue in large-scale multiobjective optimization.

Recent advancements in deep neural networks have made remarkable leap-forwards in dense image prediction. However, the issue of feature alignment remains as neglected by most existing approaches for simplicity. Direct pixel addition between upsampled and local features leads to feature maps with misaligned contexts that, in turn, translate to mis-classifications in prediction, especially on object boundaries. In this paper, we propose a feature alignment module that learns transformation offsets of pixels to contextually align upsampled higher-level features; and another feature selection module to emphasize the lower-level features with rich spatial details. We then integrate these two modules in a top-down pyramidal architecture and present the Feature-aligned Pyramid Network (FaPN). Extensive experimental evaluations on four dense prediction tasks and four datasets have demonstrated the efficacy of FaPN, yielding an overall improvement of 1.2 - 2.6 points in AP / mIoU over FPN when paired with Faster / Mask R-CNN. In particular, our FaPN achieves the state-of-the-art of 56.7% mIoU on ADE20K when integrated within Mask-Former. The code is available from https://github.com/EMI-Group/FaPN.

Dense video captioning aims to generate multiple associated captions with their temporal locations from the video. Previous methods follow a sophisticated "localizethen-describe" scheme, which heavily relies on numerous hand-crafted components. In this paper, we proposed a simple yet effective framework for end-to-end dense video captioning with parallel decoding (PDVC), by formulating the dense caption generation as a set prediction task. In practice, through stacking a newly proposed event counter on the top of a transformer decoder, the PDVC precisely segments the video into a number of event pieces under the holistic understanding of the video content, which effectively increases the coherence and readability of predicted captions. Compared with prior arts, the PDVC has several appealing advantages: (1) Without relying on heuristic non-maximum suppression or a recurrent event sequence selection network to remove redundancy, PDVC directly produces an event set with an appropriate size; (2) In contrast to adopting the two-stage scheme, we feed the enhanced representations of event queries into the localization head and caption head in parallel, making these two sub-tasks deeply interrelated and mutually promoted through the optimization; (3) Without bells and whistles, extensive experiments on ActivityNet Captions and YouCook2 show that PDVC is capable of producing high-quality captioning results, surpassing the state-of-the-art two-stage methods when its localization accuracy is on par with them. Code is available at https://github.com/ttengwang/PDVC.

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

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

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

Many real-world optimization problems are dynamic. The field of dynamic optimization deals with such problems where the search space changes over time. In this two-part article, we present a comprehensive survey of the research in evolutionary dynamic optimization for single-objective unconstrained continuous problems over the last two decades. In Part A of this survey, we propose a new taxonomy for the components of dynamic optimization algorithms (DOAs), namely, convergence detection, change detection, explicit archiving, diversity control, and population division and management. In comparison to the existing taxonomies, the proposed taxonomy covers some additional important components, such as convergence detection and computational resource allocation. Moreover, we significantly expand and improve the classifications of diversity control and multipopulation methods, which are underrepresented in the existing taxonomies. We then provide detailed technical descriptions and analysis of different components according to the suggested taxonomy. Part B of this survey provides an in-depth analysis of the most commonly used benchmark problems, performance analysis methods, static optimization algorithms used as the optimization components in the DOAs, and dynamic real-world applications. Finally, several opportunities for future work are pointed out.

This article presents the second Part of a two-Part survey that reviews evolutionary dynamic optimization (EDO) for single-objective unconstrained continuous problems over the last two decades. While in the first part, we reviewed the components of dynamic optimization algorithms (DOAs); in this part, we present an in-depth review of the most commonly used benchmark problems, performance analysis methods, static optimization methods used in the framework of DOAs, and real-world applications. Compared to the previous works, this article provides a new taxonomy for the benchmark problems used in the field based on their baseline functions and dynamics. In addition, this survey classifies the commonly used performance indicators into fitness/error-based and efficiency-based ones. Different types of plots used in the literature for analyzing the performance and behavior of algorithms are also reviewed. Furthermore, the static optimization algorithms that are modified and utilized in the framework of DOAs as the optimization components are covered. We then comprehensively review some real-world dynamic problems that are optimized by EDO methods. Finally, some challenges and opportunities are pointed out for future directions.

