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

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.