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

Abstract

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, variations of the mutation probabilities permit 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 controllers 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. Many simulation studies have used fuzzy controllers to adjust the parameters in order to improve the performance of the genetic algorithm. However, no previous investigation has discussed the conditions that must be met by the controller in order to ensure convergence of the genetic algorithm. A generalized example will be used to illustrate how sufficient conditions for the algorithm convergence can be readily achieved. And finally, numerical simulations are used to compare the proposed algorithm with the canonical genetic algorithm.