Convergence analysis of an elitist non-homogeneous genetic algorithm with mutation probability adjusted by a fuzzy controller

In recent years, several attempts to improve the efficiency of the Canonical Genetic Algorithm have been presented. The advantage of the elitist non-homogeneous genetic algorithm is that variation of the mutation probabilities permits the algorithm to broaden its search space at the start and restrict it later on, however the way in which the mutation probabilities vary is defined before the algorithm is initiated. To solve this problem various types of controller can be used to adjust such changes. This work presents an elitist non-homogeneous genetic algorithm where the mutation probability is adjusted by a fuzzy controller. Although there are some studies in which fuzzy controllers have been used to adjust the parameters of a genetic algorithm, the goal of this work is that it describes the conditions needed so that a fuzzy controller can provide guaranteed convergence of the genetic algorithm. A generalized example illustrates that the conditions of convergence can be readily achieved. And finally, numeric simulations are used to compare the proposed algorithm with the canonical genetic algorithm.