Understanding differential evolution: A Poisson law derived from population interaction network

Differential evolution (DE) is one of evolutionary algorithms to effectively handle optimization problems. We propose a population interaction network (PIN) to investigate the relationship constituted by populations. The cumulative distribution function (CDF) of degree in PIN is analyzed by five fitting models on 12 benchmark functions. The goodness of fit is used to measure the fitting results. The experimental results demonstrate the CDF meets cumulative Poisson distribution. Besides, the number of nodes in PIN and the rate parameter λ in the fitted Poisson distribution are further studied using different control parameters of DE, which exhibits the effect and characteristic of the population interaction.