New Designs of k-means Clustering and Crossover Operator for Solving Traveling Salesman Problems using Evolutionary Algorithms

Abstract

The traveling salesman problem is a well-known combinatorial optimization problem with permutation-based variables, which has been proven to be an NP-complete problem. Over the last few decades, many evolutionary algorithms have been developed for solving it. In this study, a new design that uses the k-means clustering method, is proposed to be used as a repairing method for the individuals in the initial population. In addition, a new crossover operator is introduced to improve the evolving process of an evolutionary algorithm and hence its performance. To investigate the performance of the proposed mechanism, two popular evolutionary algorithms (genetic algorithm and differential evolution) have been implemented for solving 18 instances of traveling salesman problems and the results have been compared with those obtained from standard versions of GA and DE, and 3 other state-of-the-art algorithms. Results show that the proposed components can significantly improve the performance of EAs while solving TSPs with small, medium and large-sized problems.