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Simplex particle swarm optimization with arithmetical crossover for solving global optimization problems

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Abstract

In this paper, we propose a new hybrid algorithm by combining the particle swarm optimization with a genetic arithmetical crossover operator after applying a modification on it in order to avoid the problem of stagnation and premature convergence of the population. In the final stage of the algorithm, we applied the Nelder-Mead method as a local search method in order to accelerate the convergence and avoid running the algorithm without any improvements in the results. We call the new proposed algorithm by simplex particle swarm optimization with a modified arithmetical crossover (SPSOAC). We test SPSOAC on 7 integer programming optimization benchmark functions, 10 minimax problems and 10 CEC05 functions. We present the general performance of the proposed algorithm by comparing SPSOAC against 13 benchmark algorithms. The Experiments results show the proposed algorithm is a promising algorithm and has a powerful performance.

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Acknowledgments

We thank the reviewers for their thorough review and highly appreciate the comments and suggestions, which significantly contributed to improving the quality of the paper. The research of the 1st author is supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC). The postdoctoral fellowship of the 2nd author is supported by NSERC.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Faculty of Science, Thompson Rivers University, V2C 0C8, Kamloops, British Columbia, Canada

    Mohamed A. Tawhid & Ahmed F. Ali

  2. Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, Moharam Bey, 21511, Alexandria, Egypt

    Mohamed A. Tawhid

  3. Department of Computer Science, Faculty of Computers & Informatics, Suez Canal University, Ismailia, Egypt

    Ahmed F. Ali

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  1. Mohamed A. Tawhid
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Correspondence to Mohamed A. Tawhid.

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Tawhid, M.A., Ali, A.F. Simplex particle swarm optimization with arithmetical crossover for solving global optimization problems. OPSEARCH 53, 705–740 (2016). https://doi.org/10.1007/s12597-016-0256-7

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