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Hybrid Operator and Strengthened Diversity Improving for multimodal multi-objective optimization

Tsinghua Science and Technology 2024年第5期29卷 1409-1421页

作者： Guoting Zhang Yonghao Du Xiaobin Zhu Xiaolu Liu Beijing Institute of Tracking and Telecommunication Technology Beijing 100094China College of Systems Engineering National University of Defense TechnologyChangsha 410073China

multimodal multi-objective optimization problems(MMOPs)contain multiple equivalent Pareto subsets(PSs)corresponding to a single Pareto front(PF),resulting in difficulty in maintaining promising diversities in both objective and decision spaces to find these *** used to solve MMOPs,evolutionary algorithms mainly consist of evolutionary operators that generate new solutions and fitness evaluations of the *** enhance performance in solving MMOPs,this paper proposes a multimodal multi-objective optimization evolutionary algorithm based on a hybrid operator and strengthened diversity ***,a hybrid operator mechanism is devised to ensure the exploration of the decision space in the early stage and approximation to the optima in the latter ***,an elitist-assisted differential evolution mechanism is designed for the early exploration *** addition,a new fitness function is proposed and used in environmental and mating selections to simultaneously evaluate diversities for PF and *** studies on 11 widely used benchmark instances from a test suite verify the superiority or at least competitiveness of the proposed methods compared to five state-of-the-art algorithms tailored for MMOPs.

关键词： multimodal multi-objective optimization evolutionary algorithm hybrid operator strengthened diversity

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multimodal multi-objective optimization: Comparative study of the state-of-the-art

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SWARM AND EVOLUTIONARY COMPUTATION 2023年 77卷

作者： Li, Wenhua Zhang, Tao Wang, Rui Huang, Shengjun Liang, Jing Natl Univ Def Technol Coll Syst Engn Changsha Peoples R China Hunan Key Lab Multienergy Syst Intelligent Interco Changsha Peoples R China Zhengzhou Univ Sch Elect Engn Zhengzhou Peoples R China

multimodal multi-objective problems (MMOPs) commonly arise in the real world where distant solutions in decision space correspond to very similar objective values. To obtain more Pareto optimal solutions for MMOPs, many multimodal multi-objective evolutionary algorithms (MMEAs) have been proposed. For now, few studies have encompassed most of the representative MMEAs and made a comparative comparison. In this study, we first review the related works during the last two decades. Then, we choose 15 state-of-the-art algorithms that utilize different diversity-maintaining techniques and compared their performance on different types of the existing test suites. Experimental results indicate the strengths and weaknesses of different techniques on different types of MMOPs, thus providing guidance on how to select/design MMEAs in specific scenarios.

关键词： multimodal multi-objective optimization Evolutionary computation Comparative study Review

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A novel multimodal multi-objective optimization algorithm for multi-robot task allocation

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TRANSACTIONS OF THE INSTITUTE OF MEASUREMENT AND CONTROL 2023年

作者： Miao, Zhenhua Huang, Wentao Jiang, Qingchao Fan, Qinqin Shanghai Maritime Univ Logist Res Ctr Shanghai Peoples R China Minist Educ China Key Lab Power Transmiss & Power Convers Control Beijing Peoples R China East China Univ Sci & Technol Key Lab Smart Mfg Energy Chem Proc Minist Educ Shanghai Peoples R China Shanghai Maritime Univ Logist Res Ctr 1550 Haigang Ave Shanghai 201306 Peoples R China

multi-robot task allocation (MRTA) is widely used in various fields and plays an important role in some complex task environments due to its ability to distribute parallel processing tasks. However, the multi-robot cooperative system is susceptible to actual environments or preferences of decision-makers. Therefore, providing enough solutions/schemes in the MRTA is important. To improve the reliability and feasibility of obtained solution set, an improved multimodal multi-objective differential evolution algorithm hybrid with a simulated annealing algorithm (IMMODE-SA) is proposed to solve MRTA problems in this study. In the proposed IMMODE-SA, a novel population initialization method is used to improve the population quality, and a redundant solution deletion method is employed to delete redundant solutions during the search process. Moreover, a simulated annealing algorithm is utilized to improve the exploitation capability in the last generation of evolutionary process. To verify the performance of the proposed algorithm, extensive simulation experiments are conducted on three MRTA instances. Experimental results show that the proposed algorithm performs better than other competitors on MRTA instances in terms of Hypervolume (HV). Also, the validity of the proposed algorithm is demonstrated via three experiments and experimental analysis results indicate that the IMMODE-SA can provide more equivalent optimal schemes to decision makers. Finally, it is crucial to solve MRTA problems with time window constraints.

