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Stabilized dynamic constraint aggregation for solving set partitioning problems

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

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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  • 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

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    1. Ahmed Hadjar & Odile Marcotte & François Soumis, 2006. "A Branch-and-Cut Algorithm for the Multiple Depot Vehicle Scheduling Problem," Operations Research, INFORMS, vol. 54(1), pages 130-149, February.
    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.
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    5. Stefan Irnich & Guy Desaulniers, 2005. "Shortest Path Problems with Resource Constraints," Springer Books, in: Guy Desaulniers & Jacques Desrosiers & Marius M. Solomon (ed.), Column Generation, chapter 0, pages 33-65, Springer.
    6. Marco E. Lübbecke & Jacques Desrosiers, 2005. "Selected Topics in Column Generation," Operations Research, INFORMS, vol. 53(6), pages 1007-1023, December.
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    Cited by:

    1. 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.
    2. Kulkarni, Sarang & Krishnamoorthy, Mohan & Ranade, Abhiram & Ernst, Andreas T. & Patil, Rahul, 2018. "A new formulation and a column generation-based heuristic for the multiple depot vehicle scheduling problem," Transportation Research Part B: Methodological, Elsevier, vol. 118(C), pages 457-487.
    3. 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.
    4. Sebastian Ruther & Natashia Boland & Faramroze G. Engineer & Ian Evans, 2017. "Integrated Aircraft Routing, Crew Pairing, and Tail Assignment: Branch-and-Price with Many Pricing Problems," Transportation Science, INFORMS, vol. 51(1), pages 177-195, February.
    5. 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.
    6. Daniel Porumbel & François Clautiaux, 2017. "Constraint Aggregation in Column Generation Models for Resource-Constrained Covering Problems," INFORMS Journal on Computing, INFORMS, vol. 29(1), pages 170-184, February.

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