郑州大学计算智能实验室

Computational Intelligence Laboratory

MMO

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Research on Multimodal Multi-objective Problems 


Important activities on Multimodal multiobjective optimization (MMO)

Competition and Special Session on Multimodal Multiobjective Optimization was organized along with the CEC 2021. The competition information is available on http://www5.zzu.edu.cn/ecilab/info/1036/1251.htm.


1. Simple introduction to multimodal multiobjective optimization (MMO)

 

For a multiobjective optimization problem, if it meets one of the following conditions, it is a multimodal multiobjective optimization problem:

1) It has at least one local Pareto optimal solution;

2) It has at least two global Pareto optimal solutions corresponding to the same point on the PF.

The local Pareto optimal solution represents the solution which is not dominated by any neighborhood solution. The global Pareto optimal solution is not dominated by any solutions in the feasible space.

Fig. 1 shows a bi-objective minimization problem with two Global PSs. Note that a certain multimodal multiobjective problem may have several Local PSs and Global PSs.

Fig. 1. Illustration of multimodal multiobjective problem.

 

 

2. Multimodal multiobjective optimization (MMO) related reference list

 

  1. Wang R, Ma W, Tan M, et al. Preference-inspired coevolutionary algorithm with active diversity strategy for multi-objective multi-modal optimization[J]. Information Sciences, 2021(546): 1148-1165.(paper

  2. Yue C, Suganthan P N, Liang J, et al. Differential evolution using improved crowding distance for multimodal multiobjective optimization[J]. Swarm and Evolutionary Computation, 2021, 62: 100849.(paper

  3. Jha K, Saha S. Incorporation of multimodal multiobjective optimization in designing a filter based feature selection technique[J]. Applied Soft Computing, 2021, 98: 106823.(paper

  4. Pal M, Bandyopadhyay S. Decomposition in decision and objective space for multi-modal multi-objective optimization[J]. Swarm and Evolutionary Computation, 2021, 62: 100842.(paper

  5. Zhang K, Chen M, Xu X, et al. Multi-objective evolution strategy for multimodal multi-objective optimization[J]. Applied Soft Computing, 2021, 101: 107004.(paper

  6. Li G, Wang W, Zhang W, et al. Grid search based multi-population particle swarm optimization algorithm for multimodal multi-objective optimization[J]. Swarm and Evolutionary Computation, 2021: 100843. (paper)

  7. Yang Q, Wang Z, Luo J, et al. Balancing performance between the decision space and the objective space in multimodal multiobjective optimization[J]. Memetic Computing, 2021: 1-17. (paper)

  8. Javadi M, Ramirez-Atencia C, Mostaghim S. Combining manhattan and crowding distances in decision space for multimodal multi-objective optimization problems[M]//Advances in Evolutionary and Deterministic Methods for Design, Optimization and Control in Engineering and Sciences. Springer, Cham, 2021: 131-145.(paper

  9. Javadi M, Zille H, Mostaghim S. The effects of crowding distance and mutation in multimodal and multi-objective optimization problems[M]//Advances in Evolutionary and Deterministic Methods for Design, Optimization and Control in Engineering and Sciences. Springer, Cham, 2021: 115-130.(paper

  10. Zhang K, Shen C, He J, et al. Knee based multimodal multi-objective evolutionary algorithm for decision making[J]. Information Sciences, 2021, 544: 39-55.(paper

  11. Liu C, Shen W, Zhang L, et al. Improved Membrane Algorithm Under the Framework of P Systems to Solve Multimodal Multiobjective Problems[J]. International Journal of Pattern Recognition and Artificial Intelligence, 2021: 2159024.(paper

  12. Luo N, Lin W, Huang P, et al. An Evolutionary Algorithm with Clustering-Based Assisted Selection Strategy for Multimodal Multiobjective Optimization[J]. Complexity, 2021, 2021.(paper

  13. Yi Hu, Boyang Qu, Jie Wang, Jing Liang, et al. Short-term load forecasting using multimodal evolutionary algorithm and random vector functional link network based ensemble learning[J]. Applied Energy, 285 (2021): 116415. (paper)

  14. Lin W, Li Y, Luo N. A Novel Decomposition-Based Multimodal Multi-objective Evolutionary Algorithm[C]//International Conference on Intelligent Computing. Springer, Cham, 2020: 571-582. (paper)

  15. Yue C T, Liang J J, Suganthan P N, et al. MMOGA for Solving Multimodal Multiobjective Optimization Problems with Local Pareto Sets[C]// 2020 IEEE Congress on Evolutionary Computation (CEC). IEEE, 2020: 1-8. (paper

  16. Li G, Yan L, Qu B. Multi-Objective Particle Swarm Optimization Based on Gaussian Sampling[J]. IEEE Access, 2020, 8: 209717-209737.(paper

  17. 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). IEEE, 2020: 1-8.(paper

