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Using Cluster Barycenters for the Generalized Traveling Salesman Problem

  • Mehdi El KrariEmail author
  • Belaïd Ahiod
  • Bouazza El Benani
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 557)

Abstract

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.

Keywords

Generalized Traveling Salesman Problem Clustering Initialization Barycenter Combinatorial optimization problem 

Notes

Acknowledgments

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.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Mehdi El Krari
    • 1
    • 2
    Email author
  • Belaïd Ahiod
    • 1
    • 3
  • Bouazza El Benani
    • 1
    • 2
  1. 1.Faculty of ScienceMohammed V University in RabatRabatMorocco
  2. 2.Computer Science LaboratoryMohammed V University in RabatRabatMorocco
  3. 3.LRIT, Associated Unit to CNRST (URAC 29)Mohammed V University in RabatRabatMorocco

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