Solving a Multi-Traveling Salesmen Problem using a Mamdani Fuzzy Inference Engine and Simulated Annealing Search Algorithm

The multi-traveling salesmen problem (MTSP) is an extended situation of the standard traveling salesman problem (TSP), in which there is more than one salesman. In this matter, several salesmen are determined to visit N city with the goal of the shortest route to selling their goods, assuming they have crossed all of them, via just once each. The aim is to minimize the total cost of travel for salesman. Thus, it can be modeled as an optimization problem. Regarding the complexity degree, this problem is well known as a NP-Hard problem. Therefore, several meta-heuristic algorithms have been developed at the frontiers of knowledge to solve this problem. Nevertheless, the computational and time complexities are the most important challenges of such algorithms. In this paper, we first convert the MTSP using a fuzzy approach with a linear complexity level, to several TSPs. Then, we solve each problem using the simulated annealing (SA) optimization algorithm. In this way, the time complexity of the system is significantly reduced using the proposed method as well as the accuracy of the system is satisfactory. To assess the proposed algorithm, this method is implemented in the TSPLIB library dataset.