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Reinforcement learning assisted differential evolution with adaptive resource allocation strategy for multimodal optimization problems

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SWARM AND EVOLUTIONARY COMPUTATION 2025年 94卷

作者： Ma, Tao Zhao, Hong Li, Xiangqian Yang, Fang Liu, Chun-sheng Liu, Jing Natl Univ Def Technol Hefei 230000 Peoples R China Xidian Univ Guangzhou Inst Technol Guangzhou 510555 Peoples R China

multimodal optimization problems (MMOPs) present the challenge of identifying multiple optimal solutions within a search space, requiring algorithms to effectively balance exploration and exploitation. To enhance solution accuracy, the local search methods often focus on elite individuals, allocating additional fitness evaluations (FEs) to refine their solutions. However, once the optima near these elite individuals are identified, continued allocation of FEs becomes inefficient, leading to a waste of limited resources. This highlights the inherent difficulty of achieving a balance between exploration and exploitation within the population under constrained resources. To solve this problem, this paper proposes a new reinforcement learning-assisted differential evolution (RLDE) algorithm with adaptive resource allocation strategy. Firstly, the exploitation population is proposed, and the original population focuses on exploring undiscovered optimal regions and generating exploitation populations, while each exploitation population focuses on finding high-precision optima within its responsible optimal region. Secondly, a reinforcement learning-assisted adaptive resource allocation (RLRA) strategy is proposed to allocate FEs, which can reduce the waste of FEs and balance the exploration and exploitation ability among multiple populations. Finally, a local greedy mutation (LGM) strategy is proposed to help individuals evolve toward the neighborhood with better fitness values. Compared with 11 state-of-the-art multimodal algorithms, the RLDE achieves better or more competitive results in all accuracy levels. Besides, the results on the dielectric composite optimization problem verify the practicality of RLDE.

关键词： multimodal optimization problems Differential evolution Reinforcement learning Adaptive resource allocation

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A Novel Quantum Entanglement-Inspired Meta-heuristic Framework for Solving multimodal optimization problems

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Chinese Journal of Electronics 2021年第1期30卷 145-152页

作者： ZHAO Shijie MA Shilin GAO Leifu YU Dongmei Institute of Optimization and Decision College of Science Liaoning Technical University Institute for Optimization and Decision Analytics Liaoning Technical University

To solve multimodal optimization problems(MOPs), a Novel Quantum entanglement-inspired meta-heuristic framework(NMF-QE) is proposed. Its main inspirations are two concepts of quantum physics:quantum entanglement and quantum superposition. When given Proto-born particles(PBPs) of a population, these two concepts are mathematically developed to generate twin-born and combination-born particles, *** if any elite-born particles would be created by a local re-searching strategy. These three or four groups of particles come together as a whole search population of NMF-QE to realize exploration and exploitation of algorithms. To guarantee dynamical optimization capability of NMF-QE, the individual evolutionary mechanism of some existing meta-heuristics will be adopted to iteratively create PBPs. A selected meta-heuristic is coupled with NMF-QE to present its improved variant. Numerical results show that the proposed NMF-QE can effectively improve optimization performance of meta-heuristics on MOPs.

关键词： optimisation quantum entanglement NMF-QE quantum superposition genetic algorithms search problems combination-born particles quantum physics evolutionary computation given Proto-born particles multimodal optimization problems elite-born particles Novel Quantum entanglement-inspired meta-heuristic framework existing meta-heuristics

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A new differential evolution algorithm for solving multimodal optimization problems with high dimensionality

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SOFT COMPUTING 2018年第13期22卷 4361-4388页

作者： Tuo, Shouheng Zhang, Junying Yuan, Xiguo Yong, Longquan Xidian Univ Sch Comp Sci & Technol Xian 710071 Peoples R China Shaanxi Univ Technol Sch Math & Comp Sci Hanzhong 723000 Peoples R China

