An Iterated Local Search Heuristic for a Capacitated Hub Location Problem

  • Inmaculada Rodríguez-Martín
  • Juan-José Salazar-González
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4030)


This paper addresses a capacitated hub problem consisting of choosing the routes and the hubs to use in order to send a set of commodities from sources to destinations in a given capacitated network with minimum cost. The capacities and costs of the arcs and hubs are given, and the graph connecting the hubs is not assumed to be complete. For solving this problem we propose a heuristic approach that makes use of a linear programming relaxation in an Iterated Local Search scheme. The heuristic turns out to be very effective and the results of the computational experiments show that near-optimal solutions can be derived rapidly for instances of large size.


Local Search Linear Programming Relaxation Local Search Procedure Mixed Integer Programming Model Good Feasible Solution 
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  1. 1.
    Aykin, T.: Lagrangian relaxation based approaches to capacitated hub-and-spoke network design problems. European Journal of Operational Research 79, 501–523 (1994)zbMATHCrossRefGoogle Scholar
  2. 2.
    Barahona, F.: Network design using cut inequalities. SIAM Journal on Optimization 6, 823–837 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Boland, N., Krishnamoorthy, M., Ernst, A.T., Ebery, J.: Preprocessing and cutting for multiple allocation hub location problems. European Journal of Operational Research 155, 638–653 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Campbell, J.F.: Integer programming formulations of discrete hub location problems. European Journal of Operational Research 72, 387–405 (1994)zbMATHCrossRefGoogle Scholar
  5. 5.
    Carello, G., Della Croce, F., Ghirardi, M., Tadei, R.: Solving the hub location problem in telecommunication network design: a local search approach. Networks 44, 94–105 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Ebery, J., Krishnamoorthy, M., Ernst, A., Boland, N.: The capacitated multiple allocation hub location problem: Formulations and algorithms. European Journal of Operational Research 120, 614–631 (2000)zbMATHCrossRefGoogle Scholar
  7. 7.
    Ernst, E., Krishnamoorthy, M.: Exact and heuristic algorithms for the uncapacitated multiple allocation p-hub problem. European Journal of Operational Research 104, 100–112 (1998)zbMATHCrossRefGoogle Scholar
  8. 8.
    Ernst, E., Krishnamoorthy, M.: Solution algorithms for the capacitated single allocation hub location problem. Annals of Operations Research 86, 141–159 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Hamacher, H.W., Labbé, M., Nickel, S., Sonneborn, T.: Adapting polyhedral properties from facility to hub location problems. Discrete Applied Mathematics 145, 104–116 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Holmberg, K., Yuan, D.: A Langrangian heuristic based branch-and-bound approach for the capacitated network design problem. Operations Research 48, 461–481 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Lourenço, H.R., Martin, O.C., Stützle, T.: Iterated local search. In: Glover, F., Kochenberger, G.A. (eds.) Handbook of Metaheuristics, Kluwer’s International Series in Operations Research & Management Science, Norwell (2002)Google Scholar
  12. 12.
    Magnanti, T.L., Wong, R.T.: Network design and transportation planning: models and algorithms. Transportation Science 18, 1–55 (1984)CrossRefGoogle Scholar
  13. 13.
    Mayer, G., Wagner, B.: HubLocator: an exact solution method for the multiple allocation hub location problem. Computer & Operations Research 29, 715–739 (2002)zbMATHCrossRefGoogle Scholar
  14. 14.
    O’Kelly, M., Bryan, D., Skorin-Kapov, D., Skorin-Kapov, J.: Hub network design with single and multiple allocation: A computational study. Location Science 4, 125–138 (1996)zbMATHCrossRefGoogle Scholar
  15. 15.
    Rodríguez-Martín, I., Salazar-González, J.J.: Decomposition approaches for a Capacitated Hub Problem. In: Lemaître, C., Reyes, C.A., González, J.A. (eds.) IBERAMIA 2004. LNCS (LNAI), vol. 3315, pp. 154–164. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  16. 16.
    Skorin-Kapov, D., Skorin-Kapov, J., O’Kelly, M.: Tight linear programming relaxations of uncapacitated p-hub median problems. European Journal of Operational Research 94, 582–593 (1996)zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Inmaculada Rodríguez-Martín
    • 1
  • Juan-José Salazar-González
    • 1
  1. 1.DEIOCUniversidad de La LagunaLa Laguna, TenerifeSpain

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