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Using mathematical programming heuristics in a multicriteria network flow context

Author

Listed:
  • J Figueira

    (LAMSADE, Université Paris-Dauphine)

  • H M'Silti

    (LAMSADE, Université Paris-Dauphine)

  • P Tolla

    (LAMSADE, Université Paris-Dauphine)

Abstract

In this paper, we propose a local search procedure to test the robustness of a specific ‘satisfying point’ neighbourhood. It consists of the following steps: (1) build an indifference area around the satisfying point in the criteria space by using thresholds (this takes into account the possible uncertainty, vagueness and/or inaccuracy of data); (2) find some points in the satisfying point neighbourhood and the corresponding solutions in the decision variables space; (3) test the quality of these solutions from the point of view of user preference. The indifference area is defined by adding constraints to the network model. This approach, which allows us to verify the adequacy of the model, has been applied to a set of multicriteria network flow problems. A heuristic method, based on Lagrangian duality and subgradient techniques, exploits the combinatorial structure of network flow problems in order to find certain feasible points.

Suggested Citation

  • J Figueira & H M'Silti & P Tolla, 1998. "Using mathematical programming heuristics in a multicriteria network flow context," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 49(8), pages 878-885, August.
    • Handle: RePEc:pal:jorsoc:v:49:y:1998:i:8:d:10.1057_palgrave.jors.2600571
    DOI: 10.1057/palgrave.jors.2600571
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    Citations

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    Cited by:

    1. Hamacher, Horst W. & Pedersen, Christian Roed & Ruzika, Stefan, 2007. "Multiple objective minimum cost flow problems: A review," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1404-1422, February.
    2. Nikolaos Argyris & José Figueira & Alec Morton, 2011. "Identifying preferred solutions to Multi-Objective Binary Optimisation problems, with an application to the Multi-Objective Knapsack Problem," Journal of Global Optimization, Springer, vol. 49(2), pages 213-235, February.

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