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Integral column generation for the set partitioning problem

Author

Listed:
  • Adil Tahir

    (GERAD and Department of Mathematics and Industrial Engineering, Polytechnique Montréal)

  • Guy Desaulniers

    (GERAD and Department of Mathematics and Industrial Engineering, Polytechnique Montréal)

  • Issmail El Hallaoui

    (GERAD and Department of Mathematics and Industrial Engineering, Polytechnique Montréal)

Abstract

The integral simplex using decomposition (ISUD) algorithm was recently developed to solve efficiently set partitioning problems containing a number of variables that can all be enumerated a priori. This primal algorithm generates a sequence of integer solutions with decreasing costs, leading to an optimal or near-optimal solution depending on the stopping criterion used. In this paper, we develop an integral column generation (ICG) heuristic that combines ISUD and column generation to solve set partitioning problems with a very large number of variables. Computational experiments on instances of the public transit vehicle and crew scheduling problem and of the airline crew pairing problem involving up to 2000 constraints show that ICG clearly outperforms two popular column generation heuristics (the restricted master heuristic and the diving heuristic). ICG can yield optimal or near-optimal solutions in less than 1 hour of computational time, generating up to 300 integer solutions during the solution process.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:eurjtl:v:8:y:2019:i:5:d:10.1007_s13676-019-00145-6
    DOI: 10.1007/s13676-019-00145-6
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    Cited by:

    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.
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