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A Generative Adversarial Networks Model Based Evolutionary Algorithm for multimodal multi-objective optimization

IEEE TRANSACTIONS ON EMERGING TOPICS IN COMPUTATIONAL INTELLIGENCE 2024年 1-10页

作者： Dang, Qianlong Zhang, Guanghui Wang, Ling Yang, Shuai Zhan, Tao Northwest A&F Univ Coll Sci Yangling 712100 Peoples R China Hebei Agr Univ Sch Informat Sci & Technol Baoding 071001 Peoples R China Tsinghua Univ Dept Automat Beijing 100084 Peoples R China Anhui Agr Univ Sch Informat & Artificial Intelligence Hefei 230036 Peoples R China Northwest A&F Univ Coll Informat Engn Yangling 712100 Peoples R China

The key to solving multimodal multi-objective optimization problems is to achieve good diversity in the decision space. However, the existing algorithms usually adopt the reproduction operation based on random mechanism, which do not make full use of the distribution features of promising solutions in the population, resulting in the defects of the diversity of the obtained Parteo optimal solution sets. In order to solve the above problem, this paper proposes a multimodal multi-objective optimization evolutionary algorithm (MMOEA) based on generative adversarial networks (GANs). Specifically, we firstly design a classification strategy to distinguish good solutions from poor solutions. The solutions in the population are classified as real samples and fake samples by non-dominated selection sorting based on special crowding distance, and the training data of GANs are obtained. Secondly, a GANs-based offspring generation method is proposed. Through the adversarial training of GANs, the generator can simulate the distribution of promising solutions in the population and generate offspring with good diversity. Thirdly, an environment selection strategy based on GANs is constructed. By sorting the classification probability of the solutions output by the discriminator, the population are selected and updated. Finally, the proposed algorithm is compared with seven other competitive multimodal multi-objective optimization evolutionary algorithms on the CEC 2019 test suite and a real-word problem, and experimental results indicate its superior performance.

关键词： Environment selection strategy evolutionary algorithm generative adversarial networks (GANs) multimodal multi-objective optimization

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A distributed individuals based multimodal multi-objective optimization differential evolution algorithm

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MEMETIC COMPUTING 2024年第3期16卷 505-517页

作者： Wang, Wei Wei, Zhifang Huang, Tianqi Gao, Xiaoli Gao, Weifeng Sichuan Jiuzhou Elect Grp Co Ltd Mianyang Peoples R China Shanxi Univ Inst Big Data Sci & Ind Taiyuan 030006 Shanxi Peoples R China Xidian Univ Sch Math & Stat Xian 710126 Peoples R China

There may exist a one-to-many mapping between objective and decision spaces in multimodal multi-objective optimization problems (MMOPs), which requires the evolutionary algorithm to locate multiple non-dominated solution sets. In order to enhance the diversity of the population, we develop a multimodal multi-objective differential evolution algorithm based on distributed individuals and lifetime mechanism. First, every individual can be seen as a distributed unit to locate multiple non-dominated solutions. The solutions with the good diversity are generated by adopting virtual population, and the range of virtual population is adjusted by an adaptive adjustment strategy to locate more non-dominated solutions. Second, it is considered that each individual has a limited lifespan inspired by natural phenomenon. As the search area of individuals becoming adaptively smaller, the individuals with good quality are archived and they can reinitialize with a new lifespan for enhancing diversity of the search space. Then the probability selection strategy is applied in the environment selection to balance exploration and exploitation. The test results on 22 multimodal multi-objective benchmark test functions verify the superior performance of the proposed method.

关键词： multimodal multi-objective optimization Distributed individuals Differential evolution Lifespan mechanism

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A Zoning Search-Based multimodal multi-objective Brain Storm optimization Algorithm for multimodal multi-objective optimization

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ALGORITHMS 2023年第7期16卷 350-350页

作者： Fan, Jiajia Huang, Wentao Jiang, Qingchao Fan, Qinqin Shanghai Maritime Univ Logist Res Ctr Shanghai 201306 Peoples R China Shanghai Jiao Tong Univ Minist Educ Key Lab Control Power Transmiss & Convers Shanghai 200240 Peoples R China East China Univ Sci & Technol Minist Educ Key Lab Smart Mfg Energy Chem Shanghai 200237 Peoples R China