Differential evolution (DE) is an efficient intelligent optimization algorithm which has been widely applied to real-world problems, however poor in solution quality and convergence performance for complex multimodal optimization problems. To tackle this problem, a new improving strategy for DE algorithm is presented, in which crossover operator, mutation operator and a new local variables adjustment strategy are integrated together to make the DE more efficient and effective. An improved dynamic crossover rate is adopted to manage the three operators, so to decrease the computational cost of DE. To investigate the performance of the proposed DE algorithm, some frequently referred mutation operators, i.e., DE/rand/1, DE/Best/1, DE/current-to-best/1, DE/Best/2, DE/rand/2, are employed, respectively, in proposed method for comparing with standard DE algorithm which also uses the same mutation operators as our method. Three state-of-the-art evolutionary algorithms (SaDE, CoDE and CMAES) and seven large-scale optimization algorithms on seven high-dimensional optimization problems of CEC2008 are compared with the proposed algorithm. We employ Wilcoxon Signed-Rank Test to further test the difference significance of performance between our algorithm and other compared algorithms. Experimental results demonstrate that the proposed algorithm is more effective in solution quality but with less CPU time (e.g., when dimensionality equals 1000, its mean optimal fitness is less than and the CPU time reduces by about 19.3% for function Schwefel 2.26), even with a very small population size, no matter which mutation operator is adopted.

关键词： Differential evolution Dynamic crossover operator Local adjustment strategy High dimensionality multimodal optimization problems

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A Multi-Angle Hierarchical Differential Evolution Approach for multimodal optimization problems

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IEEE ACCESS 2020年 8卷 178322-178335页

作者： Hong, Zhao Chen, Zong-Gan Liu, Dong Zhan, Zhi-Hui Zhang, Jun South China Univ Technol Sch Comp Sci & Engn Guangzhou 510006 Peoples R China Henan Normal Univ Sch Comp & Informat Engn Xinxiang 453007 Henan Peoples R China Hanyang Univ Ansan 15588 South Korea

multimodal optimization problem (MMOP) is one of the most common problems in engineering practices that requires multiple optimal solutions to be located simultaneously. An efficient algorithm for solving MMOPs should balance the diversity and convergence of the population, so that the global optimal solutions can be located as many as possible. However, most of existing algorithms are easy to be trapped into local peaks and cannot provide high-quality solutions. To better deal with MMOPs, considerations on the solution quality angle and the evolution stage angle are both taken into account in this paper and a multi-angle hierarchical differential evolution (MaHDE) algorithm is proposed. Firstly, a fitness hierarchical mutation (FHM) strategy is designed to balance the exploration and exploitation ability of different individuals. In the FHM strategy, the individuals are divided into two levels (i.e., low/high-level) according to their solution quality in the current niche. Then, the low/high-level individuals are applied to different guiding strategies. Secondly, a directed global search (DGS) strategy is introduced for the low-level individuals in the late evolution stage, which can improve the population diversity and provide these low-level individuals with the opportunity to re-search the global peaks. Thirdly, an elite local search (ELS) strategy is designed for the high-level individuals in the late evolution stage to refine their solution accuracy. Extensive experiments are developed to verify the performance of MaHDE on the widely used MMOPs test functions i.e., CEC'2013. Experimental results show that MaHDE generally outperforms the compared state-of-the-art multimodal algorithms.

关键词： Sociology Statistics optimization Convergence Licenses Perturbation methods Evolution (biology) Multi-angle hierarchical two-stage search differential evolution multimodal optimization problems

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Distributed minimum spanning tree differential evolution for multimodal optimization problems

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SOFT COMPUTING 2019年第24期23卷 13339-13349页

作者： Wang, Zi-Jia Zhan, Zhi-Hui Zhang, Jun Sun Yat Sen Univ Sch Data & Comp Sci Guangzhou 510006 Guangdong Peoples R China South China Univ Technol Sch Comp Sci & Engn Guangzhou 510006 Guangdong Peoples R China Guangdong Prov Key Lab Computat Intelligence & Cy Guangzhou Guangdong Peoples R China

multimodal optimization problem (MMOP) requires to find optima as many as possible for a single problem. Recently, many niching techniques have been proposed to tackle MMOPs. However, most of the niching techniques are either sensitive to the niching parameters or causing a waste of fitness evaluations. In this paper, we proposed a novel niching technique based on minimum spanning tree (MST) and applied it into differential evolution (DE), termed as MSTDE, to solve MMOPs. In every generation, an MST is built based on the distance information among the individuals. After that, we cut the M largest weighted edges of the MST to form some subtrees, so-called subpopulations. The DE operators are executed within the subpopulations. Besides, a dynamic pruning ratio (DPR) strategy is proposed to determine M with an attempt to reduce its sensitivity, so as to enhance the niching performance. Meanwhile, the DPR strategy can achieve a good balance between diversity and convergence. Besides, taking the advantage of fast availability in time from virtual machines (VMs), a distributed model is applied in MSTDE, where different subpopulations run concurrently on distributed VMs. Experiments have been conducted on the CEC2013 multimodal benchmark functions to test the performance of MSTDE, and the experimental results show that MSTDE can outperform many existed multimodal optimization algorithms.

