A Comparative Study on Population-Based Evolutionary Algorithms for Multiple Traveling Salesmen Problem with Visiting Constraints

The multiple traveling salesmen problem with visiting constraints (VCMTSP) is an extension of the multiple traveling salesmen problem (MTSP). In this problem, some cities are restricted to be only accessed by certain salesmen, which is very common in real-world applications. In the literature, evolutionary algorithms (EAs) have been demonstrated to effectively solve MTSP. In this paper, we aim to adapt three widely used EAs in solving MTSP, namely the genetic algorithm (GA), the ant colony optimization algorithm (ACO), and the artificial bee colony algorithm (ABC), to solve VCMTSP. Then, we conduct extensive experiments to investigate the optimization performance of the three EAs in solving VCMTSP. Experimental results on various VCMTSP instances demonstrate that by means of its strong local exploitation ability, ABC shows much better performance than the other two algorithms, especially on large-scale VCMTSP. Though GA and ACO are effective to solve small-scale VCMTSP, their effectiveness degrades drastically on large-scale instances. Particularly, it is found that local exploitation is very vital for EAs to effectively solve VCMTSP. With the above observations, it is expected that this paper could afford a basic guideline for new researchers who want to take attempts in this area.