Genetic Algorithms with Fitness- & Diversity-guided Adaptive Operating Probabilities and Analyses of its Convergence

Abstract

Abstract The paper has analyzed global convergence GAs, especially when attempts are made to avoid properties of adaptive genetic algorithms combining adaptive probabilities of crossover and mutation with diversity-guided crossover and mutation. By means of homogeneous finite Markov chains, it is proved that AGAD, which is present in this paper, and GAD (genetic algorithms with diversity-guided mutation) maintaining the best solution converge to the global optimum, which is the main contributions of this paper. The performance of AGA(adaptive genetic algorithms with adaptive probabilities of crossover and mutation), GAD and AGAD in optimizing several unimodal and multimodal functions has been compared. For multimodal functions, the AGAD converges to the global optimum for fewer generations than AGA and GAD, and it hardly has premature convergence. Key Diversity-guided mutation; Adaptive genetic algorithm; Markov chain analysis; Global convergence