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Abstract

This paper describes a branch-and-cut algorithm to solve the Team Orienteering Problem (TOP). TOP is a variant of the Vehicle Routing Problem (VRP) in which the aim is to maximize the total amount of collected profits from visiting customers while not exceeding the predefined travel time limit of each vehicle. In contrast to the exact solving methods in the literature, our algorithm is based on a linear formulation with a polynomial number of binary variables. The algorithm features a new set of useful dominance properties and valid inequalities. The set includes symmetric breaking inequalities, boundaries on profits, generalized subtour eliminations and clique cuts from graphs of incompatibilities. Experiments conducted on the standard benchmark for TOP clearly show that our branch-and-cut is competitive with the other methods in the literature and allows us to close 29 open instances.

Keywords

branch-and-cut dominance property incompatibility clique cut 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Duc-Cuong Dang
    • 1
    • 3
  • Racha El-Hajj
    • 1
    • 2
  • Aziz Moukrim
    • 1
  1. 1.Département Génie Informatique, Laboratoire Heudiasyc, UMR 7253 CNRSUniversité de Technologie de CompiègneCompiègneFrance
  2. 2.Faculté de Génie, Département Contrôle IndustrielUniversité LibanaiseBeyrouthLiban
  3. 3.School of Computer ScienceUniversity of NottinghamNottinghamUnited Kingdom

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