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A distributed individuals based multimodal multi-objective optimization differential evolution algorithm

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Abstract

There may exist a one-to-many mapping between objective and decision spaces in multimodal multi-objective optimization problems (MMOPs), which requires the evolutionary algorithm to locate multiple non-dominated solution sets. In order to enhance the diversity of the population, we develop a multimodal multi-objective differential evolution algorithm based on distributed individuals and lifetime mechanism. First, every individual can be seen as a distributed unit to locate multiple non-dominated solutions. The solutions with the good diversity are generated by adopting virtual population, and the range of virtual population is adjusted by an adaptive adjustment strategy to locate more non-dominated solutions. Second, it is considered that each individual has a limited lifespan inspired by natural phenomenon. As the search area of individuals becoming adaptively smaller, the individuals with good quality are archived and they can reinitialize with a new lifespan for enhancing diversity of the search space. Then the probability selection strategy is applied in the environment selection to balance exploration and exploitation. The test results on 22 multimodal multi-objective benchmark test functions verify the superior performance of the proposed method.

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References

  1. Qi R, Yen GG (2017) Hybrid bi-objective portfolio optimization with pre-selection strategy. Inf Sci 417:401–419

    Article  Google Scholar 

  2. Han Y, Gong D, Jin Y, Pan Q (2016) Evolutionary multi-objective blocking lot-streaming flow shop scheduling with interval processing time. Appl Soft Comput 42:229–245

    Article  Google Scholar 

  3. Yue CT, Liang JJ, Qu BY, Yu KJ, Song H (2019) Multimodal multiobjective optimization in feature selection. IEEE Cong Evol Comput (CEC) 2019:302–309. https://doi.org/10.1109/CEC.2019.8790329

    Article  Google Scholar 

  4. Kudo F, Yoshikawa T, Furuhashi T (2011) A study on analysis of design variables in pareto solutions for conceptual design optimization problem of hybrid rocket engine. IEEE Cong Evol Comput (CEC) 2011:2558–2562. https://doi.org/10.1109/CEC.2011.5949936

    Article  Google Scholar 

  5. Jaszkiewicz A (2002) On the performance of multiple-objective genetic local search on the 0/1 knapsack problem: a comparative experiment. IEEE Trans Evol Comput 6:402–412

    Article  Google Scholar 

  6. Han Y, Gong D, Jin Y, Pan Q (2019) Evolutionary multiobjective blocking lot-streaming flow shop scheduling with machine breakdowns. IEEE Trans Cybern 49:184–197

    Article  Google Scholar 

  7. Ulrich T, Bader J, Thiele L (2010) Defining and optimizing indicator-based diversity measures in multiobjective search. In: PPSN

  8. Ishibuchi H, Yamane M, Akedo N, Nojima Y (2012) Two-objective solution set optimization to maximize hypervolume and decision space diversity in multiobjective optimization. In: The 6th international conference on soft computing and intelligent systems, and the 13th international symposium on advanced intelligence systems, pp 1871–1876. https://doi.org/10.1109/SCIS-ISIS.2012.6505243

  9. Tanabe R, Ishibuchi H (2019) A niching indicator-based multi-modal many-objective optimizer. Swarm Evol Comput 49:134–146

    Article  Google Scholar 

  10. Hu C, Ishibuchi H (2018) Incorporation of a decision space diversity maintenance mechanism into moea/d for multi-modal multi-objective optimization. In: Proceedings of the genetic and evolutionary computation conference companion

  11. Peng Y, Ishibuchi H (2021) A decomposition-based hybrid evolutionary algorithm for multi-modal multi-objective optimization. In: 2021 IEEE international conference on systems, man, and cybernetics (SMC), pp 160–167. https://doi.org/10.1109/SMC52423.2021.9659132

  12. Deb K, Tiwari S (2005) Omni-optimizer: a procedure for single and multi-objective optimization. In: Coello Coello CA, Hernández Aguirre A, Zitzler E (eds) Evolutionary multi-criterion optimization. Springer, Berlin, pp 47–61