关键词： multi-robot task allocation multi-robot cooperation path planning multimodal multi-objective optimization evolutionary computation

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Balancing Convergence and Diversity in objective and Decision Spaces for multimodal multi-objective optimization

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IEEE TRANSACTIONS ON EMERGING TOPICS IN COMPUTATIONAL INTELLIGENCE 2023年第2期7卷 474-486页

作者： Ming, Fei Gong, Wenyin Wang, Ling Gao, Liang China Univ Geosci Sch Comp Sci Wuhan 430074 Peoples R China Tsinghua Univ Dept Automat Beijing 100084 Peoples R China Huazhong Univ Sci & Technol State Key Lab Digital Mfg Equipment & Technol Wuhan 430074 Peoples R China

Solving multimodal multi-objective optimization problems (MMOPs) via evolutionary algorithms receives increasing attention recently. Maintaining good diversity in both decision and objective spaces is essential to handling MMOPs. Unfortunately, most of the existing methods prefer convergence in the objective space, resulting in the elimination of poorly converged solutions that may be helpful to improve the diversity in the decision space. To overcome this drawback, we propose a coevolutionary algorithm to balance the convergence and the diversity in both objective and decision spaces to better solve MMOPs. In the proposed method, a convergence-first population aims at pursuing a solution set well distributed on both the Pareto front and Pareto set assisted by a convergence-relaxed population. Further, a novel objective relaxation technique is developed for the convergence-relaxed population, which can supplement Pareto set segments not detected by the convergence-first population. Additionally, the environmental selections, mating selection, and fitness evaluation strategies are customized to bring about the balance of convergence and diversity in both objective and decision spaces. Experimental studies on four MMOP benchmarks demonstrated the superiority of the proposed algorithm over six state-of-the-art methods tailored for MMOPs.

关键词： multimodal multi-objective optimization evolutionary algorithm coevolution objective relaxation

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A decomposition-based evolutionary algorithm using an estimation strategy for multimodal multi-objective optimization

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INFORMATION SCIENCES 2022年 606卷 531-548页

作者： Gao, Weifeng Xu, Wei Gong, Maoguo Yen, Gary G. Xidian Univ Sch Math & Stat Xian 710126 Peoples R China Xidian Univ Sch Elect Engn Xian 710126 Peoples R China Oklahoma State Univ Sch Elect & Comp Engn Stillwater OK 74078 USA

multimodal multi-objective optimization problems (MMOPs) are commonly seen in real-world applications and have attracted a growing attention in recent years. In this paper, a decomposition-based evolutionary algorithm using an estimation strategy is presented to handle MMOPs. In the proposed algorithm, multiple individuals who are assigned to the same weight vector form a subpopulation. Then, the estimation strategy is designed for estimating the amount of Pareto optimal sets (PSs), where the mean-shift algorithm is adopted to classify subpopulation into some clusters. In essence, the number of clusters is considered to be the estimated number of PSs. Finally, an environmental selection method, which combines the estimation strategy and the greedy selection, is adopted to dynamically adjust the subpopulation scale for maintaining the population diversity. The experimental results illustrate that the devised algorithm performs pass beyond the selected up-to-date competing algorithms. (c) 2022 Elsevier Inc. All rights reserved.

