Theoretical Analysis of Differential Evolution

Abstract

Differential evolution has proven to be a simple yet efficient optimization approach since its invention by Storn and Price in 1995 [1], [2]. Despite its success in various practical applications, only a few theoretical results [2], [13], [14], [15] have been obtained concerning its stochastic behavior and most of them focus on the mutation and crossover operations while omitting detailed analysis of selection that is immediately related to objective function values and characteristics. The control parameters of DE, both the mutation factor and the crossover probability, are sensitive to the characteristics of different problems and the varied landscapes of a single problem at different evolutionary search stages. Thus, it is necessary to consider the selection operation in investigating the effect of control parameters on the stochastic convergence behavior of differential evolution.