Coevolutionary Framework for Generalized Multimodal Multi-Objective Optimization

Wenhua Li; Xingyi Yao; Kaiwen Li; Rui Wang; Tao Zhang; Ling Wang

doi:10.1109/JAS.2023.123609

Volume 10 Issue 7

Jul. 2023

IEEE/CAA Journal of Automatica Sinica

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Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2023 > 10(7): 1544-1556

W. H. Li, X. Y. Yao, K. W. Li, R. Wang, T. Zhang, and L. Wang, “Coevolutionary framework for generalized multimodal multi-objective optimization,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 7, pp. 1544–1556, Jul. 2023. doi: 10.1109/JAS.2023.123609

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W. H. Li, X. Y. Yao, K. W. Li, R. Wang, T. Zhang, and L. Wang, “Coevolutionary framework for generalized multimodal multi-objective optimization,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 7, pp. 1544–1556, Jul. 2023. doi: 10.1109/JAS.2023.123609

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Coevolutionary Framework for Generalized Multimodal Multi-Objective Optimization

doi: 10.1109/JAS.2023.123609

Funds: This work was supported by the Open Project of Xiangjiang Laboratory (22XJ02003) and the National Natural Science Foundation of China (62122093, 72071205)

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Author Bio:
Wenhua Li received the B.S. and M.S. degrees in 2018 and 2020 from National University of Defense Technology (NUDT), respectively. He is now a Ph.D. candidate in management science and technology at the College of Systems Engineering, National University of Defense Technology. He has authored more than 20 papers, including those published in IEEE Transactions on Evolutionary Computation and Swarm and Evolutionary Computation. His current research interests include multi-objective evolutionary algorithms, energy management in microgrids, and artificial intelligence

Xingyi Yao received the B.S. degree from National University of Defense Technology (NUDT) in 2017. She is currently purchasing the master degree at the College of Systems Engineering, NUDT. Her main research interests include multi-criteria decision-making, optimal scheduling, data mining, and optimization methods

Kaiwen Li received the B.S., M.S. and Ph.D. degrees from National University of Defense Technology (NUDT), in 2016 and 2018, respectively.He is a Lecturer with the College of System Engineering, NUDT. His research interests include neural combinatorial optimization, prediction technique, multiobjective optimization, reinforcement learning, data mining, and optimization methods on energy internet

Rui Wang received the B.S. degree from National University of Defense Technology (NUDT) in 2008, and the Ph.D. degree from the University of Sheffield, UK in 2013. Currently, he is currently with National University of Defense Technology. His current research interest includes multiobjective optimization and the development of algorithms applicable in practice. He has authored more than 40 referred papers including those published in IEEE Transactions on Evolutionary Computation and IEEE Transactions on Cybernetics. Dr. Wang serves as an Associate Editor of the IEEE Transactions on Evolutionary Computation, Swarm and Evolutionary Computation, Expert System With Applications, etc. He is the recipients of the Operational Research Society Ph.D. Prize in 2014, of the Funds for Distinguished Young Scientists from the Natural Science Foundation of Hunan Province at 2016, of the Wu Wen-Jun Artificial Intelligence Outstanding Young Scholar at 2017, of the National Science Fund for Outstanding Young Scholars at 2021

Tao Zhang received the B.S., M.S., Ph.D. degrees from National University of Defense Technology (NUDT), in 1998, 2001, and 2004, respectively. He is a Full Professor with the College of System Engineering, NUDT. He is also the Director of the Hunan Key Laboratory of Multi-Energy System Intelligent Interconnection Technology (HKL-MSI2T). His current research interests include optimal scheduling, data mining, and optimization methods on energy internet. He was the recipient of the Science and Technology Award of Provincial Level (First Place in 2020, 2021, and Second Place in 2015, 2018)

Ling Wang received the B.Sc. degree in automation and the Ph.D. degree in control theory and control engineering from Tsinghua University, in 1995 and 1999, respectively. Since 1999, he has been with the Department of Automation, Tsinghua University, where he became a Full Professor in 2008. His current research interests include intelligent optimization and production scheduling. He was the recipient of the National Natural Science Fund for Distinguished Young Scholars of China, the National Natural Science Award (Second Place) in 2014, the Science and Technology Award of Beijing City in 2008, and the Natural Science Award (First Place in 2003, and Second Place in 2007) nominated by the Ministry of Education of China
Corresponding author: Rui Wang, e-mail: ruiwangnudt@gmail.com; Tao Zhang, e-mail: zhangtao@nudt.edu.cn
1¹ Source code of CoMMEA and supplementary material can be found at https://github.com/Wenhua-Li/CoMMEA.
Received Date: 2023-02-10
Revised Date: 2023-04-04
Accepted Date: 2023-04-12

Available Online: 2023-05-16

Abstract

Abstract

Most multimodal multi-objective evolutionary algorithms (MMEAs) aim to find all global Pareto optimal sets (PSs) for a multimodal multi-objective optimization problem (MMOP). However, in real-world problems, decision makers (DMs) may be also interested in local PSs. Also, searching for both global and local PSs is more general in view of dealing with MMOPs, which can be seen as generalized MMOPs. Moreover, most state-of-the-art MMEAs exhibit poor convergence on high-dimension MMOPs and are unable to deal with constrained MMOPs. To address the above issues, we present a novel multimodal multi-objective coevolutionary algorithm (CoMMEA) to better produce both global and local PSs, and simultaneously, to improve the convergence performance in dealing with high-dimension MMOPs. Specifically, the CoMMEA introduces two archives to the search process, and coevolves them simultaneously through effective knowledge transfer. The convergence archive assists the CoMMEA to quickly approach the Pareto optimal front. The knowledge of the converged solutions is then transferred to the diversity archive which utilizes the local convergence indicator and the ϵ-dominance-based method to obtain global and local PSs effectively. Experimental results show that CoMMEA is competitive compared to seven state-of-the-art MMEAs on fifty-four complex MMOPs.
- Coevolution,
- ${\boldsymbol{\epsilon}}$-dominance,
- generalized multimodal multi-objective optimization (MMO),
- local convergence,
- two archives

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¹ Source code of CoMMEA and supplementary material can be found at https://github.com/Wenhua-Li/CoMMEA.

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Highlights

A coevolutionary framework for GMMOPs is proposed, which integrates a novel algorithm CoMMEA
The ϵ-dominance method and local convergence indicator are used to balance diversity and convergence
The framework can handle almost all types of MMOPs with different characteristics and complexities
Theoretical and empirical studies are provided to demonstrate its effectiveness and efficiency
The paper contributes to the advancement of GMMOPs research and applications

Coevolutionary Framework for Generalized Multimodal Multi-Objective Optimization

doi: 10.1109/JAS.2023.123609

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