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Enhancing differential evolution algorithm with repulsive behavior

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Abstract

In the real world, differential evolution (DE) algorithm can effectively solve optimization problems in engineering; thus, DE has been applied in various fields. However, in complex multimodal problems, DE may encounter stagnation during iterations. Thus, we propose an improved DE algorithm with repulsive behavior, named RBDE. The core idea of RBDE is that offsprings no longer simply learn from the current optima but continue to explore the direction in which the current optimal individual is repelled by poorer individuals. This mechanism increases the diversity of the learning direction of a population. RBDE includes two types of repulsive behaviors: In the first, RBDE selects two parents as the source of repulsion and generates two different repulsive forces to promote the offspring to explore the optimal individual; the other considers that the gradient of the repulsion between the parents is the learning direction of the offspring. The repulsive behavior can effectively alleviate the stagnation of DE when dealing with multimodal problems. To evaluate the performance of RBDE, we use CEC2017 benchmarks to test RBDE and nine other algorithms. The results show that the performance of RBDE is better than that of the other nine algorithms. In addition, RBDE is used to train an artificial neural network and is applied to the optimization problem of four-bar linkages, whose results indicate that the model obtained by RBDE is more accurate than those by the other algorithms.

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Acknowledgements

This study was supported by the National Natural Science Foundation of China (U1708254). The authors thank the anonymous reviewers for their helpful criticism in improving this manuscript.

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Authors and Affiliations

  1. Equipment Reliability Institute, Shenyang University of Chemical Technology, Shenyang, China

    Kai Zhang, Pengcheng Mu, Yimin Zhang & Zhihao Jin

  2. Peng Cheng Laboratory, Shenzhen, 518055, China

    Qiujun Huang

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  1. Kai Zhang
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  2. Pengcheng Mu
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  3. Yimin Zhang
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  4. Zhihao Jin
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  5. Qiujun Huang
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Correspondence to Pengcheng Mu, Yimin Zhang, Zhihao Jin or Qiujun Huang.

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Appendix A

Appendix A

See Tables 10 and 11.

Table 10 Benchmarks in CEC2017
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Table 11 Definitions of the basic functions in CEC2017
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Zhang, K., Mu, P., Zhang, Y. et al. Enhancing differential evolution algorithm with repulsive behavior. Soft Comput 24, 9279–9305 (2020). https://doi.org/10.1007/s00500-019-04454-w

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