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.
KeywordsGeneralized Traveling Salesman Problem Clustering Initialization Barycenter Combinatorial optimization problem
The authors of this paper sincerely thank the Agence Universitaire de la Francophonie (AUF) for the generous support and convey their gratitude to Mr. Mohamed El Yafrani for his precious remarks on this work.
- 6.Gutin, G., Karapetyan, D., Krasnogor, N.: Memetic algorithm for the generalized asymmetric traveling salesman problem. In: Krasnogor, N., Nicosia, G., Pavone, M., Pelta, D. (eds.) Nature Inspired Cooperative Strategies for Optimization (NICSO 2007), pp. 199–210. Springer, Heidelberg (2008)CrossRefGoogle Scholar
- 10.Laporte, G., Semet, F.: Computational evaluation of a transformation procedure for the symmetric generalized traveling salesman problem. INFOR Inf. Syst. Oper. Res. 37(2), 114–120 (1999)Google Scholar
- 11.Noon, C.E.: The generalized traveling salesman problem. Ph.D. thesis, University of Michigan (1988)Google Scholar
- 13.Pourhassan, M., Neumann, F.: On the impact of local search operators and variable neighbourhood search for the generalized travelling salesperson problem. In: Proceedings of the 2015 Annual Conference on Genetic and Evolutionary Computation, pp. 465–472. ACM (2015)Google Scholar
- 18.Silberholz, J., Golden, B.: The generalized traveling salesman problem: A new genetic algorithm approach. In: Baker, E.K., Joseph, A., Mehrotra, A., Trick, M.A. (eds.) Extending the Horizons: Advances In Computing, Optimization, and Decision Technologies, pp. 165–181. Springer, New York (2007)CrossRefGoogle Scholar