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Constraint Aggregation in Column Generation Models for Resource-Constrained Covering Problems

Author

Listed:
  • Daniel Porumbel

    (CEDRIC, CNAM, Conservatoire National des Arts et Métiers, Paris, 75003 France)

  • François Clautiaux

    (Université de Bordeaux, 351, cours de la Libération, 33 405 TALENCE, France)

Abstract

We propose an aggregation method to reduce the size of column generation (CG) models for covering problems in which the feasible subsets depend on a resource constraint. The aggregation relies on a correlation between the resource consumption of the elements and the corresponding optimal dual values. The resulting aggregated dual model is a restriction of the original one, and it can be rapidly optimized to obtain a feasible dual solution. A primal bound can also be obtained by restricting the set of columns to those saturated by the dual feasible solution obtained by aggregation. The convergence is realized by iterative disaggregation until the gap is closed by the bounds. Computational results show the usefulness of our method for different cutting-stock problems. An important advantage is the fact that it can produce high-quality dual bounds much faster than the traditional Lagrangian bound used in stabilized column generation.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:orijoc:v:29:y:2017:i:1:p:170-184
    DOI: 10.1287/ijoc.2016.0718
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    References listed on IDEAS

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    Cited by:

    1. Daniel Porumbel, 2022. "Projective Cutting-Planes for Robust Linear Programming and Cutting Stock Problems," INFORMS Journal on Computing, INFORMS, vol. 34(5), pages 2736-2753, September.
    2. Renaud Chicoisne, 2023. "Computational aspects of column generation for nonlinear and conic optimization: classical and linearized schemes," Computational Optimization and Applications, Springer, vol. 84(3), pages 789-831, April.

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