Ant-Balanced Multiple Traveling Salesmen: ACO-BmTSP

Resumen

A new algorithm based on the ant colony optimization (ACO) method for the multiple traveling salesman problem (mTSP) is presented and defined as ACO-BmTSP. This paper addresses the problem of solving the mTSP while considering several salesmen and keeping both the total travel cost at the minimum and the tours balanced. Eleven different problems with several variants were analyzed to validate the method. The 20 variants considered three to twenty salesmen regarding 11 to 783 cities. The results were compared with best-known solutions (BKSs) in the literature. Computational experiments showed that a total of eight final results were better than those of the BKSs, and the others were quite promising, showing that with few adaptations, it will be possible to obtain better results than those of the BKSs. Although the ACO metaheuristic does not guarantee that the best solution will be found, it is essential in problems with non-deterministic polynomial time complexity resolution or when used as an initial bound solution in an integer programming formulation. Computational experiments on a wide range of benchmark problems within an acceptable time limit showed that compared with four existing algorithms, the proposed algorithm presented better results for several problems than the other algorithms did.