On convergence of a simple genetic algorithm

Abstract

The simple genetic algorithm (SGA) and its convergence analysis are main subjects of the article. The SGA is defined on a finite multi-set of potential problem solutions (individuals) together with mutation and selection operators, and appearing with some prescribed probabilities. The selection operation acts on the basis of the fitness function defined on individuals, and is fundamental for the problem considered. Generation of new population is realized by iterative actions of those operators written in the form of a transition operator acting on probability vectors. The transition operator is a Markov one. Conditions for convergence and asymptotic stability of the transition operator are formulated. © 2008 Springer-Verlag Berlin Heidelberg.