Enhancing Differential Evolution Utilizing Eigenvector-Based Crossover Operator

Abstract

Differential evolution has been shown to be an effective methodology for solving optimization problems over continuous space. In this paper, we propose an eigenvector-based crossover operator. The proposed operator utilizes eigenvectors of covariance matrix of individual solutions, which makes the crossover rotationally invariant. More specifically, the donor vectors during crossover are modified, by projecting each donor vector onto the eigenvector basis that provides an alternative coordinate system. The proposed operator can be applied to any crossover strategy with minimal changes. The experimental results show that the proposed operator significantly improves DE performance on a set of 54 test functions in CEC 2011, BBOB 2012, and CEC 2013 benchmark sets.