On Asymptotic Behaviour of a Simple Genetic xsAlgorithm
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 random mutation and selection operators. The selection operation acts on the basis of the fitness function defined on potential solutions (individuals), and is fundamental for the problem considered. Generation of a new population from the given one, is realized by the 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 each population. The transition operator is a Markov one. Thanks to the well-developed theory of Markov operators [5,8,9] new conditions for stability of the transition operator are formulated. The obtained results are related to the class of genetic operators and are not restricted to binary operators.
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