  18. Rivera C, Inostroza-Ponta M, Villalobos-Cid M. A multimodal multi-objective optimisation approach to deal with the phylogenetic inference problem[C]//2020 IEEE Conference on Computational Intelligence in Bioinformatics and Computational Biology (CIBCB). IEEE, 2020: 1-7.(paper

  19. Lin Q , Lin W , Zhu Z , et al. Multimodal Multi-objective Evolutionary Optimization with Dual Clustering in Decision and Objective Spaces[J]. IEEE Transactions on Evolutionary Computation, 2020, PP(99):1-1. (paper)(code)

  20. J. Liang, K. J. Qiao, C. T. Yue, et al. A Clustering-Based Differential Evolution Algorithm for Solving Multimodal Multi-Objective Optimization Problems[J]. Swarm and Evolutionary Computation, 2020.(paper)(code)

  21. B. Y. Qu, C. Li, J. Liang, et al. A self-organized speciation based multi-objective particle swarm optimizer for multimodal multi-objective problems[J]. Applied Soft Computing, 2020.(paper)(code)

  22. 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. (paper)

    YUE Caitong. Research  on  multimodal  multiobjective  optimization algorithm and application based on swarm intelligence [D]. Zhengzhou: Zhengzhou University, 2020. (paper)

  23. 李志梦. 用于多模态多目标优化的膝区间进化算法 [D]. 郑州: 郑州大学, 2020. (paper)

    LI Zhimeng. Knee region evolution algorithm for multimodal multiobjective optimization [D]. Zhengzhou: Zhengzhou University, 2020. (paper)

  24. 位盼盼. 基于多模态多目标进化的集成学习器的选择及优化研究 [D]. 郑州: 郑州大学, 2020. (paper)

    WEI Panpan. Research on selection and optimization of ensemble learning based on multimodal multiobjective optimization [D]. Zhengzhou: Zhengzhou University, 2020. (paper)

  25. 李超. 自组织物种形成的多模态多目标粒子群算法的研究与应用 [D]. 郑州: 中原工学院, 2020. (paper)

    LI Chao. The research and applicationof multimodal multiobjective particle swarm optimization for self-organizing speciation [D]. Zhengzhou: Zhongyuan University of Technology, 2020. (paper)

  26. 王铂. 基于多模态多目标差分进化的集成极限学习机算法研究 [D]. 郑州: 郑州大学, 2020. (paper)

    WANG Bo. Research on ensemble extreme learning machine algorithm based on multimodal and multi-objective differential evolution [D]. Zhengzhou: Zhengzhou University, 2020. (paper)

  27. 胡晨旭. 多目标演化优化算法的决策空间多样性维护机制研究 [D]. 哈尔滨: 哈尔滨工业大学, 2020. (paper)

    HU Chenxu. Incorporation of a decision space diversity maintenance mechanism into evolutionary multi-objective optimization algorithms [D]. Harbin: Harbin Institute of Technology, 2020. (paper)

  28. 李国森,闫李,郭倩倩,周同驰,王永林,岳彩通. 基于参考点的多模态多目标粒子群算法 [J]. 计算机应用与软件, 2020,37 11 198-205. (paper)

    Li Guosen, Yan Li, Guo Qianqian, et al. Reference-point-based multimodal multi-objective particle swarm optimization [J]. Computer Applications and Software, 2020,37 11 198-205. (paper)

  29. 汪慎文,王佳莹,高娜,周瑶. 结合两种拓扑结构的多模态多目标粒子群优化算法 [J]. 南昌工程学院学报,2020,39(147), 04 70-75+99. (paper)

    WANG Shenwen, WANG Jiaying, GAO Na, ZHOU Yao. Multi-modal and multi-objective particle swarm optimization with two topology structure [J]. Journal of Nanchang Institute of Technology,2020,39(147), 04 70-75+99. (paper)

  30. 高海军,潘大志. 星型结构的多目标粒子群算法求解多模态多目标问题 [J]. 计算机工程与科学,2020,42(308), 08 145-154. (paper)

    GAO Haijun, PAN Dazhi. A multi-objective particle swarm optimization algorithm with star structure to solve the multi-modal multi-objective problem [J]. Computer Engineering and Science,2020,42(308), 08 145-154. (paper)

  31. 闫李,李国森,瞿博阳,朱小培,马佳慧. 基于双层协同进化的多目标粒子群算法 [J]. 计算机工程与设计,2020,41(407), 11 137-144. (paper)

    YAN Li, LI Guosen, QU Boyang, et al. Double-layer co-evolutionary multi-objective particle swarm optimization algorithm [J]. Computer Engineering and Design,2020,41(407), 11 137-144. (paper)

  32. Q. Q. Fan, X. F. Yan. Solving Multimodal Multiobjective Problems Through Zoning Search, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2019.(paper)

  33. W. Z. Zhang , G. S. Li , W. W. Zhang, J. J. Liang, G. Y. Gary. A cluster based PSO with leader updating mechanism and ring-topology for multimodal multi-objective optimization[J]. Swarm and Evolutionary Computation, 2019.(paper)

