Hybrid Genetic Algorithms and Tour Construction and Improvement Algorithms Used for Optimizing the Traveling Salesman Problem

Abstract

The traveling salesman problem (TSP) aims at finding the shortest tour that passes through each vertex in a given graph exactly once. To address TSP, many exact and approximate algorithms have been proposed. In this paper, we propose three new algorithms for TSP based on a genetic algorithm (GA) and an order crossover operator. In the first algorithm, a generic version of a GA with random population is introduced. In the second algorithm, after the random population is introduced, the selected parents are improved with a 2-OPT algorithm and processed further with a GA. Finally, in the third algorithm, the initial solutions are obtained with a nearest neighbor algorithm (NNA) and a nearest insertion algorithm (NIA); afterwards they are improved with a 2-OPT and processed further with a GA. Our approach differs from previous papers for using a GA for TSP in two ways. First, every successive generation of individuals is generated based primarily on 4 best parents from the previous generation regardless the number of individuals in each population. Second, we have proposed the new hybridization between GA, NNA, NIA and 2-OPT. The overall results demonstrate that the proposed GAs offer promising results, particularly for large-sized instances.