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Mathematical Programming Computation

, Volume 5, Issue 1, pp 27–55 | Cite as

The time dependent traveling salesman problem: polyhedra and algorithm

  • Hernán Abeledo
  • Ricardo FukasawaEmail author
  • Artur Pessoa
  • Eduardo Uchoa
Full Length Paper

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 100 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. We obtain good computational results with a branch-cut-and-price algorithm using the new cuts, solving almost all instances from the TSPLIB with up to 107 vertices.

Keywords

Integer programming Polyhedral combinatorics Cutting planes Branch-price-and-cut Time dependent traveling salesman 

Mathematics Subject Classification (2000)

90C11 90C27 90C57 

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Copyright information

© Springer and Mathematical Optimization Society 2012

Authors and Affiliations

  • Hernán Abeledo
    • 1
  • Ricardo Fukasawa
    • 2
    Email author
  • Artur Pessoa
    • 3
  • Eduardo Uchoa
    • 3
  1. 1.Department of Engineering Management and Systems EngineeringThe George Washington UniversityWashingtonUSA
  2. 2.Department of Combinatorics and OptimizationUniversity of WaterlooWaterlooCanada
  3. 3.Departamento de Engenharia de ProduçãoUniversidade Federal FluminenseNiteróiBrazil

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