Clustering-Based Adaptive Crossover and Mutation Probabilities for Genetic Algorithms

Research into adjusting the probabilities of crossover and mutation p_m in genetic algorithms (GAs) is one of the most significant and promising areas in evolutionary computation. p_x and p_m greatly determine whether the algorithm will find a near-optimum solution or whether it will find a solution efficiently. Instead of using fixed values of p_x and p_m , this paper presents the use of fuzzy logic to adaptively adjust the values of p_x and p_m in GA. By applying the K-means algorithm, distribution of the population in the search space is clustered in each generation. A fuzzy system is used to adjust the values of p_x and p_m. It is based on considering the relative size of the cluster containing the best chromosome and the one containing the worst chromosome. The proposed method has been applied to optimize a buck regulator that requires satisfying several static and dynamic operational requirements. The optimized circuit component values, the regulator´s performance, and the convergence rate in the training are favorably compared with the GA using fixed values of p_x and p_m. The effectiveness of the fuzzy-controlled crossover and mutation probabilities is also demonstrated by optimizing eight multidimensional mathematical functions