The performance of deep neural networks is heavily dependent on its architecture and various neural architecture search strategies have been developed for automated network architecture design. Recently, evolutionary neural architecture search (EvoNAS) has received increasing attention due to the attractive global optimization capability of evolutionary algorithms. However, EvoNAS suffers from extremely high computational costs because a large number of performance evaluations are usually required in evolutionary optimization, and training deep neural networks is itself computationally very expensive. To address this issue, this article proposes a computationally efficient framework for the evolutionary search of convolutional networks based on a directed acyclic graph, in which parents are randomly sampled and trained on each mini-batch of training data. In addition, a node inheritance strategy is adopted so that the fitness of all offspring individuals can be evaluated without training them. Finally, we encode a channel attention mechanism in the search space to enhance the feature processing capability of the evolved neural networks. We evaluate the proposed algorithm on the widely used datasets, in comparison with 30 state-of-the-art peer algorithms. Our experimental results show that the proposed algorithm is not only computationally much more efficient but also highly competitive in learning performance.

With the increase in the number of optimization objectives, balancing the convergence and diversity in evolutionary multiobjective optimization becomes more intractable. So far, a variety of evolutionary algorithms have been proposed to solve many-objective optimization problems (MaOPs) with more than three objectives. Most of the existing algorithms, however, find difficulties in simultaneously counterpoising convergence and diversity during the whole evolutionary process. To address the issue, this paper proposes to solve MaOPs via multistage evolutionary search. To be specific, a two-stage evolutionary algorithm is developed, where the convergence and diversity are highlighted during different search stages to avoid the interferences between them. The first stage pushes multiple subpopulations with different weight vectors to converge to different areas of the Pareto front. After that, the nondominated solutions coming from each subpopulation are selected for generating a new population for the second stage. Moreover, a new environmental selection strategy is designed for the second stage to balance the convergence and diversity close to the Pareto front. This selection strategy evenly divides each objective dimension into a number of intervals, and then one solution having the best convergence in each interval will be retained. To assess the performance of the proposed algorithm, 48 benchmark functions with 7, 10, and 15 objectives are used to make comparisons with five representative many-objective optimization algorithms.

Diversity preservation is a crucial technique in multiobjective evolutionary algorithms (MOEAs), which aims at evolving the population toward the Pareto front (PF) with a uniform distribution and a good extensity. In spite of many diversity preservation approaches in existing MOEAs, most of them encounter difficulties in tackling complex PFs. This article gives a detail introduction to existing diversity preservation approaches, as well as a revelation of the limitations of them. To address the limitations of existing diversity preservation approaches, this article proposes a multistage MOEA for better diversity performance. The proposed MOEA divides the optimization process into multiple stages according to the population in each generation, and updates the population by different steady-state selection schemes in different stages. According to the experimental results on 21 benchmark problems, the proposed MOEA exhibits better diversity performance than 11 existing MOEAs.

Due to the curse of dimensionality, two main issues remain challenging for applying evolutionary algorithms (EAs) to large-scale multiobjective optimization. The first issue is how to improve the efficiency of EAs for reducing computation cost. The second one is how to improve the diversity maintenance of EAs to avoid local optima. Nevertheless, these two issues are somehow conflicting with each other, and thus it is crucial to strike a balance between them in practice. Thereby, we propose an iterated problem reformulation based EA for large-scale multiobjective optimization, where the problem reformulation based method and the decomposition based method are used iteratively to address the aforementioned issues. The proposed method is compared with several state-of-the-art EAs on a variety of large-scale multiobjective optimization problems. Experimental results demonstrate the effectiveness of our proposed iterated method in large-scale multiobjective optimization.

