Differential mutation based on population covariance matrix

Abstract

In this paper we analyze the impact of mutation schemes using many difference vectors in Differential Evolution (DE) algorithm. We show that for an infinite (sufficiently large) number of difference vectors, distribution of their sum weakly converges to a normal distribution. This facilitates theoretical analysis of DE and leads to introduction of a mutation scheme generalizing differential mutation using multiple difference vectors. The novel scheme uses Gaussian mutation with covariance matrix proportional to the covariance matrix of the current population instead of calculating difference vectors directly. Such modification, called DE/rand/∞, and its hybridization with DE/best/1 were tested on the CEC 2005 benchmark and performed comparable or better than DE/rand/1. Both modified mutation schemes may be easily incorporated into other DE variants. In this paper we provide theoretical analysis, discussion of obtained mutation distributions, and experimental results. © 2010 Springer-Verlag.