关键词： Decomposition-based evolutionary algorithms Diversity maintenance multimodal multi-objective optimization

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A neighborhood-assisted evolutionary algorithm for multimodal multi-objective optimization

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MEMETIC COMPUTING 2024年第2期16卷 139-158页

作者： Zhang, Weiwei Li, Jiaqiang Li, Guoqing Zhang, Weizheng Zhengzhou Univ Light Ind Sch Comp Sci & Technol Zhengzhou 450000 Peoples R China Ningbo Univ Fac Elect Engn & Comp Sci Ningbo 315211 Peoples R China

multi-modal multi-objective optimization problems (MMOPs) involve multiple Pareto sets (PSs) in decision space corresponding to the same Pareto front (PF) in objective space. The difficulty lies in locating multiple equivalent PSs while ensuring a well-converged and well-distributed PF. To address this, a neighborhood-assisted reproduction strategy is proposed. Through interactions with non-dominated solutions, the generated offspring could spread out along the PF, while ineractions with neighbors could improve the convergence ability. Importantly, individuals can participate in multiple neighborhoods, reducing the computational burden. Additionally, a neighborhood-assisted environmental selection strategy is prposed to encourage exploration of diverse solution regions, ensuring a balanced distribution of the population and preservation of multiple PSs. Comparative experiments are implemented on the CEC 2019 MMOPs test suite, and the superior performance of the proposed algorithm is demonstrated in comparison to several state-of-the-art approaches.

关键词： multimodal multi-objective optimization Neighborhood Evolutionary algorithm Niching based algorithm

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Altruistic population algorithm: A metaheuristic search algorithm for solving multimodal multi-objective optimization problems

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MATHEMATICS AND COMPUTERS IN SIMULATION 2023年 210卷 296-319页

作者： Ouyang, Haibin Chen, Jianhong Li, Steven Xiang, Jianhua Zhan, Zhi-Hui Guangzhou Univ Sch Mech & Elect Engn Guangzhou 510006 Peoples R China RMIT Univ Grad Sch Business & Law Melbourne 3000 Australia South China Univ Technol Sch Comp Sci & Engn Guangzhou 510006 Peoples R China

Although many intelligent optimization algorithms have been applied to the multimodal multi-objective optimization problems (MMOPs) which are complex and difficult, challenges of MMOP such as loss of PS in decision space and low efficiency have not been well solved. To better solve these problems, an altruistic population algorithm (APA) which is based on the altruism behavior in some animal populations, is proposed in this paper. The proposed APA has five major operations: parent selection, procreation variation, altruistic nurturing, crowd competition and archive updating. A few important features of the proposed APA are: (1) The nurturing cost according to a pair of parents' condition is introduced. It can accelerate the convergence speed while maintaining the diversity of the Pareto optimal solutions (PS). (2) The application of altruism allows the transfer of nurturing cost between descendant siblings to improve the efficiency and decrease the unnecessary variations. (3) A selection strategy called neighboring selection based on the distance in the objective space is proposed. It is an effective way to delete the redundant individuals in the objective space. The experimental results reveal that APA preforms better than other existing algorithms for solving various MMOPs.(c) 2023 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

关键词： Altruistic population algorithm Selection strategy multimodal multi-objective optimization

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Competitive swarm optimization with subset selection based manifold learning for multimodal multi-objective optimization

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INFORMATION SCIENCES 2024年 654卷

作者： Zhang, Weiwei Fan, Yan Yen, Gary G. Wang, Feiyu Li, Guoqing Zhengzhou Univ Light Ind Sch Comp & Commun Engn Zhengzhou 450000 Peoples R China Oklahoma State Univ Sch Elect & Comp Engn Stillwater OK 74078 USA Ningbo Univ Fac Elect Engn & Comp Sci Ningbo 315211 Peoples R China

There are two major challenges when handling the multimodal multi-objective optimization (MMO) problems. One is the loss of diversity since most of the evolutionary algorithms designed for MMO prefer the base algorithm with rapid convergence. Therefore, the extra niching or other diversity preserving mechanism is inevitable. The other is the distribution of the Pareto optimal solutions with imbalanced density. Since the Pareto optimal sets may show different characteristics in the decision space, it is tough to converge the solutions to the Pareto front uniformly. To address these issues, subset selection and manifold learning based competitive swarm optimiza-tion algorithm, namely MMO_CSO, is proposed. Competitive swarm optimizer which has well balance on both diversity and convergence is adopted. Moreover, a subset selection strategy is applied to select diversified individuals for learning the manifold structure of the Pareto set. Thereby, the subset selection based manifold learning mechanism is designed to generate the promising solutions which could approach the real Pareto solutions and fill the sparse Pareto subregion. Compared against six state-of-the-art peer algorithms, the proposed MMO_CSO has a better performance to search for the Pareto optimal solutions both in decision space and objective space on CEC2019 MMO benchmarks.

