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

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  • Mohamed A. Tawhid

    (Thompson Rivers University
    Alexandria University)

  • Ahmed F. Ali

    (Thompson Rivers University
    Suez Canal University)

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.

Suggested Citation

  • Mohamed A. Tawhid & Ahmed F. Ali, 2016. "Simplex particle swarm optimization with arithmetical crossover for solving global optimization problems," OPSEARCH, Springer;Operational Research Society of India, vol. 53(4), pages 705-740, December.
    • Handle: RePEc:spr:opsear:v:53:y:2016:i:4:d:10.1007_s12597-016-0256-7
    DOI: 10.1007/s12597-016-0256-7
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    References listed on IDEAS

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    1. Y. Petalas & K. Parsopoulos & M. Vrahatis, 2007. "Memetic particle swarm optimization," Annals of Operations Research, Springer, vol. 156(1), pages 99-127, December.
    2. Chang, Wei-Der, 2009. "PID control for chaotic synchronization using particle swarm optimization," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 910-917.
    3. E. L. Lawler & D. E. Wood, 1966. "Branch-and-Bound Methods: A Survey," Operations Research, INFORMS, vol. 14(4), pages 699-719, August.
    4. E. Polak & J. O. Royset & R. S. Womersley, 2003. "Algorithms with Adaptive Smoothing for Finite Minimax Problems," Journal of Optimization Theory and Applications, Springer, vol. 119(3), pages 459-484, December.
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    Cited by:

    1. Mohamed A. Tawhid & Ahmed F. Ali, 2017. "Multi-directional bat algorithm for solving unconstrained optimization problems," OPSEARCH, Springer;Operational Research Society of India, vol. 54(4), pages 684-705, December.

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