It has been widely recognized that evolutionary computation is one of the most effective techniques for solving complex optimization problems. As a group of meta-heuristics inspired by nature, the superiority of evolutionary algorithms is mainly attributed to the evolution of multiple candidate solutions, which can strike a balance between exploration and exploitation. However, the effectiveness of evolutionary algorithms is generally at the expense of efficiency, which reduces the prevalence of evolutionary algorithms in solving real-world optimization problems. In 2017, we proposed the evolutionary multi-objective optimization platform PlatEMO to facilitate the use of multi-objective evolutionary algorithms (MOEAs), where some delicate techniques were developed to improve the computational efficiency of MOEAs. These techniques have not been introduced before, since users need not care about them when using existing MOEAs or developing new MOEAs. To deepen the understanding of the core mechanisms of PlatEMO, this paper gives a comprehensive introduction to these techniques, including new non-dominated sorting approaches, matrix calculation, and parallel computing. Several comparative experiments are conducted for a quantitative understanding of the efficiency improvement brought by these techniques.

In evolutionary multiobjective optimization, the Pareto front (PF) is approximated by using a set of representative candidate solutions with good convergence and diversity. However, most existing multiobjective evolutionary algorithms (MOEAs) have general difficulty in the approximation of PFs with complicated geometries. To address this issue, we propose a generic front modeling method for evolutionary multiobjective optimization, where the shape of the nondominated front is estimated by training a generalized simplex model. On the basis of the estimated front, we further develop an MOEA, where both the mating selection and environmental selection are driven by the approximate nondominated fronts modeled during the optimization process. For performance assessment, the proposed algorithm is compared with several state-of-the-art evolutionary algorithms on a wide range of benchmark problems with various types of PFs and different numbers of objectives. Experimental results demonstrate that the proposed algorithm performs consistently on a variety of multiobjective optimization problems.

Ratio error (RE) estimation of the voltage transformers (VTs) plays an important role in modern power delivery systems. Existing RE estimation methods mainly focus on periodical calibration but ignore the time-varying property. Consequently, it is difficult to efficiently estimate the state of the VTs in real time. To address this issue, we formulate a time-varying RE estimation (TREE) problem into a large-scale multiobjective optimization problem, where the multiple objectives and inequality constraints are formulated by statistical and physical rules extracted from the power delivery systems. Furthermore, a set of TREE problems from different substations is systematically formulated into a benchmark test suite for characterizing their different properties. The formulation of these TREE problems not only transfers an expensive RE estimation task to a relatively cheaper optimization problem but also promotes the research in large-scale multiobjective optimization by providing a real-world benchmark test suite with complex variable interactions and correlations to different objectives. To the best of our knowledge, this is the first time to formulate a real-world problem into a benchmark test suite for large-scale multiobjective optimization, and it is also the first work proposing to solve TREE problems via evolutionary multiobjective optimization.

Surrogate-assisted evolutionary algorithms have played an important role in expensive optimization where a small number of real-objective function evaluations are allowed. Usually, the surrogate models are used for the same purpose, e.g., to approximate the real-objective function or the aggregation fitness function. However, there is little work on surrogate-assisted optimization by model fusion, i.e., different surrogate models are fused for different purposes to improve the performance of the algorithm. In this work, we propose a surrogate-assisted approach by model fusion for solving expensive many-objective optimization problems, in which the Kriging assisted objective function approximation method is fused with the classifier assisted approach. The proposed algorithm is compared with some state-of-the-art surrogate-assisted algorithms on DTLZ problems and a real-world problem, and some encouraging results have been achieved by our proposed model fusion based approach.

Many real-world optimization problems are challenging because the evaluation of solutions is computationally expensive. As a result, the number of function evaluations is limited. Surrogate-assisted evolutionary algorithms are promising approaches to tackle this kind of problems. However, their performance highly depends on the number of objectives. Thus, they may not be suitable for many-objective optimization. This paper proposes a novel hybrid algorithm for computationally expensive many-objective optimization, called C-M-EA. The proposed approach combines two surrogate-assisted evolutionary algorithms during the search process. We compare the performance of the proposed approach with seven multi-objective evolutionary algorithms. Our experimental results show that our approach is competitive for solving computationally expensive many-objective optimization problems.

