Solving the Multiple Travelling Salesman Problem using Gaussian Mixture Model and Artificial Neural Network

Multiple travelling salesman problem (MTSP) is considered as one of the common critical problems in the operational research area to find a solution for many complex issues. In this research, a novel approach is proposed to find a sufficient solution for the MTSP based on Gaussian mixture model (GMM) and artificial neural network (ANN). Clustering the cities is the first step in this research which is done using the GMM clustering, then we used a part of self-organizing map (SOM) to obtain the best path with the minimum distance and time for the salesmen using distance neural network (DNN) depending on the Euclidian distance. The results of the proposed approach are compared with the various common previous work using optimization algorithms like genetic algorithm (GA), gravitational emulation algorithm (GEA), and ant colony optimization (ACO). Experimental results showed that the proposed approach has outperformed recent approaches for solving the MTSP for all instances in terms of average travel distance and error deviation.