Multi-type ant colony system for solving the multiple traveling salesman problem

The Multiple Traveling Salesman problem (mTSP) is an extension of the well-known Traveling Salesman Problem (TSP), where more than one salesman is allowed to be used in order to visit some cities just once. Furthermore, the formulation of the mTSP applies to a wide range of reallife applications, and can be extended to a wide variety of Vehicle Routing Problems (VRPs) by incorporating some additional side constraints, such as the vehicle capacity and customer demands. Although the literature for the TSP and the VRP is definitely wide, the mTSP has not received the same amount of attention yet. This paper proposes a new algorithm based on Ant Colony Optimization (ACO) for the mTSP, specifically Multi-type Ant Colony System (M-ACS), where each colony represents a set of possible global solutions. Moreover, these colonies cooperate by means of “frequent” pheromone exchanges in order to find a competitive solution for the mTSP. The algorithm performance has been compared with one of the most efficient local search algorithms for TSP, the Lin-Kernighan algorithm. Computational results confirm the competitiveness and efficiency of the strategy we propose.