An Effective Genetic Algorithm for Solving the Multiple Traveling Salesman Problem

Subject Areas : Design of Experiment

Mohammad Sedighpour ¹ , Majid Yousefikhoshbakht ² , Narges Mahmoodi Darani ³

1 - Instructor, Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, Iran
2 - Instructor, Young Researchers Club, Hamedan Branch, Islamic Azad University, Hamedan, Iran
3 - Instructor, Department of Mathematics, Malayer Branch, Islamic Azad University, Malayer, Iran

Received: 2011-01-22 Accepted : 2011-03-05 Published : 2012-07-09

Keywords: Genetic Algorithm, Multiple Traveling Salesman Problem, NP-hard Problems, 2-Opt local search algorithm,

Abstract :

The multiple traveling salesman problem (MTSP) involves scheduling m > 1 salesmen to visit a set of n > m nodes so that each node is visited exactly once. The objective is to minimize the total distance traveled by all the salesmen. The MTSP is an example of combinatorial optimization problems, and has a multiplicity of applications, mostly in the areas of routing and scheduling. In this paper, a modified hybrid metaheuristic algorithm called GA2OPT for solving the MTSP is proposed. In this algorithm, at the first stage, the MTSP is solved by the modified genetic Algorithm (GA) in each iteration, and, at the second stage, the 2-Opt local search algorithm is used for improving solutions for that iteration. The proposed algorithm was tested on a set of 6 benchmark instances from the TSPLIB and in all but four instances the best known solution was improved. For the rest instances, the quality of the produced solution deviates less than 0.01% from the best known solutions ever.