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. Li W, Zhang T, Wang R, et al. Weighted indicator-based evolutionary algorithm for multimodal multi-objective optimization[J]. IEEE Transactions on Evolutionary Computation, 2021.(paper)

  2. Fan Q, Ersoy O K. Zoning Search With Adaptive Resource Allocating Method for Balanced and Imbalanced Multimodal Multi-Objective Optimization[J]. IEEE/CAA Journal of Automatica Sinica, 2021, 8(6): 1163-1176.(paper)

  3. Li Z, Zou J, Yang S, et al. A two-archive algorithm with decomposition and fitness allocation for multi-modal multi-objective optimization[J]. Information Sciences, 2021, 574: 413-430.(paper)

  4. Moshaiov A, Breslav Y, Farhi E. Multi-Modal Multi-Objective Evolutionary Optimization for Problems with Solutions of Variable-Length[C]//2021 IEEE Congress on Evolutionary Computation (CEC). IEEE, 2021: 1193-1200.(paper)

  5. Grimme C, Kerschke P, Aspar P, et al. Peeking beyond peaks: Challenges and research potentials of continuous multimodal multi-objective optimization[J]. Computers & Operations Research, 2021: 105489.(paper)

  6. Q. L. Dang, W. Xu, Y. F. Yuan. A Dynamic Resource Allocation Strategy with Reinforcement Learning for Multimodal Multi-objective Optimization[J]. International Journal of Automation and Computing, 2021, 18: 1-15.(paper)

  7. W. L. Wang, G. Q. Li, Y. L. Wang, F. Wu, W. W. Zhang, L. Li. Clearing-based multimodal multi-objective evolutionary optimization with layer-to-layer strategy[J]. Swarm and Evolutionary Computation, 2021: 100976.(paper)

  8. R. Wang, W. Ma, M. Tan, G. H. Wu, L. Wang, D. W. Gong, J. Xiong. Preference-inspired coevolutionary algorithm with active diversity strategy for multi-objective multi-modal optimization[J]. Information Sciences, 2021(546): 1148-1165.(paper

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

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

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

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

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

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

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

  18. C. Liu, W. Shen, L. Zhang, H. Yang, Y. Du, Z. Yuan, H. Zhao. 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

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  20. Y. Hu, B. Y. Qu, J. Wang, J. Liang, Y. L. Wang, K. J. Yu, Y. X. Li, K. J. Qiao. Short-term load forecasting using multimodal evolutionary algorithm and random vector functional link network based ensemble learning[J]. Applied Energy, 285 (2021): 116415. (paper)

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  22. C. T. Yue, J. 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). IEEE, 2020: 1-8. (paper

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

  24. M. Javadi, C. Ramirez-Atencia. S, Mostaghim. A Novel Grid-based Crowding Distance for Multimodal Multi-objective Optimization[C]//2020 IEEE Congress on Evolutionary Computation (CEC). IEEE, 2020: 1-8.(paper

  25. C. Rivera, M. Inostroza-Ponta, M. Villalobos-Cid. 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

  26. Q. Lin, W. Lin, Z. Zhu, M. Gong, J. Li, C. A. Coello Coello. 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)

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

  28. B. Y. Qu, C. Li, J. Liang, L. Yan, K. J. Yu, Y. S. Zhu.  A self-organized speciation based multi-objective particle swarm optimizer for multimodal multi-objective problems[J]. Applied Soft Computing, 2020.(paper)(code)

  29. X. W. Zhang, H. Liu, L. P. Tu. A modified particle swarm optimization for multimodal multi-objective optimization[J]. Engineering Applications of Artificial Intelligence, 2020, 95: 103905.(paper

  30. C. T. Yue. Research  on  multimodal  multiobjective  optimization algorithm and application based on swarm intelligence [D]. Zhengzhou: Zhengzhou University, 2020. (paper)

  31. Z. M. Li. Knee region evolution algorithm for multimodal multiobjective optimization [D]. Zhengzhou: Zhengzhou University, 2020. (paper)

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

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

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

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

  36. G. S. Li, L. Yan, Q. Q. Guo, T. C. Zhou, Y. L. Wang, C. T. Yue. Reference-point-based multimodal multi-objective particle swarm optimization [J]. Computer Applications and Software, 2020,37 11 198-205. (paper)

  37. S. W. Wang, J. Y. Wang, N. Gao, Y. Zhou. 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)

  38. H. J. Gao, D. Z. Pan. 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)

  39. Y. Li, G. S. Li, B. Y. Qu, X. P. Zhu, J. H. Ma. Double-layer co-evolutionary multi-objective particle swarm optimization algorithm [J]. Computer Engineering and Design,2020,41(407), 11 137-144. (paper)

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

  41. 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)

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

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

  44. 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, IEEE Congress on Evolutionary Computation, 2019, pp. 1275-1282.(paper)

  45. R. Z. Shi, W. Lin, Q. Z. Lin, Z. X. Zhu, 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)

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

  47. Y. Liu, H. Ishibuchi, Y. Nojima, N. Masuyama, 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)

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

  49. 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

  50. 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)

  51. 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)

  52. Y. Hu, J. Wang, J. Liang, K. Yu, H. Song, Q. Guo, C. Yue, Y. Wang. A self-organizing multimodal multi-objective pigeon-inspired optimization algorithm[J]. SCIENCE CHINA Information Sciences, 2019, 62(7): 1-17.paper)(code

  53. W. W. Xu, J. J. Liang, C. T. Yue, B. Y. Qu. Multimodal multi-objective differential evolution algorithm for solving nonlinear equations [J]. Application Research of Computers, 2019,36(331), 05 31-36.paper)(code

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

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

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

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

  58. 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. Springer, Cham, 2018: 550-560.paper)(code)

  59. C. T. Yue, B. Y. Qu, J. J. Liang. A multiobjective particle swarm optimizer using ring topology for solving multimodal multiobjective problems[J]. IEEE Transactions on Evolutionary Computation, 2018, 22(5): 805-817.(paper)code

  60. 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)

  61. R. Tanabe, H. Ishibuchi. A decomposition-based evolutionary algorithm for multi-modal multi-objective optimization[C]// International Conference on Parallel Problem Solving from Nature. 2018, 261: 249-261.(paper

  62. Y. Liu, H. Ishibuchi, Y. Nojima, N. Masuyama, K. Shang. A double-niched evolutionary algorithm and its behavior on polygon-based problems[C]// International Conference on Parallel Problem Solving from Nature. 2018, 261: 262-273.(paper

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