    Chapter  Google Scholar 

  13. Liu Y, Ishibuchi H, Nojima Y, Masuyama N, Shang K (2018) A double-niched evolutionary algorithm and its behavior on polygon-based problems. In: PPSN

  14. Liang JJ, Yue CT, Qu BY (2016) Multimodal multi-objective optimization: a preliminary study. IEEE Cong Evol Comput (CEC) 2016:2454–2461. https://doi.org/10.1109/CEC.2016.7744093

    Article  Google Scholar 

  15. Kim M, Hiroyasu T, Miki M, Watanabe S (2004) Spea2+: improving the performance of the strength pareto evolutionary algorithm 2. In: Yao X, Burke EK, Lozano JA, Smith J, Merelo-Guervós JJ, Bullinaria JA, Rowe JE, Tino P, Kabán A, Schwefel H-P (eds) Parallel problem solving from nature: PPSN VIII. Springer, pp 742–751

    Google Scholar 

  16. Liu Y, Yen GG, Gong D (2019) A multimodal multiobjective evolutionary algorithm using two-archive and recombination strategies. IEEE Trans Evol Comput 23:660–674

    Article  Google Scholar 

  17. Liu Y, Ishibuchi H, Yen GG, Nojima Y, Masuyama N (2020) Handling imbalance between convergence and diversity in the decision space in evolutionary multimodal multiobjective optimization. IEEE Trans Evol Comput 24:551–565

    Google Scholar 

  18. Yue C, Qu B, Liang J (2018) A multiobjective particle swarm optimizer using ring topology for solving multimodal multiobjective problems. IEEE Trans Evol Comput 22:805–817

    Article  Google Scholar 

  19. Biswas S, Kundu S, Das S (2015) Inducing niching behavior in differential evolution through local information sharing. IEEE Trans Evol Comput 19:246–263

    Article  Google Scholar 

  20. Zhang Y-H, Gong Y-J, Zhang H-X, Gu T-L, Zhang J (2017) Toward fast niching evolutionary algorithms: a locality sensitive hashing-based approach. IEEE Trans Evol Comput 21:347–362

    Google Scholar 

  21. Xu Y (2010) A niching particle swarm segmentation of infrared images. In: 2010 sixth international conference on natural computation, vol 7, pp 3739–3742. https://doi.org/10.1109/ICNC.2010.5583389

  22. Mengshoel OJ, Goldberg DE (2008) The crowding approach to niching in genetic algorithms. Evol Comput 16:315–354

    Article  Google Scholar 

  23. Qing L, Gang W, Zaiyue Y, Qiuping W (2008) Crowding clustering genetic algorithm for multimodal function optimization. Appl Soft Comput 8:88–95

    Article  Google Scholar 

  24. Sareni B, Krahenbuhl L (1998) Fitness sharing and niching methods revisited. IEEE Trans Evol Comput 2:97–106

    Article  Google Scholar 

  25. DellaCioppa A, De Stefano C, Marcelli A (2004) On the role of population size and niche radius in fitness sharing. IEEE Trans Evol Comput 8:580–592

    Article  Google Scholar 

  26. Li X (2005) Efficient differential evolution using speciation for multimodal function optimization. In: GECCO ’05

  27. BoÅkovi B, Brest J (2017) Clustering and differential evolution for multimodal optimization. IEEE Cong Evol Comput (CEC) 2017:698–705. https://doi.org/10.1109/CEC.2017.7969378

    Article  Google Scholar 

  28. Wang ZJ, Zhan ZH, Lin Y, Yu W-J, Yuan HQ, Gu TL, Kwong S, Zhang J (2018) Dual-strategy differential evolution with affinity propagation clustering for multimodal optimization problems. IEEE Trans Evol Comput 22:894–908

    Article  Google Scholar 

  29. Petrowski A (1996) A clearing procedure as a niching method for genetic algorithms. In: Proceedings of IEEE international conference on evolutionary computation, pp 798–803. https://doi.org/10.1109/ICEC.1996.542703

  30. Dick G (2010) Automatic identification of the niche radius using spatially-structured clearing methods. In: IEEE congress on evolutionary computation, pp 1–8. https://doi.org/10.1109/CEC.2010.5586085

