Correlation between Mutations and Self-adaptation in Evolutionary Programming

Abstract

It has been taken for granted that long jumps of Cauchy mutation in a fast evolutionary programming (FEP) increase the probability of finding a near-optimum when the distance between the current search point and the optimum is large, but decrease the probability when such distance is small [1]. By explicitly measuring the search step sizes, this paper gives sound evidence that not long jumps but large variances in Cauchy mutation have contributed to the better performance of FEP than that of classical evolutionary programming (CEP). It has been discovered that smaller step-size mutations among Cauchy mutations had led to the faster convergence of FEP in some test functions, while these helpful Cauchy mutations could actually have shorter search step sizes than Gaussian mutations used in CEP. The reason that Cauchy mutations could have shorter step sizes than Gaussian mutations is that Cauchy mutations and Gaussian mutations could radically alter self-adaptation in FEP and CEP. This paper further discusses the correlation between mutations and self-adaptation in CEP and FEP.