关键词： Differential evolution Minimum spanning tree multimodal optimization problems Distributed model

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Fitness and Distance Based Local Search With Adaptive Differential Evolution for multimodal optimization problems

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IEEE TRANSACTIONS ON EMERGING TOPICS IN COMPUTATIONAL INTELLIGENCE 2023年第3期7卷 684-699页

作者： Wang, Zi-Jia Zhan, Zhi-Hui Li, Yun Kwong, Sam Jeon, Sang-Woon Zhang, Jun Guangzhou Univ Sch Comp Sci & Cyber Engn Guangzhou 510006 Peoples R China Univ Elect Sci & Technol China Shenzhen Inst Adv Study Shenzhen 518110 Peoples R China i4AI Ltd London WCIN 3AX England City Univ Hong Kong Dept Comp Sci Hong Kong Peoples R China Hanyang Univ Dept Elect & Commun Engn Ansan 15588 South Korea Zhejiang Normal Univ Jinhua 321004 Peoples R China Hanyang Univ Ansan 15588 South Korea

Local search has been regarded as a promising technique in multimodal algorithms to refine the accuracy of found multiple optima. However, how to execute the local search operations precisely on the found global optima and avoid the meaningless local search operations on local optima or found similar areas is still a challenge. In this paper, we propose a novel local search technique based on the individual information from two aspects, termed as fitness and distance based local search (FDLS). The fitness information can avoid the ineffective local search operations on the local optima, while the distance information can avoid the meaningless local search operations on the similar areas. These two kinds of information act in different roles and complement each other, which ensures that the local search is executed in different (ensured by distance information) and promising (ensured by fitness information) areas, leading to successful local search. Based on this, we design an adaptive DE (ADE) with adaptive parameters scheme and apply FDLS to ADE, termed as FDLS-ADE. Experimental results on the CEC2015 multimodal competition show the effectiveness and superiority of the FDLS-ADE, including comparisons with the winner of the CEC2015 multimodal competition. Furthermore, compared with other multimodal algorithms, the performance of the FDLS-ADE is seen relatively insensitive to niching parameters. Besides, experiments conducted also show that the FDLS can be applied to other multimodal algorithms easily and can further improve their performance. Finally, an application to a real-world nonlinear equations system further illustrates the applicability of the FDLS-ADE.

关键词： Iron Search problems Sociology optimization Clustering algorithms Transforms Sensitivity Fitness and distance local search differential evolution multimodal optimization problems evolutionary computation

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Adaptive Guidance-based Differential Evolution with Iterative Feedback Archive Strategy for multimodal optimization problems

Adaptive Guidance-based Differential Evolution with Iterativ...

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IEEE Congress on Evolutionary Computation (CEC) as part of the IEEE World Congress on Computational Intelligence (IEEE WCCI)

作者： Zhao, Hong Zhan, Zhi-Hui Zhang, Jun South China Univ Technol Sch Comp Sci & Engn Guangzhou 510006 Peoples R China South China Univ Technol Guangdong Prov Key Lab Computat Intelligence & Cy Guangzhou 510006 Peoples R China South China Univ Technol State Key Lab Subtrop Bldg Sci Guangzhou 510006 Peoples R China Hanyang Univ Ansan 15588 South Korea

ISBN: (纸本)9781728169293

multimodal optimization problems (MMOPs) target to locate multiple global optima simultaneously, which require the algorithms not only can maintain the population diversity to locate the global optima as many as possible, but also can ensure the convergence on each found optimal region to refine the solutions as high accuracy as possible. Aiming to these two goals and to efficiently deal with MMOPs, an adaptive guidance-based differential evolution (AGDE) with archive strategy is proposed in this paper, including three novel components. Firstly, an adaptive mutation strategy (AMS) is introduced, which guides the current individual to move towards the peak that is closest to itself. Secondly, an iterative feedback archive (IFA) strategy is used to store the global optima of the population in every iteration. Thirdly, a Gaussian disturbance-based elite learning (GDEL) strategy is performed on the archive to refine the accuracy of the solutions. The AMS strategy helps to locate more peaks, while the [FA and GDEL strategies help to maintain the found solutions and refine their accuracy. The performance of AGDE is tested on 20 widely used multimodal benchmark functions of CEC'2013. The experimental results of AGDE are competitive with the results obtained by the state-of-the-art multimodal algorithms.

关键词： Differential evolution multimodal optimization problems Adaptive mutation strategy

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Solving multimodal optimization problems through a Multiobjective optimization Approach 7

Solving Multimodal Optimization Problems through a Multiobje...

