Solving the Multiple Traveling Salesman Problem under Demand Uncertainty with Imperialist Competitive and Water flow-like Algorithms (Case study: Pegah Bazar-Gostar region 1 Company)

The Multiple Traveling Salesman Problem (MTSP) is a generalization of the famous Traveling Salesman Problem (TSP), whose goal is to determine the minimum cost of travels to n cities; so that salespersons begin their travels from one point as an origin and return to it after visiting all the cities. They must also visit each city exactly once. In this paper, which is implemented in Pegah Bazar-Gostar region 1 company, customer demands is considered as a fuzzy model. Dividing the city into smaller areas and allocating them to salesmen (vehicles) is so time-consuming and uncertain. In this research, by using meta-heuristic algorithms (imperialist competitive and water flow-like), the optimal routes are determined. Results specify that imperialist competitive algorithm is better in solution quality and water flow-like algorithm is better in computation time; so, based on this, the method of allocation and customer service prioritization has been corrected and balanced.