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Stabilized dynamic constraint aggregation for solving set partitioning problems

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  • Benchimol, Pascal
  • Desaulniers, Guy
  • Desrosiers, Jacques
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    Abstract

    Dynamic constraint aggregation (DCA) and dual variable stabilization (DVS) are two methods that can reduce the negative impact of degeneracy when solving linear programs. The first uses a projection to reduce the primal space whereas the second acts in the dual space. In this paper, we develop a new method, called stabilized dynamic constraint aggregation (SDCA), that combines DCA and DVS for solving set partitioning problems. It allows to fight degeneracy from both primal and dual perspectives simultaneously. To assess the effectiveness of SDCA, we report computational results obtained for highly degenerate multi-depot vehicle scheduling problem instances solved by column generation. These results indicate that SDCA can reduce the average computational time of the master problem by a factor of up to 7 with respect to the best of the two combined methods. Furthermore, they show that its performance is robust with regard to increasing levels of degeneracy in test problems.

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    Bibliographic Info

    Article provided by Elsevier in its journal European Journal of Operational Research.

    Volume (Year): 223 (2012)
    Issue (Month): 2 ()
    Pages: 360-371

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    Handle: RePEc:eee:ejores:v:223:y:2012:i:2:p:360-371

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    Web page: http://www.elsevier.com/locate/eor

    Related research

    Keywords: Primal degeneracy; Set partitioning; Dynamic constraint aggregation; Dual variable stabilization; Column generation;

    References

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    1. Carraresi, P. & Gallo, G., 1984. "Network models for vehicle and crew scheduling," European Journal of Operational Research, Elsevier, vol. 16(2), pages 139-151, May.
    2. Andreas Löbel, 1998. "Vehicle Scheduling in Public Transit and Lagrangean Pricing," Management Science, INFORMS, vol. 44(12-Part-1), pages 1637-1649, December.
    3. Kliewer, Natalia & Mellouli, Taieb & Suhl, Leena, 2006. "A time-space network based exact optimization model for multi-depot bus scheduling," European Journal of Operational Research, Elsevier, vol. 175(3), pages 1616-1627, December.
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    Cited by:
    1. Desrosiers, Jacques & Gauthier, Jean Bertrand & Lübbecke, Marco E., 2014. "Row-reduced column generation for degenerate master problems," European Journal of Operational Research, Elsevier, vol. 236(2), pages 453-460.

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