عنوان مقاله [English]
The Multiple Traveling Salesmen Problem (MTSP) is a well-known generalization of the Traveling Salesman Problem (TSP). In general, The MTSP can be defined as follows:Given a set of n nodes (cities), let there be m salesmen located at a single depot node. The remaining nodes that are to be visited are called intermediate nodes. Then, the MTSP consists of finding tours for m salesmen. All of them start and end at the depot, such that each intermediate node is visited exactly once. Our aim is to minimize the total cost of visited nodes by the salesmen.
There is a broad variety of versions of MTSP and a wide range of literature on this class of problems. The variants include MTSP with pickup and delivery, time windows, multi depots, and others. There have been important advances in the development of exact and approximate algorithms for solving the MTSP, as an important NP-hard combinatorial optimization problem.
Although heuristic methods solve NP-hard problems, they become trapped in local optima and cannot gain a good suboptimal solution. As a result, in the last 30 years, a new kind of approximate algorithm called meta-heuristics has emerged. Basically, this type of algorithm tries to combine basic heuristic methods into higher level frameworks aimed at efficiently and effectively exploring a search space.In contrast, the research on the MTSP has received less attention than the TSP. Therefore, in this paper for the MTSP, a new meta-heuristic algorithm called
the Imperialist Competitive Algorithm (ICA), is proposed. This algorithm has been motivated by the notion of imperialism and imperialistic competition in order to solve optimization problems. The proposed algorithm is tested using two benchmark data sets available from the literature. The computational results show that the ICA is competitive with other published results for solving MTSP. In addition, for some instances, the proposed algorithm gives better solutions.