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Stabilized dynamic constraint aggregation for solving set partitioning problems


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


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.

Suggested Citation

  • Benchimol, Pascal & Desaulniers, Guy & Desrosiers, Jacques, 2012. "Stabilized dynamic constraint aggregation for solving set partitioning problems," European Journal of Operational Research, Elsevier, vol. 223(2), pages 360-371.
  • Handle: RePEc:eee:ejores:v:223:y:2012:i:2:p:360-371
    DOI: 10.1016/j.ejor.2012.07.004

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    References listed on IDEAS

    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. 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.
    3. Andreas Löbel, 1998. "Vehicle Scheduling in Public Transit and Lagrangean Pricing," Management Science, INFORMS, vol. 44(12-Part-1), pages 1637-1649, 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.
    2. Christensen, Tue R.L. & Labbé, Martine, 2015. "A branch-cut-and-price algorithm for the piecewise linear transportation problem," European Journal of Operational Research, Elsevier, vol. 245(3), pages 645-655.
    3. Jean Bertrand Gauthier & Jacques Desrosiers & Marco E. Lübbecke, 2016. "Tools for primal degenerate linear programs: IPS, DCA, and PE," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 5(2), pages 161-204, June.


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