An Ant Colony Optimization Algorithm for the Multiple Traveling Salesmen Problem

The multiple traveling salesmen problem (MTSP) is a generalization of the famous traveling salesman problem (TSP), where more than one salesman is used in the solution. Though the MTSP is a typical computationally complex combinatorial optimization problem, it can be extended to a wide variety of routing and scheduling problems. The paper proposed an ant colony optimization (ACO) algorithm for the MTSP with two objectives: the objective of minimizing the maximum tour length of all the salesmen and the objective of minimizing the maximum tour length of each salesman. In the algorithm, the pheromone trail updating and limits followed the MAX-MIN Ant System (MMAS) scheme, and a local search procedure was used to improve the performance of the algorithm. We compared the results of our algorithm with genetic algorithm (GA) on some benchmark instances in literatures. Computational results show that our algorithm is competitive on both the objectives.