The time dependent traveling salesman problem: polyhedra and branch-cut-and-price algorithm

  • Authors:

  • Hernán Abeledo;Ricardo Fukasawa;Artur Pessoa;Eduardo Uchoa

  • Affiliations:

  • Department of Engineering Management and Systems Engineering, The George Washington University, Washington, DC;Department of Combinatorics and Optimization, University of Waterloo, Waterloo, ON, Canada;Departamento de Engenharia de Produção, Universidade Federal Fluminense, Niterói, RJ, Brazil;Departamento de Engenharia de Produção, Universidade Federal Fluminense, Niterói, RJ, Brazil

  • Venue:
  • SEA'10 Proceedings of the 9th international conference on Experimental Algorithms
  • Year:
  • 2010

Quantified Score

Hi-index 0.00

Visualization

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.