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A partitioning algorithm for the network loading problem

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  • Babonneau, F.
  • Vial, J.-P.

Abstract

This paper proposes a Benders-like partitioning algorithm to solve the network loading problem. The approach is an iterative method in which the integer programming solver is not used to produce the best integer point in the polyhedral relaxation of the set of feasible capacities. Rather, it selects an integer solution that is closest to the best known integer solution. Contrary to previous approaches, the method does not exploit the original mixed integer programming formulation of the problem. The effort of computing integer solutions is entirely left to a pure integer programming solver while valid inequalities are generated by solving standard nonlinear multicommodity flow problems. The method is compared to alternative approaches proposed in the literature and appears to be efficient for computing good upper bounds.

Suggested Citation

  • Babonneau, F. & Vial, J.-P., 2010. "A partitioning algorithm for the network loading problem," European Journal of Operational Research, Elsevier, vol. 204(1), pages 173-179, July.
    • Handle: RePEc:eee:ejores:v:204:y:2010:i:1:p:173-179
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    References listed on IDEAS

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    1. Itzhak Gilboa & Sunil Chopra & S. Trilochan Sastri, 1998. "Source Sink Flows with Capacity Installation in Batches," Post-Print hal-00753123, HAL.
    2. Frédéric Babonneau & Jean-Philippe Vial, 2008. "An Efficient Method to Compute Traffic Assignment Problems with Elastic Demands," Transportation Science, INFORMS, vol. 42(2), pages 249-260, May.
    3. Thomas L. Magnanti & Prakash Mirchandani & Rita Vachani, 1995. "Modeling and Solving the Two-Facility Capacitated Network Loading Problem," Operations Research, INFORMS, vol. 43(1), pages 142-157, February.
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