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The Time Dependent Traveling Salesman Problem: Polyhedra and Branch-Cut-and-Price Algorithm

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Experimental Algorithms (SEA 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6049))

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Abstract

The Time Dependent Traveling Salesman Problem (TDTSP) is a generalization of the classical Traveling Salesman Problem (TSP), where arc costs depend on their position in the tour with respect to the source node. While TSP instances with thousands of vertices can be solved routinely, there are very challenging TDTSP instances with less than 60 vertices. In this work, we study the polytope associated to the TDTSP formulation by Picard and Queyranne, which can be viewed as an extended formulation of the TSP. We determine the dimension of the TDTSP polytope and identify several families of facet defining cuts. In particular, we also show that some facet defining cuts for the usual Asymmetric TSP formulation define low dimensional faces of the TDTSP formulation and give a way to lift them. We obtain good computational results with a branch-cut-and-price algorithm using the new cuts, solving several instances of reasonable size at the root node.

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Author information

Authors and Affiliations

  1. Department of Engineering Management and Systems Engineering, The George Washington University, Washington, DC, USA

    Hernán Abeledo

  2. Department of Combinatorics and Optimization, University of Waterloo, Waterloo, ON, Canada

    Ricardo Fukasawa

  3. Departamento de Engenharia de Produção, Universidade Federal Fluminense, Niterói, RJ, Brazil

    Artur Pessoa & Eduardo Uchoa

Authors
  1. Hernán Abeledo
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  2. Ricardo Fukasawa
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  3. Artur Pessoa
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  4. Eduardo Uchoa
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Editor information

Editors and Affiliations

  1. Department of Mathematics and Applications, University of Napoli Federico II, Compl. MSA, Via Cintia, 80126, Napoli, Italy

    Paola Festa

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Abeledo, H., Fukasawa, R., Pessoa, A., Uchoa, E. (2010). The Time Dependent Traveling Salesman Problem: Polyhedra and Branch-Cut-and-Price Algorithm. In: Festa, P. (eds) Experimental Algorithms. SEA 2010. Lecture Notes in Computer Science, vol 6049. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13193-6_18

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  • DOI: https://doi.org/10.1007/978-3-642-13193-6_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13192-9

  • Online ISBN: 978-3-642-13193-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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