Three-Step Metaheuristic for the Multiple Objective Multiple Traveling Salesmen Problem

In this article, the multiple objective multiple Traveling Salesman Problem is considered. m salesmen have to visit n cities to perform some tasks each taking a given processing time. Two objectives are considered: balance the working loads of different salesmen and minimize their total traveled distance. To solve this NP-hard problem, a 3-phase metaheuristic was developed. In the first 2 phases, the principle of center of mass and a neighborhood search technique are used to assign the n cities to the m salesmen. In the third phase, a TSP solver was used to generate an optimal tour to every salesman using its assigned cities in phase 2. The metaheuristic was tested using TSP benchmarks of different sizes. The obtained results showed almost optimal load balancing for all tested instances and optimal tours in term of total traveled distances. A conducted comparison study showed that the proposed metaheuristic outperforms a recently published clustering algorithm for the workload objective.