For multimodal multi-objective optimization problems (MMOPs), there are multiple equivalent Pareto optimal solutions in the decision space that are corresponding to the same objective value. Therefore, the main tasks of multimodal multi-objective optimization (MMO) are to find a high-quality PF approximation in the objective space and maintain the population diversity in the decision space. To achieve the above objectives, this article proposes a zoning search-based multimodal multi-objective brain storm optimization algorithm (ZS-MMBSO). At first, the search space segmentation method is employed to divide the search space into some sub-regions. Moreover, a novel individual generation strategy is incorporated into the multimodal multi-objective brain storm optimization algorithm, which can improve the search performance of the search engineering. The proposed algorithm is compared with five famous multimodal multi-objective evolutionary algorithms (MMOEAs) on IEEE CEC2019 MMOPs benchmark test suite. Experimental results indicate that the overall performance of the ZS-MMBSO is the best among all competitors.

关键词： brain storm optimization algorithm multimodal multi-objective optimization evolutionary computation zoning search

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Two-Stage Evolutionary Algorithm Using Clustering for multimodal multi-objective optimization with Imbalance Convergence and Diversity 21st

Two-Stage Evolutionary Algorithm Using Clustering for Multim...

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21st International Conference on Algorithms and Architectures for Parallel Processing (ICA3PP)

作者： Li, Guoqing Wang, Wanliang Wang, Yule Zhejiang Univ Technol Coll Comp Sci & Technol Hangzhou 310023 Peoples R China

ISBN: (纸本)9783030953911;9783030953904

This paper proposes a two-stage multimodal multi-objective evolutionary algorithm using clustering, termed as TS_MMOEAC. In the first-stage evolution of TS_MMOEAC, the convergence-penalized density (CPD) based k-means clustering is used to divide population into multiple subpopulations. Subsequently, a local archive mechanism is adopted to maintain diverse local Pareto optimal solutions in decision space. In the second-stage evolution, an identical k-means clustering based on distance among individuals in decision space is applied to form multiple subpopulations. In this case, the convergence performance of local Pareto optimal solutions is accelerated. Meanwhile, equivalent Pareto optimal solutions with the imbalance between convergence and diversity are located by a similar local archive method with a larger clearing radius. Experimental results validate the superior performance of TS_MMOEAC, and the proposed TS_MMOEAC is capable of finding equivalent Pareto optimal solutions with the imbalance between convergence and diversity.

关键词： Two-stage evolutionary algorithm Clustering multimodal multi-objective optimization Imbalance

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A Particle Swarm Optimizer with adaptive dynamic neighborhood for multimodal multi-objective optimization 35

A Particle Swarm Optimizer with adaptive dynamic neighborhoo...

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35th Chinese Control and Decision Conference (CCDC)

作者： Wei, Jingyue Zhang, Enze Ge, Rui Yangzhou Univ Informat Engn Coll Yangzhou Jiangsu Peoples R China

ISBN: (纸本)9798350334722

In this paper, a multi-objective particle swarm optimizer based on adaptive dynamic neighborhood (ADN-MOPSO) is proposed to locate multiple Pareto optimal solutions to solve multimodal multi-objective problems. In the proposed algorithm, a spatial distance-based non-overlapping ring topology is used to form multiple subpopulations for parallel search to enhance the local search capability of the algorithm. In addition, an adaptive dynamic neighborhood selection strategy is proposed to balance the exploration and exploitation capabilities of the algorithm, allowing the size of the subpopulation to change automatically when the neighborhood switch time is met. To prevent the algorithm from premature convergence, a stagnation detection strategy is introduced to apply a Gaussian perturbation operation to the particles that fall into the neighborhood optimum. Finally, the proposed algorithm is used to solve multimodal multi-objective test problems and compared with existing multimodal multi-objective optimization algorithms. The results show that the proposed algorithm can obtain more Pareto solutions when solving different types of multimodal multi-objective functions.

关键词： multi-objective optimization multimodal multi-objective optimization particle swarm optimization algorithm sub-swarm regrouping ring topology

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Two-Stage Dual-Archive Fireworks Algorithm for multimodal multi-objective optimization 2022

Two-Stage Dual-Archive Fireworks Algorithm for Multimodal Mu...

