An Analysis on Crossovers for Real Number Chromosomes in an Infinite Population Size

Abstract

In this paper, as one approach for mathematical analysis of evolutionary algorithms with real number chromosomes, we focus our attention on crossovers, give a general framework of the description for the change of the distribution of the population through them, and verify the properties of crossovers based on the framework. This framework includes various crossover which have been proposed and we apply our result to these crossover methods. 1 Introduction A lot of experimental and theoretical researches on Evolutionary Algorithms (EA) have been recently reported. In the theoretical results, most of them are ones for EAs using bit strings as chromosomes, in particular, the Simple Genetic Algorithms (SGA). These are based on the theory of Finite Markov Chain [ Dawid, 1994; Davis and Principe, 1993; Nix and Vose, 1992; Rudolph, 1994 ] because the SGA uses bit strings with a constant length. However, the state spaces of EAs using real number chromosomes are infinite and uncountable sets...