Effect of Multivariate Cauchy Mutation in Evolutionary Programming

Abstract

In this paper, we apply a mutation operation based on a multivariate Cauchy distribution to fast evolutionary programming and analyze its effect in terms of various function optimizations. The conventional fast evolutionary programming in-cooperates the univariate Cauchy mutation in order to overcome the slow convergence rate of the canonical Gaussian mutation. For a mutation of n variables, while the conventional method utilizes n independent random variables from a univariate Cauchy distribution, the proposed method adopts n mutually dependent random variables that satisfy a multivariate Cauchy distribution. The multivariate Cauchy distribution naturally has higher probabilities of generating random variables in inter-variable regions than the univariate Cauchy distribution due to the mutual dependence among variables. This implies that the multivariate Cauchy random variable enhances the search capability especially for a large number of correlated variables, and, as a result, is more appropriate for optimization schemes characterized by interdependence among variables. In this sense, the proposed mutation possesses the advantage of both the univariate Cauchy and Gaussian mutations. The proposed mutation is tested against various types of real-valued function optimizations. We empirically find that the proposed mutation outperformed the conventional Cauchy and Gaussian mutations in the optimization of functions having correlations among variables, whereas the conventional mutations showed better performance in functions of uncorrelated variables.