On asymptotic behaviour of a binary genetic algorithm

Abstract

The simple genetic algorithm (SGA) and its convergence analysis are main subjects of the article. A particular SGA is defined on a finite multi-set of individuals (chromosomes) together with mutation and proportional selection operators, each of which with some prescribed probability. The selection operation acts on the basis of the fitness function defined on individuals. Generation of a new population from a given one is made by iterative actions of those operators. Each iteration is written in the form of a transition operator acting on probability vectors which describe probability distributions of all populations. The transition operator is power of Markovian matrix. Based on the theory of Markov operators [1-3] new conditions for asymptotic stability of the transition operator are formulated.