Effects of crossover operator combined with mutation operator in genetic algorithms for the generalized travelling salesman problem

Abstract

Here, we consider the generalized travelling salesman problem (GTSP), which is a generalization of the travelling salesman problem (TSP). This problem has several real-life applications. Since the problem is complex and NP-hard, solving this problem by exact methods is very difficult. Therefore, researchers have applied several heuristic algorithms to solve this problem. We propose the application of genetic algorithms (GAs) to obtain a solution. In the GA, three operators—selection, crossover, and mutation—are successively applied to a group of chromosomes to obtain a solution to an optimization problem. The crossover operator is applied to create better offspring and thus to converge the population, and the mutation operator is applied to explore the areas that cannot be explored by the crossover operator and thus to diversify the search space. All the crossover and mutation operators developed for the TSP can be used for the GTSP with some modifications. A better combination of these two operators can create a very good GA to obtain optimal solutions to the GTSP instances. Therefore, four crossover and three mutation operators are used here to develop GAs for solving the GTSP. Then, GAs is compared on several benchmark GTSPLIB instances. Our experiment shows the effectiveness of the sequential constructive crossover operator combined with the insertion mutation operator for this problem.