  34. R. Tanabe; and H. Ishibuchi, A Review of Evolutionary Multi-modal Multi-objective Optimization, IEEE Transactions on Evolutionary Computation, 2019.(paper)

  35. C. T. Yue, J. J. Liang, B. Y. Qu, K. J. Yu, and H. Song, Multimodal Multiobjective Optimization in Feature Selection, IEEE Congress on Evolutionary Computation, 2019, pp. 302-309.(paper)

  36. L. Yan, G. S. Li, Y. C. Jiao, B. Y. Qu, C. T. Yue, and S. K. Qu, A Performance Enhanced Niching Multi-objective Bat algorithm for Multimodal Multi-objective Problems, IEEE Congress on Evolutionary Computation, 2019, pp. 1275-1282.(paper)

  37. R. Z. Shi, W. Lin, Q. Z. Lin, Z. X. Zhu, and J. Y. Chen, Multimodal Multi-Objective Optimization Using A Density-based One-by-One Update Strategy, IEEE Congress on Evolutionary Computation, 2019, pp. 295-301.(paper)

  38. K. Maity, R. Sengupta, and S. Sha, MM-NAEMO : Multimodal Neighborhood-sensitive Archived Evolutionary Many-objective Optimization Algorithm, IEEE Congress on Evolutionary Computation, 2019, pp. 286-294.(paper)

  39. Y. Liu, H. Ishibuchi, Y. Nojima, N. Masuyama, and Y. Han, Searching for Local Pareto Optimal Solutions: A Case Study on Polygon-Based Problems, IEEE Congress on Evolutionary Computation, 2019, pp. 896-903.(paper)

  40. S. Maree, T. Alderliesten, and P. Bosman, Real-valued evolutionary multi-modal multi-objective optimization by hill-valley clustering, Genetic and Evolutionary Computation Conference, 2019, pp. 568-576.(paper)

  41. Z. H. Li , L. Shi, 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, 49: 234-244, 2019.(paper

  42. C. T. Yue, B. Y. Qu, K. J. Yu, J. J. Liang, X. D. Li. A Novel Scalable Test Problem Suite for Multimodal Multiobjective Optimization, Swarm and Evolutionary Computation, vol. 48, pp. 62-71, 2019.paper)(code)

  43. J. J. Liang, W. Xu, C. Yue, K. Yu, H. Song, O. D. Crisalle, and B. Qu, “Multimodal Multiobjective Optimization with Diffierential Evolution,” Swarm and Evolutionary Computation, vol. 44, pp. 1028-1059, 2018.paper)(code)

  44. Hu Y, Wang J, Liang J, et al. A self-organizing multimodal multi-objective pigeon-inspired optimization algorithm[J]. SCIENCE CHINA Information Sciences, 2019, 62(7): 1-17.paper)(code

  45. 许伟伟, 梁静, 岳彩通,等. 多模态多目标差分进化算法求解非线性方程组[J]. 计算机应用研究. 2019,36(331), 05 31-36.paper)(code

    XU Weiwei, LIANG Jing, YUE Caitong, et al. Multimodal multi-objective differential evolution algorithm for solving nonlinear equations [J]. Application Research of Computers, 2019,36(331), 05 31-36.paper)(code

  46. 李国庆. 面向复杂多模态多目标优化问题的粒子群算法研究 [D]. 郑州: 郑州轻工业大学, 2019. (paper)

    LI Guoqing. Research on particle swarm optimization algorithm multimodal multi-objective optimization problems [D]. Zhengzhou: Zhengzhou University of Light Industry, 2019. (paper)

  47. 李国森. 多模态多目标进化算法的研究与应用 [D]. 郑州: 中原工学院, 2019. (paper)

    Li Guosen. The research and application of multimodal multi-objective algorithms [D]. Zhengzhou: Zhongyuan University of Technology, 2019. (paper)

  48. 许伟伟. 多模态多目标差分进化算法研究及在非线性方程组的应用 [D]. 郑州: 郑州大学, 2018. (paper)

    XU Weiwei. Multimodal multi-objective differential evolution algorithm and its application in nonlinear equations [D]. Zhengzhou: Zhengzhou University, 2018. (paper)

  49. 郭倩倩. 基于自组织映射网络的多目标粒子群优化算法 [D]. 郑州: 郑州大学, 2018. (paper)

    GUO Qianqian. A multi-objective particle swarm optimization algorithm based on self-organizing map network [D]. Zhengzhou: Zhengzhou University, 2018. (paper)

  50. Liang J, Guo Q, Yue C, et al. A self-organizing multi-objective particle swarm optimization algorithm for multimodal multi-objective problems[C]// International Conference on Swarm Intelligence. Springer, Cham, 2018: 550-560.paper)(code)

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  52. Y. Liu, G. G. Yen and D. Gong, A multi-modal multi-objective evolutionary algorithm using two-archive and recombination strategies, IEEE Transactions on Evolutionary Computation, 2018, Early Access. DOI: 10.1109/TEVC.2018.2879406. (paper) (code)

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