AI Chat Paper
Discover the SciOpen Platform and Achieve Your Research Goals with Ease.
Search articles, authors, keywords, DOl and etc.
{{expandStatus?'Exit ':''}}Advanced Search
Multimodal multi-objective optimization problems (MMOPs) contain multiple equivalent Pareto sub-sets (PSs) corresponding to a single Pareto front (PF), resulting in difficulty in maintaining promising diversities in both objective and decision spaces to find these PSs. Widely used to solve MMOPs, evolutionary algorithms mainly consist of evolutionary operators that generate new solutions and fitness evaluations of the solutions. To enhance performance in solving MMOPs, this paper proposes a multimodal multi-objective optimization evolutionary algorithm based on a hybrid operator and strengthened diversity improving. Specifically, 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 stage. Moreover, an elitist-assisted differential evolution mechanism is designed for the early exploration stage. In addition, a new fitness function is proposed and used in environmental and mating selections to simultaneously evaluate diversities for PF and PSs. Experimental 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.
F. Ming and W. Gong, Exploring a promising region and enhancing decision space diversity for multimodal multi-objective optimization, Tsinghua Science and Technology, vol. 29, no. 2, pp. 325–342, 2024.
Y. Tian, R. Liu, X. Zhang, H. Ma, K. C. Tan, and Y. Jin, A multipopulation evolutionary algorithm for solving large-scale multimodal multiobjective optimization problems, IEEE Trans. Evol. Comput., vol. 25, no. 3, pp. 405–418, 2021.
V. Barichard and J. K. Hao, Genetic tabu search for the multi-objective knapsack problem, Tsinghua Science and Technology, vol. 8, no. 1, pp. 8–13, 2003.
S. Han, K. Zhu, M. Zhou, and X. Cai, Competition-driven multimodal multiobjective optimization and its application to feature selection for credit card fraud detection, IEEE Trans. Syst. Man Cybern, Syst., vol. 52, no. 12, pp. 7845–7857, 2022.
X. Ma, Y. Fu, K. Gao, L. Zhu, and A. Sadollah, A multi-objective scheduling and routing problem for home health care services via brain storm optimization, Complex System Modeling and Simulation, vol. 3, no. 1, pp. 32–46, 2023.
H. Zhang, L. Ma, J. Wang, and L. Wang, Furnace-grouping problem modeling and multi-objective optimization for special aluminum, IEEE Trans. Emerg. Top. Comput. Intell., vol. 6, no. 3, pp. 544–555, 2022.
L. Wang, Z. Pan, and J. Wang, A review of reinforcement learning based intelligent optimization for manufacturing scheduling, Complex System Modeling and Simulation, vol. 1, no. 4, pp. 257–270, 2021.
R. Tanabe and H. Ishibuchi, A review of evolutionary multimodal multiobjective optimization, IEEE Trans. Evol. Comput., vol. 24, no. 1, pp. 193–200, 2020.
W. Gong, Z. Liao, X. Mi, L. Wang, and Y. Guo, Nonlinear equations solving with intelligent optimization algorithms: A survey, Complex System Modeling and Simulation, vol. 1, no. 1, pp. 15–32, 2021.
F. Ming, W. Gong, L. Wang, and L. Gao, Balancing convergence and diversity in objective and decision spaces for multimodal multi-objective optimization, IEEE Trans. Emerg. Top. Comput. Intell., vol. 7, no. 2, pp. 474–486, 2023.
E. Zitzler, M. Laumanns, and L. Thiele, SPEA2: improving the strength Pareto evolutionary algorithm, Tech. Rep. 103, ETH Zurich, Zurich, Switzerland, 2001.
Y. Liu, G. G. Yen, and D. Gong, A multimodal multiobjective evolutionary algorithm using two-archive and recombination strategies, IEEE Trans. Evol. Comput., vol. 23, no. 4, pp. 660–674, 2019.
Y. Liu, H. Ishibuchi, G. G. Yen, Y. Nojima, and N. Masuyama, Handling imbalance between convergence and diversity in the decision space in evolutionary multi-modal multi-objective optimization, IEEE Trans. Evol. Comput., vol. 24, no. 3, pp. 551–565, 2020.
F. Ming, W. Gong, Y. Yang, and Z. Liao, Constrained multimodal multi-objective optimization: Test problem construction and algorithm design, Swarm Evol. Comput., vol. 76, pp. 101209, 2023.
J. Liang, H. Lin, C. Yue, K. Yu, Y. Guo, and K. Qiao, Multiobjective differential evolution with speciation for constrained multimodal multiobjective optimization, IEEE Trans. Evol. Comput., vol. 27, no. 4, p. 1115–1129, 2023.
C. Grimme, P. Kerschke, P. Aspar, H. Trautmann, M. Preuss, A. H. Deutz, H. Wang, and M. Emmerich, Peeking beyond peaks: Challenges and research potentials of continuous multimodal multi-objective optimization, Comput. Oper. Res., vol. 136, p. 105489, 2021.
K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, A fast and elitist multiobjective genetic algorithm: NSGA-II, IEEE Trans. Evol. Comput., vol. 6, no. 2, pp. 182–197, 2002.
