Clustering-Based Adaptive Crossover and Mutation Probabilities for Genetic Algorithms

Abstract

Research into adjusting the probabilities of crossover and mutation p <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sub> in genetic algorithms (GAs) is one of the most significant and promising areas in evolutionary computation. p <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x </sub> and p <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sub> 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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> and p <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m </sub> , this paper presents the use of fuzzy logic to adaptively adjust the values of p <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> and p <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sub> 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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> and p <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sub> . 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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> and p <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sub> . The effectiveness of the fuzzy-controlled crossover and mutation probabilities is also demonstrated by optimizing eight multidimensional mathematical functions