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Convergence analysis of standard particle swarm optimization algorithm and its improvement

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Abstract

Standard particle swarm optimization (PSO) algorithm is a kind of stochastic optimization algorithm. Its convergence, based on probability theory, is analyzed in detail. We prove that the standard PSO algorithm is convergence with probability 1 under certain condition. Then, a new improved particle swarm optimization (IPSO) algorithm is proposed to ensure that IPSO algorithm is convergence with probability 1. In order to balance the exploration and exploitation abilities of IPSO algorithm, we propose the exploration and exploitation operators and weight the two operators in IPSO algorithm. Finally, IPSO algorithm is tested on 13 benchmark test functions and compared with the other algorithms published in the recent literature. The numerical results confirm that IPSO algorithm has the better performance in solving nonlinear functions.

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Acknowledgements

This work is partly supported by the National Natural Science Foundation of China (11371071) and Scientific Research Foundation of Liaoning Province Educational Department (L2013426).

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Authors and Affiliations

  1. College of Mathematics and Physics, Bohai University, Jinzhou, 121000, China

    Weiyi Qian & Ming Li

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  1. Weiyi Qian
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  2. Ming Li
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Correspondence to Weiyi Qian.

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The authors declare that there is no conflict of interests regarding the publication of this paper.

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This article does not contain any studies with human participants or animals performed by any of the authors.

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Communicated by V. Loia.

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Qian, W., Li, M. Convergence analysis of standard particle swarm optimization algorithm and its improvement. Soft Comput 22, 4047–4070 (2018). https://doi.org/10.1007/s00500-017-2615-6

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  • DOI: https://doi.org/10.1007/s00500-017-2615-6

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