  31. Thomsen R (2004) Multimodal optimization using crowding-based differential evolution. In: Proceedings of the 2004 congress on evolutionary computation (IEEE Cat. No.04TH8753), vol 2, pp 1382–1389. https://doi.org/10.1109/CEC.2004.1331058

  32. Yue C, Qu B, Yu K, Liang J, Li X (2019) A novel scalable test problem suite for multimodal multiobjective optimization. Swarm Evol Comput 48:62–71

    Article  Google Scholar 

  33. Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: Nsga-ii. IEEE Trans Evol Comput 6:182–197

    Article  Google Scholar 

  34. Lin Q, Lin W, Zhu Z, Gong M, Li J, Coello CAC (2021) Multimodal multiobjective evolutionary optimization with dual clustering in decision and objective spaces. IEEE Trans Evol Comput 25:130–144

    Article  Google Scholar 

  35. Zhang Q, Li H (2007) Moea/d: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans Evol Comput 11:712–731

    Article  Google Scholar 

  36. Tanabe R, Ishibuchi H (2018) A decomposition-based evolutionary algorithm for multi-modal multi-objective optimization. In: Auger A, Fonseca CM, Lourenco N, Machado P, Paquete L, Whitley D (eds) Parallel problem solving from nature: PPSN XV. Springer, Cham, pp 249–261

    Chapter  Google Scholar 

  37. Tanabe R, Ishibuchi H (2020) A framework to handle multimodal multiobjective optimization in decomposition-based evolutionary algorithms. IEEE Trans Evol Comput 24:720–734

    Article  Google Scholar 

  38. Li W, Zhang T, Wang R, Ishibuchi H (2021) Weighted indicator-based evolutionary algorithm for multimodal multiobjective optimization. IEEE Trans Evol Comput 25:1064–1078

    Article  Google Scholar 

  39. Liang J, Qu B, Gong D, Yue C (2019) Problem definitions and evaluation criteria for the cec 2019 special session on multimodal multiobjective optimization. https://doi.org/10.13140/RG.2.2.33423.64164

  40. Zhou A, Zhang Q, Jin Y (2009) Approximating the set of pareto-optimal solutions in both the decision and objective spaces by an estimation of distribution algorithm. IEEE Trans Evol Comput 13:1167–1189

    Article  Google Scholar 

  41. Liang J, Xu W, Yue C, Yu K, Song H, Crisalle OD, Qu B (2019) Multimodal multiobjective optimization with differential evolution. Swarm Evol Comput 44:1028–1059

    Article  Google Scholar 

Download references

Funding

The funding was provided by National Nature Science Foundation of China under (Grant 62276202), Fundamental Research Funds for the Central Universities (Grant No. QTZX22047), Natural Science Basic Research Plan in Shaanxi Province of China (Grant No. 2022JQ-670).

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Authors and Affiliations

  1. Sichuan Jiuzhou Electronic Group Co.Ltd, Mianyang, China

    Wei Wang & Xiaoli Gao

  2. Institute of Big Data Science and Industry, Shanxi University, Taiyuan, 030006, Shanxi, China

    Zhifang Wei

  3. School of Mathematics and Statistics, Xidian University, Xi’an, 710126, China

    Tianqi Huang & Weifeng Gao

Authors
  1. Wei Wang
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  2. Zhifang Wei
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  3. Tianqi Huang
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  4. Xiaoli Gao
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  5. Weifeng Gao
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Contributions

Wei Wang: Investigation, Methodology, Writing – review & editing. Zhifang Wei: Methodology, Writing – review & editing. Tian Huang: Methodology, Writing – review & editing. Xiaoli Gao: Review, Methodology. Weifeng Gao: Software, Validation, Methodolgy, Resources

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Correspondence to Zhifang Wei.

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Wang, W., Wei, Z., Huang, T. et al. A distributed individuals based multimodal multi-objective optimization differential evolution algorithm. Memetic Comp. 16, 505–517 (2024). https://doi.org/10.1007/s12293-024-00413-7

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