Multi-Dimensional Gaussian and Cauchy Mutations

Abstract

The aim of this work is to focus the attention of researchers concerned with evolutionary algorithms on the fact that the most probable location of the mutated points in multi-dimensional Gaussian and Cauchy mutations is not in a close neighborhood of the origin, but at a certain distance from it. In the case of the Gaussian mutation this distance is proportional to the norm of the standard deviation vector and increases with the landscape dimension. This may cause a decrease in the sensitivity of the evolutionary algorithm to narrow peaks when the landscape dimension increases. Moreover, it is proved that the multi-dimensional Cauchy mutation is not isotropic and the directions parallel to the axes of the reference frame are preferred. The effectiveness of the evolutionary algorithm using the Cauchy mutation strongly depends on the choice of the reference frame. New Gaussian-like and Cauchy-like mutations are proposed in order to overcome the considered difficulties.