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7th International Conference on Information Science and Technology (ICIST)

作者： Ji, Jing-Yu Yu, Wei-Jie Chen, Wei-Neng Zhan, Zhi-Hui Zhang, Jun Sun Yat Sen Univ Guangzhou Guangdong Peoples R China South China Univ Technol Guangzhou Guangdong Peoples R China

ISBN: (纸本)9781509054015

This paper proposes a novel multiobjective optimization approach for solving multimodal optimization problems (MMOPs). An MMOP at hand is first transformed into a bi-objective optimization problem. The two objectives are constructed totally conflict by using the distance information and the objective function value. In this way, multiple optima of an MMOP are converted into the nondominated solutions of the transformed bi-objective optimization problem. Then, multi-objective optimization techniques based on differential evolution are applied to solve the bi-objective problem. In addition, a modified solution comparison criterion is proposed to improve the accuracy level of the final solutions. The performance of the proposed approach is evaluated on a suite of benchmark functions. Experimental results show that the proposed approach is very competitive compared with six state-of-the-art multimodal optimization algorithms on most of the benchmark functions.

关键词： multimodal optimization problems multiobjective optimization differential evolution

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Localized Distance and Time-based Differential Evolution for multimodal optimization problems 22

Localized Distance and Time-based Differential Evolution for...

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Genetic and Evolutionary Computation Conference (GECCO)

作者： Zhao, Hong Li, JiaRui Liu, Jing Xidian Univ Guangzhou Inst Technol Guangzhou Guangdong Peoples R China

ISBN: (纸本)9781450392686

multimodal optimization problems (MMOPs) aim to find global multiple optimal solutions with high accuracy. Although many state-of-the-art algorithms are proposed to deal with MMOPs, there are still some challenges as how to avoid local optima and how to refine the solutions accuracy. Aim to these, this paper proposes a Localized Distance and Time-based Differential Evolution (LDTDE) for MMOPs, which includes three contributions. Firstly, a Random and Neighborhood-based Mutation (RNM) strategy is proposed to avoid local optima and refine the accuracy of found solutions. That is each individual not only performs random-based mutation operation but also performs neighborhood-based mutation operation by Euclidean distance. Secondly, a Locality-based Crowding Selection (LCS) strategy is introduced to accelerate the convergence and further approach the global optima. Thirdly, an Adaptive Parameter Control (APC) strategy is proposed to reduce the sensitivity of parameters, which can dynamically calculate the appropriate parameters for each individual based on the state of itself. The performance of LDTDE is tested on CEC'2013 and compared with state-of-the-art multimodal optimization algorithms.

关键词： Differential evolution multimodal optimization problems Temporal locality Adaptive parameter control

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Particle Swarm optimization with Hybrid Ring Topology for multimodal optimization problems

Particle Swarm Optimization with Hybrid Ring Topology for Mu...

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IEEE International Conference on Systems, Man, and Cybernetics (SMC)

作者： Chen, Zong-Gan Zhan, Zhi-Hui Liu, Dong Kwong, Sam Zhang, Jun South China Univ Technol Sch Comp Sci & Engn Guangzhou 510006 Peoples R China South China Univ Technol Guangdong Prov Key Lab Computat Intelligence & Cy Guangzhou Peoples R China Henan Normal Univ Sch Comp & Informat Engn Xinxiang 453007 Henan Peoples R China City Univ Hong Kong Dept Comp Sci Hong Kong Peoples R China Hanyang Univ Ansan 15588 South Korea

ISBN: (纸本)9781728185262

multimodal optimization problems (MMOPs) require the algorithm to locate multiple global optima and also achieve a certain accuracy on the found optima. When applying particle swarm optimization (PSO) to solve MMOPs, a fixed population communication topology may not be sufficient to handle these two requirements simultaneously. In this paper, a novel PSO with hybrid ring topology, termed HRTPSO, is proposed for MMOPs. In the early evolutionary process of HRTPSO, a sparse topology is constructed to enhance the population diversity to help locate multiple optima, while in the later evolutionary process of HRTPSO, the population communication topology is switched to a relatively dense topology for improving the convergence efficiency on the found optima. The switch of topology is controlled by a threshold and its effect is also analyzed in this paper. Experimental results on the 20 multimodal functions in CEC'2013 benchmark set show that HRTPSO has better performance than the other six multimodal optimization algorithms.

关键词： Particle swarm optimization hybrid ring topology multimodal optimization problems

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