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Differential evolution using a superior–inferior crossover scheme

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  • Yulong Xu
  • Jian-an Fang
  • Wu Zhu
  • Xiaopeng Wang
  • Lingdong Zhao

Abstract

Differential evolution (DE) is a new population-based stochastic optimization, which has difficulties in solving large-scale and multimodal optimization problems. The reason is that the population diversity decreases rapidly, which leads to the failure of the clustered individuals to reproduce better individuals. In order to improve the population diversity of DE, this paper aims to present a superior–inferior (SI) crossover scheme based on DE. Specifically, when population diversity degree is small, the SI crossover is performed to improve the search space of population. Otherwise, the superior–superior crossover is used to enhance its exploitation ability. In order to test the effectiveness of our SI scheme, we combine the SI with adaptive differential evolution (JADE), which is a recently developed DE variant for numerical optimization. In addition, the theoretical analysis of SI scheme is provided to show how the population’s diversity can be improved. In order to make the selection of parameters in our scheme more intelligently, a self-adaptive SI crossover scheme is proposed. Finally, comparative comprehensive experiments are given to illustrate the advantages of our proposed method over various DEs on a suite of 24 numerical optimization problems. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Yulong Xu & Jian-an Fang & Wu Zhu & Xiaopeng Wang & Lingdong Zhao, 2015. "Differential evolution using a superior–inferior crossover scheme," Computational Optimization and Applications, Springer, vol. 61(1), pages 243-274, May.
    • Handle: RePEc:spr:coopap:v:61:y:2015:i:1:p:243-274
    DOI: 10.1007/s10589-014-9701-9
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    References listed on IDEAS

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    1. Saber Elsayed & Ruhul Sarker & Daryl Essam, 2013. "Self-adaptive differential evolution incorporating a heuristic mixing of operators," Computational Optimization and Applications, Springer, vol. 54(3), pages 771-790, April.
    2. Wu Zhu & Jian-an Fang & Yang Tang & Wenbing Zhang & Wei Du, 2012. "Digital IIR Filters Design Using Differential Evolution Algorithm with a Controllable Probabilistic Population Size," PLOS ONE, Public Library of Science, vol. 7(7), pages 1-9, July.
    3. M. Ali & W. Zhu, 2013. "A penalty function-based differential evolution algorithm for constrained global optimization," Computational Optimization and Applications, Springer, vol. 54(3), pages 707-739, April.
    4. Yi-gui Ou & Guan-shu Wang, 2012. "A hybrid ODE-based method for unconstrained optimization problems," Computational Optimization and Applications, Springer, vol. 53(1), pages 249-270, September.
    5. Gong, Wenyin & Cai, Zhihua, 2009. "An improved multiobjective differential evolution based on Pareto-adaptive [epsilon]-dominance and orthogonal design," European Journal of Operational Research, Elsevier, vol. 198(2), pages 576-601, October.
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    Cited by:

    1. Meijun Duan & Hongyu Yang & Shangping Wang & Yu Liu, 2019. "Self-adaptive dual-strategy differential evolution algorithm," PLOS ONE, Public Library of Science, vol. 14(10), pages 1-25, October.

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