Complex networks provide a powerful tool for data representation due to its ability to describe the interplay between topological, functional, and dynamical properties of the input data. A fundamental process in network-based (graph-based) data analysis techniques is the network construction from original data usually in vector form. Here, a natural question is: How to construct an "optimal" network regarding a given processing goal? This paper investigates structural optimization in the context of network-based data classification tasks. To be specific, we propose a particle swarm optimization framework which is responsible for building a network from vector-based data set while optimizing a quality function driven by the classification accuracy. The classification process considers both topological and physical features of the training and test data and employing PageRank measure for classification according to the importance concept of a test instance to each class. Results on artificial and real-world problems reveal that data network generated using structural optimization provides better results in general than those generated by classical network formation methods. Moreover, this investigation suggests that other kinds of network-based machine learning and data mining tasks, such as dimensionality reduction and data clustering, can benefit from the proposed structural optimization method.

Engineering designs can involve multiple stages, where at each stage, the design models are incrementally modified and optimized. In contrast to traditional dynamic optimization problems, where the changes are caused by some objective factors, the changes in such incremental optimization problems (IOPs) are usually caused by the modifications made by the decision makers during the design process. While existing work in the literature is mainly focused on traditional dynamic optimization, little research has been dedicated to solving such IOPs. In this paper, we study how to adopt cooperative coevolution to efficiently solve a specific type of IOPs, namely, those with increasing decision variables. First, we present a benchmark function generator on the basis of some basic formulations of IOPs with increasing decision variables and exploitable modular structure. Then, we propose a contribution-based cooperative coevolutionary framework coupled with an incremental grouping method for dealing with them. On one hand, the benchmark function generator is capable of generating various benchmark functions with various characteristics. On the other hand, the proposed framework is promising in solving such problems in terms of both optimization accuracy and computational efficiency. In addition, the proposed method is further assessed using a real-world application, i.e., the design optimization of a stepped cantilever beam.

In this paper, we propose a framework to accelerate the computational efficiency of evolutionary algorithms on large-scale multiobjective optimization. The main idea is to track the Pareto optimal set (PS) directly via problem reformulation. To begin with, the algorithm obtains a set of reference directions in the decision space and associates them with a set of weight variables for locating the PS. Afterwards, the original large-scale multiobjective optimization problem is reformulated into a low-dimensional single-objective optimization problem. In the reformulated problem, the decision space is reconstructed by the weight variables and the objective space is reduced by an indicator function. Thanks to the low dimensionality of the weight variables and reduced objective space, a set of quasi-optimal solutions can be obtained efficiently. Finally, a multiobjective evolutionary algorithm is used to spread the quasi-optimal solutions over the approximate Pareto optimal front evenly. Experiments have been conducted on a variety of large-scale multiobjective problems with up to 5000 decision variables. Four different types of representative algorithms are embedded into the proposed framework and compared with their original versions, respectively. Furthermore, the proposed framework has been compared with two state-of-the-art algorithms for large-scale multiobjective optimization. The experimental results have demonstrated the significant improvement benefited from the framework in terms of its performance and computational efficiency in large-scale multiobjective optimization.

Both convergence and diversity are crucial to evolutionary many-objective optimization, whereas most existing dominance relations show poor performance in balancing them, thus easily leading to a set of solutions concentrating on a small region of the Pareto fronts. In this paper, a novel dominance relation is proposed to better balance convergence and diversity for evolutionary many-objective optimization. In the proposed dominance relation, an adaptive niching technique is developed based on the angles between the candidate solutions, where only the best converged candidate solution is identified to be nondominated in each niche. Experimental results demonstrate that the proposed dominance relation outperforms existing dominance relations in balancing convergence and diversity. A modified NSGA-II is suggested based on the proposed dominance relation, which shows competitiveness against the state-of-the-art algorithms in solving many-objective optimization problems. The effectiveness of the proposed dominance relation is also verified on several other existing multi- and many-objective evolutionary algorithms.

