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Population reduction with individual similarity for differential evolution

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Abstract

Choosing the appropriate population size for differential evolution (DE) is still a challenging task. Too large population size leads to slow convergence, while too small population size causes premature convergence and stagnation. To solve this problem, a population reduction with individual similarity (PRS) for DE is proposed in this paper. In the PRS, a linear differential decrease method is used to automatically determine the population size required in each generation. At the same time, the current population is divided into two subgroups with equal sizes according to individual similarity, and the individuals that need to be removed are determined from the subgroup with the lowest individual similarity in an effective manner, and thus the convergence is further accelerated without affecting the population diversity. In addition, an elite-oriented strategy is utilized to replace the random selection of individuals in the original mutation strategy of DE, which provides constructive guidance for individual evolution and improves the convergence quality. Five basic DE and six advanced DE algorithms are used to evaluate the effect of PRS, and it is further compared with four improved DE algorithms with population reduction strategy. The experimental results on CEC 2014 benchmark functions show that the proposed PRS can effectively enhance the performance of these five basic DE and six advanced DE algorithms, and is better than the four population reduction strategies.

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Data availability

The CEC 2014 benchmark functions are available in Liang et al. (2013). The source code of the compared algorithms can be replicated according to the corresponding literature, and the proposed PRS is available from the corresponding author on reasonable request.

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Acknowledgements

The authors sincerely thank the editors and reviewers for their constructive and beneficial comments.

Funding

This work was supported by the National Natural Science Foundation of China (Grant No. U20A20161, 62101363), Key Technology Research and Development Program of Henan Province (Grant No. 212102210532, 222102210041), the Project of Henan Police College (Grant No. HNJY-2021-QN-13, HNJY202220) and Key Scientific Research Projects of Higher Education Institutions in Henan Province (Grant No. 22A510002).

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Author notes

  1. Yuzhen Li and Shihao Wang have contributed equally to this work.

Authors and Affiliations

  1. National Key Laboratory of Fundamental Science on Synthetic Vision, Sichuan University, Chengdu, 610065, China

    Yuzhen Li, Bo Yang, Hu Chen & Hongyu Yang

  2. College of Computer Science, Sichuan University, Chengdu, 610065, China

    Bo Yang, Hu Chen & Hongyu Yang

  3. Department of Network Security, Henan Police College, Zhengzhou, 450046, China

    Shihao Wang & Zhiqiang Wu

Authors
  1. Yuzhen Li
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  2. Shihao Wang
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  4. Hu Chen
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Correspondence to Shihao Wang or Hongyu Yang.

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Appendix

Appendix

See Table 21

Table 21 Mean and standard deviation of fitness error obtained by six advanced DE algorithms and their corresponding PRS-DEs with \(NP_{\max } = 30\)
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, Table 22

Table 22 Mean and standard deviation of fitness error obtained by six advanced DE algorithms and their corresponding PRS-DEs with \(NP_{\max } = 50\)
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, Table 23

Table 23 Mean and standard deviation of fitness error obtained by six advanced DE algorithms and their corresponding PRS-DEs with \(NP_{\max } = 150\)
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, Table 24

Table 24 Mean and standard deviation of fitness error obtained by six advanced DE algorithms and their corresponding PRS-DEs with \(NP_{\max } = 200\)
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, Table 25

Table 25 Mean and standard deviation of fitness error obtained by six advanced DE algorithms and their corresponding PRS-DEs with \(NP_{\max } = 250\)
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, Table 26

Table 26 Nemenyi test for six advanced DE algorithms with different \(NP_{\max }\) and their corresponding PRS-DEs with \(NP_{\max } = 30\)
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, Table 27

Table 27 Nemenyi test for six advanced DE algorithms with different \(NP_{\max }\) and their corresponding PRS-DEs with \(NP_{\max } = 50\)
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, Table 28

Table 28 Nemenyi test for six advanced DE algorithms with different \(NP_{\max }\) and their corresponding PRS-DEs with \(NP_{\max } = 100\)
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, Table 29

Table 29 Nemenyi test for six advanced DE algorithms with different \(NP_{\max }\) and their corresponding PRS-DEs with \(NP_{\max } = 150\)
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, Table 30

Table 30 Nemenyi test for six advanced DE algorithms with different \(NP_{\max }\) and their corresponding PRS-DEs with \(NP_{\max } = 200\)
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, Table 31

Table 31 Nemenyi test for six advanced DE algorithms with different \(NP_{\max }\) and their corresponding PRS-DEs with \(NP_{\max } = 250\)
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, Table 32

Table 32 Nemenyi test for six advanced DE algorithms with different \(NP_{\max }\) and their corresponding PRS-DEs with \(NP_{\max } = 300\)
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Li, Y., Wang, S., Yang, B. et al. Population reduction with individual similarity for differential evolution. Artif Intell Rev 56, 3887–3949 (2023). https://doi.org/10.1007/s10462-022-10264-8

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