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An integrated learning and progressive hedging matheuristic for stochastic network design problem

Author

Listed:
  • Fatemeh Sarayloo

    (University of Illinois at Chicago)

  • Teodor Gabriel Crainic

    (École des sciences de la gestion, Université du Québec à Montréal
    Centre Interuniversitaire de Recherche sur les, Réseaux d’Entreprise, la Logistique et le Transport (CIRRELT))

  • Walter Rei

    (École des sciences de la gestion, Université du Québec à Montréal
    Centre Interuniversitaire de Recherche sur les, Réseaux d’Entreprise, la Logistique et le Transport (CIRRELT))

Abstract

We address the Multicommodity Capacitated Fixed-charge Network Design problem with uncertain demands, which we formulate as a two-stage stochastic program. We rely on the progressive hedging (PH) algorithm of Rockafellar and Wets where the subproblems are defined using scenario groups. To address the problem, we propose an efficient matheuristic approach which we refer to as the Integrated Learning and Progressive Hedging. The proposed method takes advantage of a specialized learning-based matheuristic that is able to quickly produce high-quality solutions to multi-scenario subproblems. Furthermore, we propose a novel reference point definition, at each aggregation step of the PH algorithm, which leverages subproblem information regarding promising design variables. Extensive computational experiments illustrate that the proposed approach should be the method of choice when high-quality solutions to large instances of stochastic network problems need to be found quickly.

Suggested Citation

  • Fatemeh Sarayloo & Teodor Gabriel Crainic & Walter Rei, 2023. "An integrated learning and progressive hedging matheuristic for stochastic network design problem," Journal of Heuristics, Springer, vol. 29(4), pages 409-434, December.
    • Handle: RePEc:spr:joheur:v:29:y:2023:i:4:d:10.1007_s10732-023-09515-w
    DOI: 10.1007/s10732-023-09515-w
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    References listed on IDEAS

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    1. R. T. Rockafellar & Roger J.-B. Wets, 1991. "Scenarios and Policy Aggregation in Optimization Under Uncertainty," Mathematics of Operations Research, INFORMS, vol. 16(1), pages 119-147, February.
    2. Fatemeh Sarayloo & Teodor Gabriel Crainic & Walter Rei, 2021. "A Learning-Based Matheuristic for Stochastic Multicommodity Network Design," INFORMS Journal on Computing, INFORMS, vol. 33(2), pages 643-656, May.
    3. Julia L. Higle & Stein W. Wallace, 2003. "Sensitivity Analysis and Uncertainty in Linear Programming," Interfaces, INFORMS, vol. 33(4), pages 53-60, August.
    4. Ilfat Ghamlouche & Teodor Crainic & Michel Gendreau, 2004. "Path Relinking, Cycle-Based Neighbourhoods and Capacitated Multicommodity Network Design," Annals of Operations Research, Springer, vol. 131(1), pages 109-133, October.
    5. T. L. Magnanti & R. T. Wong, 1984. "Network Design and Transportation Planning: Models and Algorithms," Transportation Science, INFORMS, vol. 18(1), pages 1-55, February.
    6. Teodor Gabriel Crainic & Mike Hewitt & Francesca Maggioni & Walter Rei, 2021. "Partial Benders Decomposition: General Methodology and Application to Stochastic Network Design," Transportation Science, INFORMS, vol. 55(2), pages 414-435, March.
    7. Crainic, Teodor Gabriel, 2000. "Service network design in freight transportation," European Journal of Operational Research, Elsevier, vol. 122(2), pages 272-288, April.
    8. Natashia Boland & Matteo Fischetti & Michele Monaci & Martin Savelsbergh, 2016. "Proximity Benders: a decomposition heuristic for stochastic programs," Journal of Heuristics, Springer, vol. 22(2), pages 181-198, April.
    9. Jitka Dupačová & Giorgio Consigli & Stein Wallace, 2000. "Scenarios for Multistage Stochastic Programs," Annals of Operations Research, Springer, vol. 100(1), pages 25-53, December.
    10. Mike Hewitt & George L. Nemhauser & Martin W. P. Savelsbergh, 2010. "Combining Exact and Heuristic Approaches for the Capacitated Fixed-Charge Network Flow Problem," INFORMS Journal on Computing, INFORMS, vol. 22(2), pages 314-325, May.
    11. Rahmaniani, Ragheb & Crainic, Teodor Gabriel & Gendreau, Michel & Rei, Walter, 2017. "The Benders decomposition algorithm: A literature review," European Journal of Operational Research, Elsevier, vol. 259(3), pages 801-817.
    12. Fatemeh Sarayloo & Teodor Gabriel Crainic & Walter Rei, 2021. "A reduced cost-based restriction and refinement matheuristic for stochastic network design problem," Journal of Heuristics, Springer, vol. 27(3), pages 325-351, June.
    13. Ilfat Ghamlouche & Teodor Gabriel Crainic & Michel Gendreau, 2003. "Cycle-Based Neighbourhoods for Fixed-Charge Capacitated Multicommodity Network Design," Operations Research, INFORMS, vol. 51(4), pages 655-667, August.
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