The effectiveness of evolutionary algorithms have been verified on multi-objective optimization, and a large number of multi-objective evolutionary algorithms have been proposed during the last two decades. To quantitatively compare the performance of different algorithms, a set of uniformly distributed reference points sampled on the Pareto fronts of benchmark problems are needed in the calculation of many performance metrics. However, not much work has been done to investigate the method for sampling reference points on Pareto fronts, even though it is not an easy task for many Pareto fronts with irregular shapes. More recently, an evolutionary multi-objective optimization platform was proposed by us, called PlatEMO, which can automatically generate reference points on each Pareto front and use them to calculate the performance metric values. In this paper, we report the reference point sampling methods used in PlatEMO for different types of Pareto fronts. Experimental results show that the reference points generated by the proposed sampling methods can evaluate the performance of algorithms more accurately than randomly sampled reference points.

Recently, by taking advantage of evolutionary multiobjective optimization techniques in diversity preservation, the means of multiobjectivization has attracted increasing interest in the studies of multimodal optimization (MMO). While most existing work of multiobjectivization aims to find all optimal solutions simultaneously, in this paper, we propose to approximate multimodal fitness landscapes via multiobjectivization, thus providing an estimation of potential optimal areas. To begin with, an MMO problem is transformed into a multiobjective optimization problem (MOP) by adding an adaptive diversity indicator as the second optimization objective, and an approximate fitness landscape is obtained via optimization of the transformed MOP using a multiobjective evolutionary algorithm. Then, on the basis of the approximate fitness landscape, an adaptive peak detection method is proposed to find peaks where optimal solutions may exist. Finally, local search is performed inside the detected peaks on the approximate fitness landscape. To assess the performance of the proposed algorithm, extensive experiments are conducted on 20 multimodal test functions, in comparison with three state-of-the-art algorithms for MMO. Experimental results demonstrate that the proposed algorithm not only shows promising performance in benchmark comparisons, but also has good potential in assisting preference-based decision-making in MMO.

During the past two decades, a variety of multiobjective evolutionary algorithms (MOEAs) have been proposed in the literature. As pointed out in some recent studies, however, the performance of an MOEA can strongly depend on the Pareto front shape of the problem to be solved, whereas most existing MOEAs show poor versatility on problems with different shapes of Pareto fronts. To address this issue, we propose an MOEA based on an enhanced inverted generational distance indicator, in which an adaptation method is suggested to adjust a set of reference points based on the indicator contributions of candidate solutions in an external archive. Our experimental results demonstrate that the proposed algorithm is versatile for solving problems with various types of Pareto fronts, outperforming several state-of-the-art evolutionary algorithms for multiobjective and many-objective optimization.

The current literature of evolutionary many-objective optimization is merely focused on the scalability to the number of objectives, while little work has considered the scalability to the number of decision variables. Nevertheless, many real-world problems can involve both many objectives and large-scale decision variables. To tackle such large-scale many-objective optimization problems (MaOPs), this paper proposes a specially tailored evolutionary algorithm based on a decision variable clustering method. To begin with, the decision variable clustering method divides the decision variables into two types: 1) convergence-related variables and 2) diversity-related variables. Afterward, to optimize the two types of decision variables, a convergence optimization strategy and a diversity optimization strategy are adopted. In addition, a fast nondominated sorting approach is developed to further improve the computational efficiency of the proposed algorithm. To assess the performance of the proposed algorithm, empirical experiments have been conducted on a variety of large-scale MaOPs with up to ten objectives and 5000 decision variables. Our experimental results demonstrate that the proposed algorithm has significant advantages over several state-of-the-art evolutionary algorithms in terms of the scalability to decision variables on MaOPs.

