A New Genetic Operator for the Traveling Salesman Problem

Abstract

This paper describes a new approach to the generation of good solutions to the TSP using evolution programs. A novel genetic crossover operator is introduced, which generates a single offspring without explicitly preserving particular characteristics like position, order or adjacency. A geometrical explanation of the heuristic lies on the fact that a good TSP tour does not have crossing edges (or knots). The crossover technique aims to untie the knots and consequently, the evolutionary search is executed over populations of lesser knotted solutions. This operator, that we have called knot-cracker, always produces legal offspring’s avoiding repairing techniques. Experiments were performed over the same benchmarks used by the authors of the Enhanced Edge Recombination operator (EER) in their seminal publication. An enhanced version of the knot-cracker is also proposed, which improves previous results, reaches high quality solutions with high consistency and shows a better performance than the EER.