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Stability bounds and almost sure convergence of improved particle swarm optimization methods

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Abstract

Particle swarm optimization (PSO) is a member of nature-inspired metaheuristic algorithms. Its formulation is simple and does not need the computation of derivatives. It and its many variants have been applied to many different types of optimization problems across several disciplines. There have been many attempts to study the convergence properties of PSO, but a rigorous and complete proof of its almost sure convergence to the global optimum is still lacking. We propose two modified versions of PSO and prove their convergence to the global optimum. We conduct simulation studies to gain further insights into their properties and evaluate their performance relative to PSO.

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Acknowledgements

X.T.T. acknowledges support from Singapore Ministry of Education Academic Research Funds Tier 1 Grant R-146-000-292-114. K.P.C. acknowledges support from Singapore Ministry of Education Academic Research Funds Tier 1 Grant R-155-000-222-114. T.L.L. acknowledges support from U.S. National Science Foundation under Grant DMS-1811818. W.W.K. acknowledges support from the National Institute of General Medical Sciences of the National Institutes of Health under Award R01GM107639, and from the Department of Statistics and Applied Probability at NUS in 2018–2019, when much of this research was carried out. All coauthors acknowledge support from the Institute for Mathematical Sciences at NUS in organizing the Workshop on Particle Swarm Optimization and Evolutionary Computation held on 20–21 Feb 2018 which led to their collaborative research on PSO.

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Authors and Affiliations

  1. Department of Mathematics, National University of Singapore, Singapore, Singapore

    Xin T. Tong

  2. Department of Statistics and Applied Probability, National University of Singapore, Singapore, Singapore

    Kwok Pui Choi

  3. Department of Statistics, Stanford University, Stanford, USA

    Tze Leung Lai

  4. Department of Biostatistics, University of California, Los Angeles, Los Angeles, USA

    Weng Kee Wong

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  1. Xin T. Tong
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  2. Kwok Pui Choi
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  3. Tze Leung Lai
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  4. Weng Kee Wong
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Correspondence to Xin T. Tong.

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Tong, X.T., Choi, K.P., Lai, T.L. et al. Stability bounds and almost sure convergence of improved particle swarm optimization methods. Res Math Sci 8, 30 (2021). https://doi.org/10.1007/s40687-020-00241-4

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