Multimodal optimization has attracted increasing interest recently. Despite the emergence of various multimodal optimization algorithms during the last decade, little work has been dedicated to the development of benchmark tools. In this paper, we propose a visualization method for benchmark studies of multimodal optimization, called parallel peaks. Inspired by parallel coordinates, the proposed parallel peaks method is capable of visualizing both distribution information and convergence information of a given candidate solution set inside a 2D coordinate plane. To the best of our knowledge, this is the first visualization method in the multimodal optimization area. Our empirical results demonstrate that the proposed parallel peaks method can be robustly used to visualize candidate solutions sets with a range of properties, including high-accuracy solutions sets, high-dimensional solution sets and solution sets with a large number of optima. Additionally, by visualizing the populations obtained during the optimization process, it can also be used to investigate search behaviors of multimodal optimization algorithms.

Graph-based dimensionality reduction has attracted a lot of attention in recent years. Such methods aim to exploit the graph representation in order to catch some structural information hidden in data. They usually consist of two steps: graph construction and projection. Although graph construction is crucial to the performance, most research work in the literature has focused on the development of heuristics and models to the projection step, and only very recently, attention was paid to network construction. In this work, graph construction is considered in the context of supervised dimensionality reduction. To be specific, using a nature-inspired optimization framework, this work investigates if an optimized graph is able to provide better projections than well-known general-purpose methods. The proposed method is compared with widely used graph construction methods on a range of real-world image classification problems. Results show that the optimization framework has achieved considerable dimensionality reduction rates as well as good predictive performance.

The interests in multiobjective and many-objective optimization have been rapidly increasing in the evolutionary computation community. However, most studies on multiobjective and many-objective optimization are limited to small-scale problems, despite the fact that many real-world multiobjective and many-objective optimization problems may involve a large number of decision variables. As has been evident in the history of evolutionary optimization, the development of evolutionary algorithms (EAs) for solving a particular type of optimization problems has undergone a co-evolution with the development of test problems. To promote the research on large-scale multiobjective and many-objective optimization, we propose a set of generic test problems based on design principles widely used in the literature of multiobjective and many-objective optimization. In order for the test problems to be able to reflect challenges in real-world applications, we consider mixed separability between decision variables and nonuniform correlation between decision variables and objective functions. To assess the proposed test problems, six representative evolutionary multiobjective and many-objective EAs are tested on the proposed test problems. Our empirical results indicate that although the compared algorithms exhibit slightly different capabilities in dealing with the challenges in the test problems, none of them are able to efficiently solve these optimization problems, calling for the need for developing new EAs dedicated to large-scale multiobjective and many-objective optimization.

Surrogate models have shown to be effective in assisting metaheuristic algorithms for solving computationally expensive complex optimization problems. The effectiveness of existing surrogate-assisted metaheuristic algorithms, however, has only been verified on low-dimensional optimization problems. In this paper, a surrogate-assisted cooperative swarm optimization algorithm is proposed, in which a surrogate-assisted particle swarm optimization (PSO) algorithm and a surrogate-assisted social learning-based PSO (SL-PSO) algorithm cooperatively search for the global optimum. The cooperation between the PSO and the SL-PSO consists of two aspects. First, they share promising solutions evaluated by the real fitness function. Second, the SL-PSO focuses on exploration while the PSO concentrates on local search. Empirical studies on six 50-D and six 100-D benchmark problems demonstrate that the proposed algorithm is able to find high-quality solutions for high-dimensional problems on a limited computational budget.

As a pivotal component in multi-objective evolutionary algorithms (MOEAs), the environmental selection determines the quality of candidate solutions to survive at each generation. In practice, different environmental selection strategies can be based on different selection criteria, where the performance metrics (or indicators) are shown to be among the most effective ones. This paper proposes an MOEA whose environmental selection is based on an enhanced inverted generational distance metric that is able to detect noncontributing solutions (termed IGD-NS), thereby considerably accelerating the convergence of the evolutionary search. Experimental results on ZDT and DTLZ test suites demonstrate the competitive performance of the proposed MOEA/IGD-NS in comparison with some representative MOEAs.

