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Differential evolution using a superior–inferior crossover scheme

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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.

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Acknowledgments

The work was supported by the Education Commission Scientific Research Innovation Key Project of Shanghai under Grant 13ZZ050, the Science and Technology Commission Innovation Plan Basic Research Key Project of Shanghai under Grant 12JC1400400, the Nursery Research Project of Henan University of Traditional Chinese Medicine under Grant MP2013-36, and The National Natural Science Foundation of China under Grant 61304062. The authors are grateful to the Editor-in-Chief, Associate Editor, and anonymous reviewers for their constructive suggestions that helped to improve the content as well as the quality of the paper

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Authors and Affiliations

  1. College of Information Science and Technology, Donghua University, Shanghai, 201620, People’s Republic of China

    Yulong Xu, Jian-an Fang & Lingdong Zhao

  2. Institute of Information and Technology, Henan University of Traditional Chinese Medicine, Zhengzhou, 450003, People’s Republic of China

    Yulong Xu & Xiaopeng Wang

  3. School of International Relations and Public Affairs, Fudan University, Shanghai, 200433, People’s Republic of China

    Wu Zhu

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  1. Yulong Xu
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  2. Jian-an Fang
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  3. Wu Zhu
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  4. Xiaopeng Wang
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  5. Lingdong Zhao
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Correspondence to Yulong Xu.

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Yulong Xu and Jian-an Fang have contributed equally to this work.

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Xu, Y., Fang, Ja., Zhu, W. et al. Differential evolution using a superior–inferior crossover scheme. Comput Optim Appl 61, 243–274 (2015). https://doi.org/10.1007/s10589-014-9701-9

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