关键词： multimodal multi-objective optimization Competitive swarm optimization Subset selection Manifold learning

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A cluster-based immune-inspired algorithm using manifold learning for multimodal multi-objective optimization

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INFORMATION SCIENCES 2021年 581卷 304-326页

作者： Zhang, Weiwei Zhang, Ningjun Zhang, Weizheng Yen, Gary G. Li, Guoqing Zhengzhou Univ Light Ind Sch Comp & Commun Engn Zhengzhou 450000 Peoples R China Oklahoma State Univ Sch Elect & Comp Engn Stillwater OK 74078 USA Zhejiang Univ Technol Coll Comp Sci & Technol Hangzhou 310023 Peoples R China

Both problem characteristics in multimodality and multi-objective are involved in multi modal multi-objective optimization problems (MMOPs). How to locate diverse Pareto sets and approximate Pareto front simultaneously is a challenging research topic. To address this issue, a cluster-based immune-inspired algorithm using manifold learning is proposed in this paper for solving MMOPs. First of all, the population is partitioned into multiple sub populations, and each of them is expected to find equivalent Pareto solutions in different regions. Subsequently, the immune-inspired algorithm with proportional cloning and hypermutation is developed for improving the diversity of the population and obtaining high-quality Pareto solutions in the decision space. Additionally, principal component analysis is adopted to learn the manifold of the Pareto set, further improve the convergence, and enhance interaction among subpopulations. The proposed algorithm is compared with six state-of-the-art algorithms. Experimental results demonstrate that the proposed algorithm is capable of locating equivalent Pareto optimal solutions in the decision space and maintaining the diversity and convergence of solutions in both decision space and objective space, simultaneously. (c) 2021 Elsevier Inc. All rights reserved.

关键词： multimodal multi-objective optimization Immune-inspired algorithm Manifold learning Principal component analysis

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Two-stage evolutionary algorithm with fuzzy preference indicator for multimodal multi-objective optimization

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SWARM AND EVOLUTIONARY COMPUTATION 2024年 85卷

作者： Xie, Yinghong Li, Junhua Li, Yufei Zhu, Wenhao Dai, Chaoqing Nanchang Hangkong Univ Key Lab Jiangxi Prov Image Proc & Pattern Recognit Nanchang 330063 Peoples R China Shanghai Jiao Tong Univ Sch Mech Engn Shanghai 200240 Peoples R China

multimodal multi-objective optimization problems (MMOPs) are multi-objective optimization problems (MOPs) involving multiple equivalent global or local Pareto optimal solution sets (PSs). For decision-makers, not only the global optimal solution sets need to be found, but also the value of local optimal solution sets cannot be ignored. However, most multimodal multi-objective evolutionary algorithms (MMOEAs) tend to select solutions with better convergence, and it is difficult to obtain the global PSs and local PSs at the same time. Therefore, we propose a fuzzy preference indicator-based two-stage evolutionary algorithm (FPITSEA) in this paper. To evaluate more comprehensively the potential of each solution in the population for locating the global and local PS during the evolutionary process, a fuzzy preference indicator is designed in FPITSEA. The fuzzy preference indicator is used to guide the evolution of the population in the first stage to find the global and local Pareto optimal regions. Subsequently, an independent evolution strategy is implemented in the second stage to distinguish different PSs as accurately as possible while also ensuring the convergence quality of the solution set. In addition, an improved distance-based subset selection method is proposed, aiming to simultaneously improve the distribution of the solution set in the decision space and objective space. Experimental results on several test sets of MMOPs show the advantages of FPITSEA over several state -of -the -art MMOEAs.

关键词： multimodal multi-objective optimization Two-stage evolutionary algorithm Fuzzy preference indicator Independent evolution strategy Subset selection method

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