While most part of the complex network models are described in function of some growth mechanism, the optimization of a goal or certain characteristics can be desirable for some problems. This paper investigates structural optimization of networks in the highlevel classification context, where the classification produced by a traditional classifier is combined with the classification provided by complex network measures. Using the recently proposed social learning particle swarm optimization (SL-PSO), a bio-inspired optimization framework, which is responsible to build up the network and adjust the parameters of the hybrid model while conducting the optimization of a quality function, is proposed. Experiments on two real-world problems, the Handwritten Digits Recognition and the Semantic Role Labeling (SRL), were performed. In both problems, the optimization framework is able to improve the classification given by a state-of-the-art algorithm to SRL. Furthermore, the optimization framework proposed here can be extended to other machine learning tasks.

In evolutionary multiobjective optimization, maintaining a good balance between convergence and diversity is particularly crucial to the performance of the evolutionary algorithms (EAs). In addition, it becomes increasingly important to incorporate user preferences because it will be less likely to achieve a representative subset of the Pareto-optimal solutions using a limited population size as the number of objectives increases. This paper proposes a reference vector-guided EA for many-objective optimization. The reference vectors can be used not only to decompose the original multiobjective optimization problem into a number of single-objective subproblems, but also to elucidate user preferences to target a preferred subset of the whole Pareto front (PF). In the proposed algorithm, a scalarization approach, termed angle-penalized distance, is adopted to balance convergence and diversity of the solutions in the high-dimensional objective space. An adaptation strategy is proposed to dynamically adjust the distribution of the reference vectors according to the scales of the objective functions. Our experimental results on a variety of benchmark test problems show that the proposed algorithm is highly competitive in comparison with five state-of-the-art EAs for many-objective optimization. In addition, we show that reference vectors are effective and cost-efficient for preference articulation, which is particularly desirable for many-objective optimization. Furthermore, a reference vector regeneration strategy is proposed for handling irregular PFs. Finally, the proposed algorithm is extended for solving constrained many-objective optimization problems.

Multiobjective evolutionary algorithms (MOEAs) usually achieve a set of nondominated solutions as the approximation of the Pareto front. In order to utilize the solutions, a final decision making process is indispensable in most cases in which a small number of solutions have to be selected. In this process a decision maker selects the solutions according to his or her preferences or based on the knowledge acquired by observing the approximated Pareto front. Due to the limited number of solutions an algorithm can obtain, in particular when the number of objectives is large, a decision maker may be interested in sampling additional solutions in some preferred regions. This paper proposes to use a reference vector based preference articulation (RVPA) method to obtain such additional solutions in preferred regions. After describing the proposed method in detail, experiments are conducted on six benchmark MOPs to assess the performance of the proposed RVPA method. Our empirical results show that, by setting reference vectors in the objective space, the proposed RVPA is able to obtain corresponding solutions in the preferred regions at a much lower cost compared to e.g. a re-start strategy. In addition, by setting the reference vectors in a uniform way, the proposed RVPA method is also able to improve the general quality (convergence and distribution) of the solutions obtained by an MOEA.

In this paper, a novel competitive swarm optimizer (CSO) for large scale optimization is proposed. The algorithm is fundamentally inspired by the particle swarm optimization but is conceptually very different. In the proposed CSO, neither the personal best position of each particle nor the global best position (or neighborhood best positions) is involved in updating the particles. Instead, a pairwise competition mechanism is introduced, where the particle that loses the competition will update its position by learning from the winner. To understand the search behavior of the proposed CSO, a theoretical proof of convergence is provided, together with empirical analysis of its exploration and exploitation abilities showing that the proposed CSO achieves a good balance between exploration and exploitation. Despite its algorithmic simplicity, our empirical results demonstrate that the proposed CSO exhibits a better overall performance than five state-of-the-art metaheuristic algorithms on a set of widely used large scale optimization problems and is able to effectively solve problems of dimensionality up to 5000.

