عنوان مقاله [English]
The Multiple Traveling Salesmen Problem (MTSP) is a generalized Traveling Salesmen Problem (TSP). The difference with the traveling salesmen problem is that all cities are visited by multiple salesmen, and each salesman from the city that initiated the move must go back to the same city, which is, in fact, suitable for modeling practical problems in real life than TSP. To solve MTSP with a few starting points, you need the minimum and maximum number of cities each salesman should visit. The total number of cities that salesmen go through should be equal to all cities. In this article, The hybrid Algorithm (IAC-PGA), which combines Parteno Genetic Algorithms (PGA) and Ant Colony (ACO)
and uses the 2-opt local search method to improve the algorithm. This method provides full double displacement to improve the response. The main idea in this article is to use the PGA algorithm to search for the best number of cities visited as well as to obtain the starting point of each salesman using the genetic algorithm, and then to use the ACO algorithm to accurately determine the cities visited and the best tour for each salesman. The objective function for this problem is to minimize the distance traveled by all salesmen. For the purpose of analysis, the parameters of each algorithm are selected according to the number of experimental samples in the most appropriate case, and then the results of the algorithm are compared with other algorithms including PGA, Improved PGA (IPGA), Two-part Wolf Pack Search (TWPS),
Artificial Bee Colony (ABC), and Invasive Weed Optimization (IWO). Statistics show the algorithm improvement for problem solving. The results of comparative experiments show that the proposed IAC-PGA algorithm is sufficiently effective in solving large-scale MTSP and is not worse than other algorithms on a small scale and performs better than the existing algorithms.