Using Cluster Barycenters for the Generalized Traveling Salesman Problem

We propose in this paper a novel idea to handle a tour for the Generalized Traveling Salesman Problem (GTSP), which is an NP-hard optimization problem very solicited for its numerous applications. Knowing that for each instance, cities are grouped in clusters. The proposed method finds for each one its barycenter in order to get in a first phase a good order of visiting clusters. Then, it uses one of the well-known methods to choose a city from each cluster. The obtained solution can be a good starting tour that can be used as an input for improvement methods. Our work is validated with some practical tests on benchmark instances. Obtained results show that our method gives feasible solution instantly.