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Population interaction network in representative differential evolution algorithms: Power-law outperforms Poisson distribution

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  • Li, Xiaosi
  • Li, Jiayi
  • Yang, Haichuan
  • Wang, Yirui
  • Gao, Shangce

Abstract

Differential evolution is a classical and effective evolutionary algorithm. In recent years, many differential evolution variants have been proposed and achieved good results on many problems. To investigate their inherent characteristics, this paper uses the population interaction network. Six representative differential evolution algorithms including DE, JADE, CJADE, SHADE, L-SHADE, and EBLSHADE are analyzed from the perspective of information interaction among individuals. The cumulative distribution function of degrees of nodes obtained from the population interaction network on thirty IEEE CEC2017 benchmark functions is fitted by seven distribution models. Results show that the cumulative distribution function of differential evolution is the Poisson distribution whereas the other variants meet the Power-law distribution. The Power-law distribution influences their performance and depends on the population size. These remarkable findings suggest that the Power-law distribution widely exists in best-performing differential evolution algorithms, which gives empirical evidence for designing Power-law distribution-based differential evolution algorithms.

Suggested Citation

  • Li, Xiaosi & Li, Jiayi & Yang, Haichuan & Wang, Yirui & Gao, Shangce, 2022. "Population interaction network in representative differential evolution algorithms: Power-law outperforms Poisson distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 603(C).
    • Handle: RePEc:eee:phsmap:v:603:y:2022:i:c:s0378437122005052
    DOI: 10.1016/j.physa.2022.127764
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    References listed on IDEAS

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    1. Petter Holme, 2019. "Rare and everywhere: Perspectives on scale-free networks," Nature Communications, Nature, vol. 10(1), pages 1-3, December.
    2. Du, Wenbo & Zhang, Mingyuan & Ying, Wen & Perc, Matjaž & Tang, Ke & Cao, Xianbin & Wu, Dapeng, 2018. "The networked evolutionary algorithm: A network science perspective," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 33-43.
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    Cited by:

    1. Yuxin Zhang & Yifei Yang & Xiaosi Li & Zijing Yuan & Yuki Todo & Haichuan Yang, 2023. "A Dendritic Neuron Model Optimized by Meta-Heuristics with a Power-Law-Distributed Population Interaction Network for Financial Time-Series Forecasting," Mathematics, MDPI, vol. 11(5), pages 1-20, March.
    2. Yifei Yang & Xiaosi Li & Haotian Li & Chaofeng Zhang & Yuki Todo & Haichuan Yang, 2023. "Yet Another Effective Dendritic Neuron Model Based on the Activity of Excitation and Inhibition," Mathematics, MDPI, vol. 11(7), pages 1-23, April.
    3. Yifei Yang & Sichen Tao & Haichuan Yang & Zijing Yuan & Zheng Tang, 2023. "Dynamic Complex Network, Exploring Differential Evolution Algorithms from Another Perspective," Mathematics, MDPI, vol. 11(13), pages 1-16, July.

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