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Machine-Learning–Based Column Selection for Column Generation

Author

Listed:
  • Mouad Morabit

    (Department of Mathematics and Industrial Engineering, Polytechnique Montréal, Québec H3C 3A7, Canada; Research Group in Decision Analysis (GERAD), Montréal, Québec H3T 2A7, Canada; Canada Excellence Research Chair in Data Science for Real-Time Decision-Making, Polytechnique Montréal, Quebec H3C 3A7, Canada)

  • Guy Desaulniers

    (Department of Mathematics and Industrial Engineering, Polytechnique Montréal, Québec H3C 3A7, Canada; Research Group in Decision Analysis (GERAD), Montréal, Québec H3T 2A7, Canada)

  • Andrea Lodi

    (Department of Mathematics and Industrial Engineering, Polytechnique Montréal, Québec H3C 3A7, Canada; Research Group in Decision Analysis (GERAD), Montréal, Québec H3T 2A7, Canada; Canada Excellence Research Chair in Data Science for Real-Time Decision-Making, Polytechnique Montréal, Quebec H3C 3A7, Canada)

Abstract

Column generation (CG) is widely used for solving large-scale optimization problems. This article presents a new approach based on a machine learning (ML) technique to accelerate CG. This approach, called column selection , applies a learned model to select a subset of the variables (columns) generated at each iteration of CG. The goal is to reduce the computing time spent reoptimizing the restricted master problem at each iteration by selecting the most promising columns. The effectiveness of the approach is demonstrated on two problems: the vehicle and crew scheduling problem and the vehicle routing problem with time windows. The ML model was able to generalize to instances of different sizes, yielding a gain in computing time of up to 30%.

Suggested Citation

  • Mouad Morabit & Guy Desaulniers & Andrea Lodi, 2021. "Machine-Learning–Based Column Selection for Column Generation," Transportation Science, INFORMS, vol. 55(4), pages 815-831, July.
    • Handle: RePEc:inm:ortrsc:v:55:y:2021:i:4:p:815-831
    DOI: 10.1287/trsc.2021.1045
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