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On convergence analysis of multi-objective particle swarm optimization algorithm

Author

Listed:
  • Xu, Gang
  • Luo, Kun
  • Jing, Guoxiu
  • Yu, Xiang
  • Ruan, Xiaojun
  • Song, Jun

Abstract

Multi-objective particle swarm optimization (MOPSO), a population-based stochastic optimization algorithm, has been successfully used to solve many multi-objective optimization problems. However, the analysis of algorithm convergence is still inadequate nowadays. In this paper, probability theory is applied to analyze the convergence of the original MOPSO. First, a convergence metric is defined. Afterwards, the global convergence of the original MOPSO is transformed into the convergence of the convergence metric sequence. Finally, the defined convergence metric is utilized to analyze the global convergence of the original MOPSO in terms of probability theory. Our results show that the original MOPSO cannot guarantee global convergence with probability one. Moreover, the analysis of the original MOPSO indicates that the improved vision of the original MOPSO is a global convergence algorithm. The proof of the original MOPSO convergence in this work is new, simple and more effective without specific implementation.

Suggested Citation

  • Xu, Gang & Luo, Kun & Jing, Guoxiu & Yu, Xiang & Ruan, Xiaojun & Song, Jun, 2020. "On convergence analysis of multi-objective particle swarm optimization algorithm," European Journal of Operational Research, Elsevier, vol. 286(1), pages 32-38.
    • Handle: RePEc:eee:ejores:v:286:y:2020:i:1:p:32-38
    DOI: 10.1016/j.ejor.2020.03.035
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    References listed on IDEAS

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    1. Liu, Ruochen & Li, Jianxia & fan, Jing & Mu, Caihong & Jiao, Licheng, 2017. "A coevolutionary technique based on multi-swarm particle swarm optimization for dynamic multi-objective optimization," European Journal of Operational Research, Elsevier, vol. 261(3), pages 1028-1051.
    2. Jianli Shi & Jin Zhang & Kun Wang & Xin Fang, 2018. "Particle Swarm Optimization for Split Delivery Vehicle Routing Problem," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 35(02), pages 1-42, April.
    3. Lin, Qiuzhen & Li, Jianqiang & Du, Zhihua & Chen, Jianyong & Ming, Zhong, 2015. "A novel multi-objective particle swarm optimization with multiple search strategies," European Journal of Operational Research, Elsevier, vol. 247(3), pages 732-744.
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    Cited by:

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    2. Ye, Wenwen & Li, Shengping, 2023. "Convergence analysis of flow direction algorithm in continuous search space and its improvement," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 212(C), pages 91-121.
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    6. Zhe Liu & Shurong Li, 2022. "A numerical method for interval multi-objective mixed-integer optimal control problems based on quantum heuristic algorithm," Annals of Operations Research, Springer, vol. 311(2), pages 853-898, April.

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