郑州大学计算智能实验室

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多模态多目标问题相关研究

1. 多模态多目标优化简介

如果一个多目标优化问题满足以下条件之一就属于多模态多目标优化

（1）存在至少一个局部最优解;

（2）存在两个以上全局最优解。

局部最优解不被邻域内任意一个解支配; 全局最优解不被可行域内任意一个解支配。

图1给出了一个多模态双目标优化问题，该问题有两个全局最优解集。注：一个多模态多目标优化问题可能有多个全局或局部最优解集。

图1 多模态多目标优化问题示意图

2. 多模态多目标优化相关论文列表

• J. Liang, H. Y. Lin, C. T. Yue*, K. J. Yu, Y. Guo, K. J. Qiao. Multiobjective differential evolution with speciation for constrained multimodal multiobjective optimization[J]. IEEE Transactions on Evolutionary Computation, 2023, 27(4): 1115-112.(paper)(code)

• G. Q. Li*, M. Y. Sun, Y. R. Wang, W. L. Wang, W. W. Zhang, C. T. Yue, G. D. Zhang. A ring-hierarchy-based evolutionary algorithm for multimodal multi-objective optimization[J]. Swarm and Evolutionary Computation, 2023, 81: 101352.

• G. Q. Li*, W. L. Wang, C. T. Yue, W. W. Zhang, Y. R. Wang. Two-stage adaptive differential evolution with dynamic dual-populations for multimodal multi-objective optimization with local Pareto solutions[J]. Information Sciences,2023: 119271.

• B. Y. Qu, G. S. Li, L. Yan*, J. Liang, C. T. Yue, K. J. Yu, O. D. Crisalle. A grid-guided particle swarm optimizer for multimodal multi-objective problems[J]. Applied Soft Computing, 2022, 117: 108381.

•  Y. Hu, J. Wang, J. Liang*, Y. L. Wang, U. Ashraf, C. T. Yue, K. J. Yu. A two-archive model based evolutionary algorithm for multimodal multi-objective optimization problems[J]. Applied Soft Computing, 2022, 119: 108606. (paper)(code)

•  J. Liang, Y. J. Zhang, C. T. Yue, K. J. Yu, W. F. Guo, K. Chen, B. Y. Qu. Application of an improved multimodal multiobjective algorithm in feature selection[C]//2022 International Conference on Advanced Robotics and Mechatronics (ICARM). IEEE, 2022: 367-372. 

•  J. Liang, J. T. Yang, C. T. Yue, G. P. Li, K. J. Yu, B. Y. Qu. A multimodal multiobjective genetic algorithm for feature selection[C]//2022 IEEE Congress on Evolutionary Computation (CEC).  2022: 1-8.

• C. T. Yue, P. N. Suganthan*, J. Liang*, B. Y. Qu, K. J. Yu, Y. S. Zhu, L. Yan. Differential evolution using improved crowding distance for multimodal multiobjective optimization[J]. Swarm and Evolutionary Computation, 2021, 62: 100849. (paper)(code)

• J. Liang, K. J. Qiao, C. T. Yue, K. J. Yu, B. Y. Qu*, R. H. Xu, Z. M. Li, Y. Hu. A clustering-based differential evolution algorithm for solving multimodal multi-objective optimization problems[J]. Swarm and Evolutionary Computation, 2020, 60: 100788. (paper)(code)

•  B. Y. Qu, C. Li, J. Liang, L. Yan*, K. J. Yu, Y. S. Zhu. A self-organized speciation based multiobjective particle swarm optimizer for multimodal multiobjective problems[J]. Applied Soft Computing, 2020, 86: 105886. (paper)

• C. T. Yue, J. Liang, P. N. Suganthan, B. Y. Qu, K. J. Yu, S. Liu. MMOGA for solving multimodal multiobjective optimization problems with local pareto sets[C]//2020 IEEE Congress on Evolutionary Computation (CEC). 2020: 1-8. 

• J. Wang, B. Wang, J. Liang*, K. J. Yu, C. T. Yue, X. Y. Ren. Ensemble learning via multimodal multiobjective differential evolution and feature selection[C]//Bio-inspired Computing: Theories and Applications. 2020: 439-453.

•  J. Liang, C. T. Yue, G. P. Li, B. Y. Qu, P. N. Suganthan, K. J. Yu. Problem definitions and evaluation criteria for the CEC 2021 on multimodal multiobjective path planning optimization. Technical Report, 2020.

•  J. Liang, W. W. Xu, C. T. Yue, K. J. Yu, H. Song, O. C. Crisalle, B. Y. Qu*. Multimodal multiobjective optimization with differential evolution[J]. Swarm and Evolutionary Computation, 2019, 44: 1028-1059. (paper)(code)

•  C. T. Yue, B. Y. Qu, K. J. Yu, J. Liang*, X. D. Li. A novel scalable test problem suite for multimodal multiobjective optimization[J]. Swarm and Evolutionary Computation, 2019, 48: 62-71. 

•  Z. H. Li, S. Li, C. T. Yue, Z. G. Shang*, B. Y. Qu. Differential evolution based on reinforcement learning with fitness ranking for solving multimodal multiobjective problems[J]. Swarm and Evolutionary Computation, 2019, 49: 234-244.

• W. Z. Zhang, G. Q. Li, W. W. Zhang, J. Liang, G. G. Yen*. A cluster based PSO with leader updating mechanism and ring-topology for multimodal multiobjective optimization[J]. Swarm and Evolutionary Computation, 2019, 50: 100569.

• Y. Hu, J. Wang, J. Liang*, K. J. Yu, H. Song, Q. Q. Guo, C. T. Yue, Y. L. Wang. A self-organizing multimodal multiobjective pigeon-inspired optimization algorithm[J]. Science China-Information Sciences, 2019, 62(7): 70206.

•  C. T. Yue, J. Liang, B. Y. Qu, K. J. Yu, H. Song. Multimodal multiobjective optimization in feature selection[C]//2019 IEEE congress on evolutionary computation (CEC). 2019: 302-309.

• L. Yan, G. S. Li, Y. C. Jiao, B. Y. Qu, C. T. Yue, S. K. Qu. A performance enhanced niching multi-objective bat algorithm for multimodal multi-objective problems[C]//2019 IEEE Congress on Evolutionary Computation (CEC).  2019: 1275-1282.

•  J. Liang, B. Y. Qu, D. W. Gong, C. T. Yue. Problem definitions and evaluation criteria for the CEC 2019 special session on multimodal multiobjective optimization. Technical Report, 2019.

• J. Liang, Q. Q. Guo, C. T. Yue, B. Y. Qu, K. J. Yu. A self-organizing multi-objective particle swarm optimization algorithm for multimodal multi-objective problems[C]//International Conference on Swarm Intelligence. 2018: 550-560.

• C. T. Yue, B. Y. Qu, J. Liang*. A multiobjective particle swarm optimizer using ring topology for solving multimodal multiobjective problems[J]. IEEE Transactions on Evolutionary Computation, 2017, 22(5): 805-817.  (paper)

• J. Liang, C. T. Yue, B. Y. Qu. Multimodal multi-objective optimization: a preliminary study[C]//2016 IEEE Congress on Evolutionary Computation (CEC).  2016: 2454-2461.

3. 相关重要活动

CEC 2021上，我们组织了关于多模态多目标路径规划的Special Session 和Competition（SS-37），相关介绍和程序可以参考链接http://www5.zzu.edu.cn/ecilab/info/1036/1251.htm。