In order to achieve the optimal solutions for multi-model multi-objective problems, in this paper a new environmental selection strategy is proposed for differential evolution approach. First, non-dominated solutions are kept to ensure the convergence in objective space; second, a population with good distribution in objective space is obtained by using its correlation with reference vectors; and then the next parent population is selected by simultaneously considering the convergence performance in objective space and the diversity performance in decision space. Experimental results on 11 multi-model multiobjective test problems show that the proposed method is efficient in solving multi-model multi-objective problems.
ZHANG Guochen, LIU Pengfei, SUN Chaoli
. Multi-model Multi-objective Optimization Algorithms with a New Environmental Selection Strategy[J]. Journal of Applied Sciences, 2022
, 40(5)
: 739
-748
.
DOI: 10.3969/j.issn.0255-8297.2022.05.003
[1] Jaszkiewicz A. On the performance of multi-objective genetic local search on the 0/1 knapsack problem-a comparative experiment[J]. IEEE Transactions on Evolutionary Computation, 2002, 6(4):402-412.
[2] Han Y Y, Gong D W, Jin Y C, et al. Evolutionary multiobjective blocking lot-streaming flow shop scheduling with machine breakdowns[J]. IEEE Transactions on Cybernetics, 2019, 49(1):184-197.
[3] Kudo F, Yoshikawa T, Furuhashi T. A study on analysis of design variables in Pareto solutions for conceptual design optimization problem of hybrid rocket engine[C]//2011 IEEE Congress of Evolutionary Computation (CEC), 2011:2558-2562.
[4] Schütze O, Vasile M, Coello C A C. Computing the set of epsilon-efficient solutions in multiobjective space mission design[J]. Journal of Aerospace Computing, Information and Communication, 2011, 8(3):53-70.
[5] Zhang S, Wang H F, Yang D, et al. Hybrid multi-objective genetic algorithm for multiobjective optimization problems[C]//27th Chinese Control and Decision Conference (2015 CCDC). IEEE, 2015:1970-1974.
[6] Zhou A M, Qu B Y, Li H, et al. Multiobjective evolutionary algorithms:a survey of the state of the art[J]. Swarm and Evolutionary Computation, 2011, 1(1):32-49.
[7] Yue C T, Qu B Y, Yu K J, et al. A novel scalable test problem suite for multimodal multiobjective optimization[J]. Swarm and Evolutionary Computation, 2019, 48:62-71.
[8] Liang J J, Yue C T, Qu B Y. Multimodal multio-bjective optimization:a preliminary study[C]//2016 IEEE Congress on Evolutionary Computation (CEC), 2016:2454-2461.
[9] Deb K, Pratap A, Agarwal S, et al. A fast and elitist multiobjective genetic algorithm:NSGA-II[J]. IEEE Transactions on Evolutionary Computation, 2002, 6(2):182-197.
[10] Zhang Q F, Li H. MOEA/D:a multiobjective evolutionary algorithm based on decomposition[J]. IEEE Transactions on Evolutionary Computation, 2007, 11(6):712-731.
[11] Zitzler E, Künzli S. Indicator-based selection in multiobjective search[C]//Parallel Problem Solving from Nature-PPSN VIII, 2004:832-842.
[12] Yang S X, Li M Q, Liu X H, et al. A grid-based evolutionary algorithm for many-objective optimization[J]. IEEE Transactions on Evolutionary Computation, 2013, 17(5):721-736.
[13] Kim M, Hiroyasu T, Miki M, et al. SPEA2+:improving the performance of the strength pareto evolutionary algorithm 2[C]//Parallel Problem Solving from Nature-PPSN VIII, 2004:742-751.
[14] Tanabe R, Ishibuchi H. A decomposition-based evolutionary algorithm for multi-modal multiobjective optimization[C]//Parallel Problem Solving from Nature-PPSN XV, 2018:249-261.
[15] Coello C C A, Reyes-Sierra M. Multi-objective particle swarm optimizers:a survey of the state-of-the-art[J]. International Journal of Computational Intelligence Research, 2006, 2(3):287-308.
[16] Lalwani S, Singhal S, Kumar R, et al. A comprehensive survey:multiobjective particle swarm optimization (MOPSO) algorithm:variants and applications[J]. Transactions on Combinatorics, 2013, 2(1):89-101.
[17] Li X D. Niching without niching parameters:particle swarm optimization using a ring topology[J]. IEEE Transactions on Evolutionary Computation, 2010, 14(1):150-169.
[18] Yue C T, Qu B Y, Liang J. A multiobjective particle swarm optimizer using ring topology for solving multimodal multiobjective problems[J]. IEEE Transactions on Evolutionary Computation, 2018, 22(5):805-817.
[19] Liang J, Guo Q Q, Yue C T, et al. A self-organizing multi-objective multi-particle swarm optimization algorithm for multimodal multi-objective problems[C]//Advances in Swarm Intelligence, 2018:550-560.
[20] Liu Y P, Yen G G, Gong D W. A multimodal multiobjective evolutionary algorithm using two-archive and recombination strategies[J]. IEEE Transactions on Evolutionary Computation, 2019, 23(4):660-674.
[21] Shi R Z, Lin W, Lin Q Z, et al. Multimodal multio-bjective optimization using a density-based one-by-one update strategy[C]//2019 IEEE Congress on Evolutionary Computation (CEC), 2019:295-301.
[22] Li W H, Zhang T, Wang R, et al. Weighted indicator-based evolutionary algorithm for multimodal multiobjective optimization[J]. IEEE Transactions on Evolutionary Computation, 2021, 25(6):1064-1078.
[23] Zhang K, Shen C N, Yen G G, et al. Two-stage double niched evolution strategy for multimodal multiobjective optimization[J]. IEEE Transactions on Evolutionary Computation, 2021, 25(4):754-768.
[24] Javadi M, Ramirez-Atencia C, Mostaghim S. A novel grid-based crowding distance for multimodal multi-objective optimization[C]//2020 IEEE Congress on Evolutionary Computation (CEC), 2020:1-8.
[25] 岳彩通. 基于群集智能的多模态多目标优化算法及其应用研究[D]. 郑州:郑州大学, 2020.
[26] Storn R, Price K. Differential evolution:a simple and efficient heuristic for global optimization over continuous spaces[J]. Journal of Global Optimization, 1997, 11(4):341-359.
[27] Storn R. On the usage of differential evolution for function optimization[C]//North American Fuzzy Information Processing. IEEE, 1996:519-523.
[28] Rudolph G, Naujoks B, Preuss M. Capabilities of EMOA to detect and preserve equivalent Pareto subsets[C]//Evolutionary Multi-Criterion Optimization, 2007:36-50.
[29] Deb K, Tiwari S. Omni-optimizer:a procedure for single and multi-objective optimization[C]//Evolutionary Multi-criterion Optimization, 2005:47-61.
[30] Zitzler E, Thiele L, Laumanns M, et al. Performance assessment of multiobjective optimizers:an analysis and review[J]. IEEE Transactions on Evolutionary Computation, 2003, 7(2):117-132.
