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.


branch-and-cut dominance property incompatibility clique cut 


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  1. 1.
    Bouly, H., Moukrim, A., Chanteur, D., Simon, L.: Un algorithme de destruction/construction itératif pour la résolution d’un problème de tournées de véhicules spécifique. In: MOSIM 2008 (2008)Google Scholar
  2. 2.
    Boussier, S., Feillet, D., Gendreau, M.: An exact algorithm for team orienteering problems. 4OR 5(3), 211–230 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Butt, S.E., Ryan, D.M.: An optimal solution procedure for the multiple tour maximum collection problem using column generation. Computers & Operations Research 26, 427–441 (1999)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Chao, I.-M., Golden, B., Wasil, E.: The team orienteering problem. European Journal of Operational Research 88, 464–474 (1996)zbMATHCrossRefGoogle Scholar
  5. 5.
    Dang, D.-C., Moukrim, A.: Subgraph extraction and metaheuristics for the maximum clique problem. Journal of Heuristics 18, 767–794 (2012)CrossRefGoogle Scholar
  6. 6.
    Dang, D.-C., Guibadj, R.-N., Moukrim, A.: A PSO-inspired algorithm for the team orienteering problem. European Journal of Operational Research (in press, accepted manuscript, available online March 2013)Google Scholar
  7. 7.
    Fischetti, M., Salazar González, J.J., Toth, P.: Solving the orienteering problem through branch-and-cut. INFORMS Journal on Computing 10, 133–148 (1998)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Poggi de Aragão, M., Viana, H., Uchoa, E.: The team orienteering problem: Formulations and branch-cut and price. In: ATMOS, pp. 142–155 (2010)Google Scholar
  9. 9.
    Tang, H., Miller-Hooks, E.: A tabu search heuristic for the team orienteering problem. Computer & Operations Research 32, 1379–1407 (2005)CrossRefGoogle Scholar
  10. 10.
    Vansteenwegen, P., Souffriau, W., Vanden Berghe, G., Van Oudheusden, D.: Metaheuristics for tourist trip planning. In: Metaheuristics in the Service Industry. Lecture Notes in Economics and Mathematical Systems, vol. 624, pp. 15–31. Springer, Heidelberg (2009)CrossRefGoogle Scholar

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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