To approximate the Pareto front, most existing multiobjective evolutionary algorithms store the nondominated solutions found so far in the population or in an external archive during the search. Such algorithms often require a high degree of diversity of the stored solutions and only a limited number of solutions can be achieved. By contrast, model-based algorithms can alleviate the requirement on solution diversity and in principle, as many solutions as needed can be generated. This paper proposes a new model-based method for representing and searching nondominated solutions. The main idea is to construct Gaussian process-based inverse models that map all found nondominated solutions from the objective space to the decision space. These inverse models are then used to create offspring by sampling the objective space. To facilitate inverse modeling, the multivariate inverse function is decomposed into a group of univariate functions, where the number of inverse models is reduced using a random grouping technique. Extensive empirical simulations demonstrate that the proposed algorithm exhibits robust search performance on a variety of medium to high dimensional multiobjective optimization test problems. Additional nondominated solutions are generated a posteriori using the constructed models to increase the density of solutions in the preferred regions at a low computational cost.

Evolutionary algorithms have been shown to be powerful for solving multiobjective optimization problems, in which nondominated sorting is a widely adopted technique in selection. This technique, however, can be computationally expensive, especially when the number of individuals in the population becomes large. This is mainly because in most existing nondominated sorting algorithms, a solution needs to be compared with all other solutions before it can be assigned to a front. In this paper we propose a novel, computationally efficient approach to nondominated sorting, termed efficient nondominated sort (ENS). In ENS, a solution to be assigned to a front needs to be compared only with those that have already been assigned to a front, thereby avoiding many unnecessary dominance comparisons. Based on this new approach, two nondominated sorting algorithms have been suggested. Both theoretical analysis and empirical results show that the ENS-based sorting algorithms are computationally more efficient than the state-of-the-art nondominated sorting methods.

Social learning plays an important role in behavior learning among social animals. Different from individual (asocial) learning, social learning has the advantage of allowing individuals to learn behaviors from others without the extra costs of individual trial-and-error. Inspired by the natural social learning phenomenon, we have transplanted the social learning mechanism into particle swarm optimization (PSO) to develop a social learning PSO (SL-PSO). Unlike classical PSO variants, the SL-PSO is performed on a sorted swarm, and instead of merely learning from historical best positions, the particles are able to learn from anyone better (demonstrators) in the current swarm. A key mechanism in the SL-PSO is the learning strategy, where an imitator will learn from different demonstrators. However, in our previous work, little discussion has been focused on demonstrator selection, i.e., which demonstrators are to learn from by the imitator. In this paper, based on the analysis of the demonstrator selection in the SL-PSO, two demonstrator selection strategies are proposed. Experimental results show that, the proposed demonstrator selection strategies have significantly enhanced the performance of the SL-PSO in comparison to five representative PSO variants on a set of benchmark problems.

Most evolutionary algorithms, including particle swarm optimization (PSO) algorithms, involve at least one population (swarm) to realize information exchange or information sharing among different individuals. To enhance the algorithms' global search ability, several multi-swarm PSO algorithms have been proposed. In this paper, a novel multi-swarm evolutionary framework based on a feedback mechanism is introduced. The framework consists of a search operator similar to those in PSO and a mutation strategy, on the top of the feedback mechanism. The framework is compared with a multi-swarm PSO and the canonical PSO on a few widely used benchmarks to demonstrate its performance.

Sexual reproduction plays an important role in evolution. However, in classic genetic algorithms(GAs), the evolutionary process is only implemented on an unisexual population. Although some sexual selection schemes for GAs have been proposed, only limited studies are focused on detailed mechanisms in sexual selection. In this paper, we focus on the modeling of some significant components in sexual selection, including the concepts of male trait, female mating preference. Thereafter, a novel evolutionary framework is constructed based on these models. The theoretical principle of this framework is the famous mechanism called Fisher's runaway process. Numeric optimization is carried out to evaluate the newly proposed framework on a large number of benchmark functions used in CEC2005 Special Session. Comparing with a classic real-coded genetic algorithm, the novel framework outperforms it on most functions. Although this framework is very preliminary, it has shown good potential in solving optimization problems.