Asymptotic and Pointwise Stability of Evolutionary Algorithms

On a finite multi-set of potential problem solutions, called individuals, fitness function together with random mutation and selection operators forming a simple genetic algorithm (SGA), are defined. Subsequent iterations of the algorithm produce sets of potential solutions, called generations. Action of SGA 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 matrix. New conditions for asymptotic and pointwise stability of the transition operator are formulated.