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6th International Conference on Machine Learning and Soft Computing (ICMLSC)

作者： Chen, Yushu Zhang, Kai Shen, Chaonan Wuhan Univ Sci & Technol Sch Comp Sci & Technol Wuhan Peoples R China

ISBN: (纸本)9781450387477

In recent years, multi-objective optimization has attracted a lot of attention in the field of high performance computing. In this paper, two-stage dual-archive fireworks algorithm (TSDA_MMOFWA) is proposed to solve the multimodal multi-objective optimization problems (MMOPs). The first stage of the algorithm uses a dual-archive genetic operator evolution strategy. Each firework performs a relatively independent decision space search guided by global information to find a large number of Pareto optimal solution set. The second stage of the algorithm distributes the solution set uniformly over multiple approximate Pareto optimal sets by means of an adaptive firework explosion strategy. The performance of the algorithm is evaluated on 16 benchmark MMOPs. The experimental results show that the proposed TSDA_MMOFWA possesses a competitive performance compared to the state-of-the-art comparison algorithms.

关键词： fireworks algorithm multimodal multi-objective optimization multimodal multi-objective evolutionary algorithm

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Differential Evolution Using Special Sorting for multimodal multi-objective optimization with Local Pareto Sets 14th

Differential Evolution Using Special Sorting for Multimodal ...

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14th International Conference on Swarm Intelligence (ICSI)

作者： Yan, Li Li, Yiran Qu, Boyang Qiao, Baihao Duan, Hongxin Guo, Shunge Zhongyuan Univ Technol Sch Elect & Informat Zhengzhou Peoples R China

ISBN: (纸本)9783031366215;9783031366222

multimodal multi-objective optimization problems (MMOPs) can be categorized into two types based on the nature of their Pareto sets (PSs): those with global PSs only and those with both global and local PSs. However, most existing multimodal multi-objective evolutionary algorithms (MMEAs) are designed for the former type, and few works focus on the latter type of MMOPs. Thus, this paper proposes an improved differential evolution algorithm that uses a new-designed special sorting to solve the MMOP with local PSs. Specifically, the special sorting is realized based on the global and local non-dominated sorting. By measuring the ranks of individuals in both the global and local regions, the potential local optimal solutions can be preserved while ensuring the global convergence of population. In addition, an elite-based differential mutation strategy is introduced to generate offspring with good convergence and diversity that can improve the search capability of the population. The experimental results on CEC2019 test suite demonstrate the effectiveness and superiority of the proposed algorithm on finding and retaining both global and local optimal solutions.

关键词： multimodal multi-objective optimization Local Pareto set Special sorting Differential mutation strategy

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Integration of preferences in multimodal multi-objective optimization

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EXPERT SYSTEMS WITH APPLICATIONS 2024年 254卷

作者： Li, Zhipan Rong, Huigui Chen, Jianguo Zhao, Zilu Huang, Yupeng Hunan Univ Coll Comp Sci & Elect Engn Changsha 410082 Peoples R China Sun Yat Sen Univ Sch Software Engn Guangzhou 519082 Peoples R China Xi An Jiao Tong Univ Sch Management Xian 710049 Peoples R China

Various existing multimodal multi-objective evolutionary algorithms (MMEAs) efficiently search for an approximation to the Pareto optimal front (PF), which consists of multiple equivalent Pareto optimal sets (PSs), when tackling multimodal multi-objective optimization problems (MMOPs). However, in practical applications, the Decision-maker (DM) often seeks specific portions of the PF, known as the Region of Interest (ROI), corresponding to particular instances rather than the whole PF. Existing MMEAs only focus on the whole PF and lack exploration of the ROI. Consequently, we propose an innovative MMEA that incorporates the DM's preferences and local convergence quality (MMEA-PLC). The proposed algorithm integrates the DM's preferences into the traditional Pareto-dominance relationship, enabling the search for multiple equivalent Pareto optimal set subsets (PSSs) within the ROI. Due to the influence of local PFs, accurately representing the ROI can be challenging when expressed across different PFs. Therefore, we design a preference-based Pareto-dominance relationship to accurately convey the preferences on different PFs by mapping solutions onto a hyperplane in the objective space. Then, we further develop a scheme for assessing local convergence quality (LCQ) to ensure that the algorithm can identify multiple equivalent PSSs within the same ROI. To verify the effectiveness of the proposed algorithm, MMEA-PLC was experimentally compared with eight stateof-the-art MMEAs on 28 benchmark functions and a real-life application problem. Experimental results show that MMEA-PLC has significant competitive advantages in different preference scenarios.

