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Dynamic constraint and variable aggregation in column generation

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  • Bouarab, Hocine
  • El Hallaoui, Issmail
  • Metrane, Abdelmoutalib
  • Soumis, François

Abstract

Starting from the improved primal simplex (IPS) decomposition, introduced by Elhallaoui et al. (2011) to tackle degeneracy in general linear programs, we introduce and discuss the mathematical foundations of improved column-generation decompositions (ICG) that are better than the standard column-generation decomposition when degeneracy is an issue. We also present an improved dynamic constraint aggregation (IDCA), which is a specialization of ICG to efficiently solve set partitioning problems. We show that IDCA improves the dynamic constraint aggregation (DCA) and the multiphase dynamic constraint aggregation (MPDCA) algorithms (Elhallaoui et al., 2005, 2010) that not only reduce degeneracy but also profit from it to efficiently solve set partitioning problems. IDCA solves at each iteration a complementary problem (CP) to obtain a group of variables that can be aggregated or pivoted into the basis to bypass degenerate pivots and decrease the objective value and to obtain more “central” dual solutions to generate new columns. Our numerical results show reduction factors in the solution times exceeding 10 for IDCA compared to a state-of-the-art standard column-generation solver.

Suggested Citation

  • Bouarab, Hocine & El Hallaoui, Issmail & Metrane, Abdelmoutalib & Soumis, François, 2017. "Dynamic constraint and variable aggregation in column generation," European Journal of Operational Research, Elsevier, vol. 262(3), pages 835-850.
    • Handle: RePEc:eee:ejores:v:262:y:2017:i:3:p:835-850
    DOI: 10.1016/j.ejor.2017.04.049
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    1. Desaulniers, G. & Desrosiers, J. & Dumas, Y. & Marc, S. & Rioux, B. & Solomon, M. M. & Soumis, F., 1997. "Crew pairing at Air France," European Journal of Operational Research, Elsevier, vol. 97(2), pages 245-259, March.
    2. Issmail Elhallaoui & Abdelmoutalib Metrane & Guy Desaulniers & François Soumis, 2011. "An Improved Primal Simplex Algorithm for Degenerate Linear Programs," INFORMS Journal on Computing, INFORMS, vol. 23(4), pages 569-577, November.
    3. Desrochers, Martin & Soumis, Francois, 1988. "A reoptimization algorithm for the shortest path problem with time windows," European Journal of Operational Research, Elsevier, vol. 35(2), pages 242-254, May.
    4. 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.
    5. François Vanderbeck, 2005. "Implementing Mixed Integer Column Generation," Springer Books, in: Guy Desaulniers & Jacques Desrosiers & Marius M. Solomon (ed.), Column Generation, chapter 0, pages 331-358, Springer.
    6. Villeneuve, Daniel & Desaulniers, Guy, 2005. "The shortest path problem with forbidden paths," European Journal of Operational Research, Elsevier, vol. 165(1), pages 97-107, August.
    7. Metrane, Abdelmoutalib & Soumis, François & Elhallaoui, Issmail, 2010. "Column generation decomposition with the degenerate constraints in the subproblem," European Journal of Operational Research, Elsevier, vol. 207(1), pages 37-44, November.
    8. Cynthia Barnhart & Ellis L. Johnson & George L. Nemhauser & Martin W. P. Savelsbergh & Pamela H. Vance, 1998. "Branch-and-Price: Column Generation for Solving Huge Integer Programs," Operations Research, INFORMS, vol. 46(3), pages 316-329, June.
    9. Omer, Jérémy & Soumis, François, 2015. "A linear programming decomposition focusing on the span of the nondegenerate columns," European Journal of Operational Research, Elsevier, vol. 245(2), pages 371-383.
    10. Issmail Elhallaoui & Daniel Villeneuve & François Soumis & Guy Desaulniers, 2005. "Dynamic Aggregation of Set-Partitioning Constraints in Column Generation," Operations Research, INFORMS, vol. 53(4), pages 632-645, August.
    11. Knut Haase & Guy Desaulniers & Jacques Desrosiers, 2001. "Simultaneous Vehicle and Crew Scheduling in Urban Mass Transit Systems," Transportation Science, INFORMS, vol. 35(3), pages 286-303, August.
    12. 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.
    13. Marco E. Lübbecke & Jacques Desrosiers, 2005. "Selected Topics in Column Generation," Operations Research, INFORMS, vol. 53(6), pages 1007-1023, December.
    14. Gondzio, Jacek & González-Brevis, Pablo & Munari, Pedro, 2013. "New developments in the primal–dual column generation technique," European Journal of Operational Research, Elsevier, vol. 224(1), pages 41-51.
    15. Range, Troels Martin & Lusby, Richard Martin & Larsen, Jesper, 2014. "A column generation approach for solving the patient admission scheduling problem," European Journal of Operational Research, Elsevier, vol. 235(1), pages 252-264.
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    1. Adil Tahir & Guy Desaulniers & Issmail El Hallaoui, 2022. "Integral Column Generation for Set Partitioning Problems with Side Constraints," INFORMS Journal on Computing, INFORMS, vol. 34(4), pages 2313-2331, July.
    2. de Lima, Vinícius L. & Alves, Cláudio & Clautiaux, François & Iori, Manuel & Valério de Carvalho, José M., 2022. "Arc flow formulations based on dynamic programming: Theoretical foundations and applications," European Journal of Operational Research, Elsevier, vol. 296(1), pages 3-21.
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    4. Selvaprabu Nadarajah & Andre A. Cire, 2020. "Network-Based Approximate Linear Programming for Discrete Optimization," Operations Research, INFORMS, vol. 68(6), pages 1767-1786, November.
    5. Abdelouahab Zaghrouti & Issmail El Hallaoui & François Soumis, 2020. "Improving set partitioning problem solutions by zooming around an improving direction," Annals of Operations Research, Springer, vol. 284(2), pages 645-671, January.
    6. Guy Desaulniers & François Lessard & Mohammed Saddoune & François Soumis, 2020. "Dynamic Constraint Aggregation for Solving Very Large-scale Airline Crew Pairing Problems," SN Operations Research Forum, Springer, vol. 1(3), pages 1-23, September.
    7. Adil Tahir & Guy Desaulniers & Issmail El Hallaoui, 2019. "Integral column generation for the set partitioning problem," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 8(5), pages 713-744, December.

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