The elitist non-homogeneous genetic algorithm: Almost sure convergence

Evolutionary algorithms are used to search for optimal points of functions. One of these algorithms, the non-homogeneous genetic algorithm, uses in its dynamics two parameters, namely mutation and crossover probabilities, which are allowed to change throughout the algorithm's evolution. In this paper, we consider the elitist version of the non-homogeneous genetic algorithm and we prove its almost sure convergence to a population which has an optimum point in it.