关键词： multimodal multi-objective optimization Region of interest Preferences Local convergence quality Hyperplane

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Two-stage species conservation for multimodal multi-objective optimization with local Pareto sets

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INFORMATION SCIENCES 2023年第1期639卷

作者： Yang, Cuicui Wu, Tongxuan Ji, Junzhong Beijing Univ Technol Fac Informat Technol Beijing Municipal Key Lab Multimedia & Intelligent Beijing 100124 Peoples R China Beijing Univ Technol Beijing Inst Artificial Intelligence Beijing 100124 Peoples R China

Compared to general multi-objective optimization problems, multimodal multi-objective opti-mization problems (MMOPs) with local Pareto sets (PSs) must determine multiple global and local PSs simultaneously. Therefore, MMOPs with local PSs are challenging. To resolve this is-sue, this study proposes a multimodal multi-objective optimization evolutionary algorithm based on two-stage species conservation (MMOEA/TSC). MMOEA/TSC divides the evolutionary process into two stages: diversity-oriented species conservation and convergence-oriented species conser-vation. The former is aimed at locating promising regions in which global and local PSs may exist. To balance the distribution of solutions, a Gaussian variation strategy is used to iteratively generate diverse offspring in regions that contain the smallest number of solutions. The latter mainly focused on obtaining one PS with good convergence in each promising region. To help the solutions converge to the global and local PSs uniformly, a species stratification strategy was adopted according to the Pareto level of the well-converged solution for each species. The pro-posed algorithm was compared with seven state-of-the-art algorithms. For the CEC 2020 MMOP test problem set, the experimental results show that MMOEA/TSC has the capacity to find global and local PSs.

关键词： multimodal multi-objective optimization Evolutionary algorithm Species conservation Gaussian variation Niching

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Two-stage adaptive differential evolution with dynamic dual-populations for multimodal multi-objective optimization with local Pareto solutions

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INFORMATION SCIENCES 2023年第1期644卷

作者： Li, Guoqing Wang, Wanliang Yue, Caitong Zhang, Weiwei Wang, Yirui Ningbo Univ Fac Elect Engn & Comp Sci Ningbo 315211 Peoples R China Zhejiang Univ Technol Coll Comp Sci & Technol Hangzhou 310023 Peoples R China Zhengzhou Univ Sch Elect & Informat Engn Zhengzhou 450001 Peoples R China Zhengzhou Univ Light Ind Coll Comp & Commun Engn Zhengzhou 450001 Peoples R China

Several distinctive Pareto Sets (PSs) with an identical Pareto Front (PF) and local PSs with acceptable quality are comprised in multimodal multi-objective optimization problems (MMOPs). Recently, many multimodal multi-objective evolutionary algorithms (MMEAs) have been proposed. However, even though most of MMEAs have the ability to discover equivalent global PSs, these methods encounter failures in developing local PSs. The main reasons are that local PSs are dominated by global PSs and are removed from the population during the evolutionary process. To tackle this matter, a two-stage adaptive differential evolution with a dynamic dual-populations strategy, termed TADE_DDS, is developed. In TADE_DDS, a dynamic population strategy is put forward to divide the population into a global population that locates equivalent global PSs and a local population that aims to locate local PSs. Subsequently, the whole procedure is completed by two evolutionary stages associated with a dynamic population strategy, and an adaptive differential evolution algorithm is adopted for both global and local populations. The first-stage evolution aims to find more favorable local PSs and the second-stage evolution concentrates on finding a variety of global PSs. Additionally, a local environmental selection and a global environmental selection are performed for developing the diversity of local PSs and improving the convergence of global PSs and local PSs, respectively. TADE_DDS and several popular MMEAs are implemented on standard test problems. Experimental results demonstrate that TADE_DDS is equipped to locate both global and local PSs, and is superior to its competing algorithms.

关键词： multimodal multi-objective optimization local Pareto solutions Dynamic dual-populations Adaptive differential evolution Two-stage evolution

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