Self-Adaptation of Mutation Operator and Probability for Permutation Representations in Genetic Algorithms

Abstract

The choice of mutation rate is a vital factor in the success of any genetic algorithm (GA), and for permutation representations this is compounded by the availability of several alternative mutation operators. It is now well understood that there is no one “optimal choice”; rather, the situation changes per problem instance and during evolution. This paper examines whether this choice can be left to the processes of evolution via self-adaptation, thus removing this nontrivial task from the GA user and reducing the risk of poor performance arising from (inadvertent) inappropriate decisions. Self-adaptation has been proven successful for mutation step sizes in the continuous domain, and for the probability of applying bitwise mutation to binary encodings; here we examine whether this can translate to the choice and parameterisation of mutation operators for permutation encodings. We examine one method for adapting the choice of operator during runtime, and several different methods for adapting the rate at which the chosen operator is applied. In order to evaluate these algorithms, we have used a range of benchmark TSP problems. Of course this paper is not intended to present a state of the art in TSP solvers; rather, we use this well known problem as typical of many that require a permutation encoding, where our results indicate that self-adaptation can prove beneficial. The results show that GAs using appropriate methods to self-adapt their mutation operator and mutation rate find solutions of comparable or lower cost than algorithms with “static” operators, even when the latter have been extensively pretuned. Although the adaptive GAs tend to need longer to run, we show that is a price well worth paying as the time spent finding the optimal mutation operator and rate for the nonadaptive versions can be considerable. Finally, we evaluate the sensitivity of the self-adaptive methods to changes in the implementation, and to the choice of other genetic operators and population models. The results show that the methods presented are robust, in the sense that the performance benefits can be obtained in a wide range of host algorithms.