C. Yue, B. Qu, and J. Liang, A multiobjective particle swarm optimizer using ring topology for solving multimodal multiobjective problems, IEEE Trans. Evol. Comput., vol. 22, no. 5, pp. 805–817, 2018.
Q. Lin, W. Lin, Z. Zhu, M. Gong, J. Li, and C. A. C. Coello, Multimodal multiobjective evolutionary optimization with dual clustering in decision and objective spaces, IEEE Trans. Evol. Comput., vol. 25, no. 1, pp. 130–144, 2021.
K. Zhang, C. Shen, G. G. Yen, Z. Xu, and J. He, Two-stage double niched evolution strategy for multimodal multiobjective optimization, IEEE Trans. Evol. Comput., vol. 25, no. 4, pp. 754–768, 2021.
B. Qu, G. Li, L. Yan, J. Liang, C. Yue, K. Yu, and O. D. Crisalle, A grid-guided particle swarm optimizer for multimodal multi-objective problems, Appl. Soft Comput., vol. 117, p. 108381, 2022.
Q. Fan and X. Yan, Solving multimodal multiobjective problems through zoning search, IEEE Trans. Syst. Man Cybern. Syst., vol. 51, no. 8, pp. 4836–4847, 2021.
W. Wang, G. Li, Y. Wang, F. Wu, W. Zhang, and L. Li, Clearing-based multimodal multi-objective evolutionary optimization with layer-to-layer strategy, Swarm Evol. Comput., vol. 68, p. 100976, 2022.
J. Liang, K. Qiao, C. Yue, K. Yu, B. Qu, R. Xu, Z. Li, and Y. Hu, A clustering-based differential evolution algorithm for solving multimodal multi-objective optimization problems, Swarm Evol. Comput., vol. 60, p. 100788, 2021.
Y. Peng and H. Ishibuchi, A diversity-enhanced subset selection framework for multimodal multiobjective optimization, IEEE Trans. Evol. Comput., vol. 26, no. 5, pp. 886–900, 2022.
W. Li, T. Zhang, R. Wang, and H. Ishibuchi, Weighted indicator-based evolutionary algorithm for multimodal multiobjective optimization, IEEE Trans. Evol. Comput., vol. 25, no. 6, pp. 1064–1078, 2021.
W. Li, X. Yao, T. Zhang, R. Wang, and L. Wang, Hierarchy ranking method for multimodal multiobjective optimization with local Pareto fronts, IEEE Trans. Evol. Comput., vol. 27, no. 1, pp. 98–110, 2023.
W. Li, M. Ming, T. Zhang, R. Wang, S. Huang, and L. Wang, Multimodal multi-objective evolutionary algorithm considering global and local Pareto fronts, Acta Autom. Sin., vol. 48, pp. 1–13, 2022.
J. Zhang, J. Zou, S. Yang, and J. Zheng, An evolutionary algorithm based on independently evolving sub-problems for multimodal multi-objective optimization, Inf. Sci., vol. 619, pp. 908–929, 2023.
Y. Tian, T. Zhang, J. Xiao, X. Zhang, and Y. Jin, A coevolutionary framework for constrained multiobjective optimization problems, IEEE Trans. Evol. Comput., vol. 25, no. 1, pp. 102–116, 2021.
M. Ming, A. Trivedi, R. Wang, D. Srinivasan, and T. Zhang, A dual-population-based evolutionary algorithm for constrained multiobjective optimization, IEEE Trans. Evol. Comput., vol. 25, no. 4, pp. 739–753, 2021.
R. Jiao, B. Xue, and M. Zhang, A multiform optimization framework for constrained multiobjective optimization, IEEE Trans. Cybern., vol. 53, no. 8, pp. 5165–5177, 2023.
K. Deb and R. B. Agrawal, Simulated binary crossover for continuous search space, Complex Syst., vol. 9, pp. 1–34, 1994.
A. Zhou, Q. Zhang, and Y. Jin, Approximating the set of Pareto-optimal solutions in both the decision and objective spaces by an estimation of distribution algorithm, IEEE Trans. Evol. Comput., vol. 13, no. 5, pp. 1167–1189, 2009.
E. Jiang, L. Wang, and J. Wang, Decomposition-based multi-objective optimization for energy-aware distributed hybrid flow shop scheduling with multiprocessor tasks, Tsinghua Science and Technology, vol. 26, no. 5, pp. 646–663, 2021.
W. Zhang, X. Chen, and J. Jiang, A multi-objective optimization method of initial virtual machine fault-tolerant placement for star topological data centers of cloud systems, Tsinghua Science and Technology, vol. 26, no. 1, pp. 95–111, 2021.
H. Zhang, C. Wang, and W. Fan, A new filter collaborative state transition algorithm for two-objective dynamic reactive power optimization, Tsinghua Science and Technology, vol. 24, no. 1, pp. 30–43, 2019.
261
Views
43
Downloads
0
Crossref
0
Web of Science
0
Scopus
0
CSCD
Altmetrics
The articles published in this open access journal are distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/).
京公网安备11010802044758号