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Proximity Benders: a decomposition heuristic for stochastic programs

Author

Listed:
  • Natashia Boland

    (Georgia Institute of Technology)

  • Matteo Fischetti

    (University of Padova)

  • Michele Monaci

    (University of Padova)

  • Martin Savelsbergh

    (Georgia Institute of Technology)

Abstract

In this paper we present a heuristic approach to two-stage mixed-integer linear stochastic programming models with continuous second stage variables. A common solution approach for these models is Benders decomposition, in which a sequence of (possibly infeasible) solutions is generated, until an optimal solution is eventually found and the method terminates. As convergence may require a large amount of computing time for hard instances, the method may be unsatisfactory from a heuristic point of view. Proximity search is a recently-proposed heuristic paradigm in which the problem at hand is modified and iteratively solved with the aim of producing a sequence of improving feasible solutions. As such, proximity search and Benders decomposition naturally complement each other, in particular when the emphasis is on seeking high-quality, but not necessarily optimal, solutions. In this paper, we investigate the use of proximity search as a tactical tool to drive Benders decomposition, and computationally evaluate its performance as a heuristic on instances of different stochastic programming problems.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joheur:v:22:y:2016:i:2:d:10.1007_s10732-015-9306-1
    DOI: 10.1007/s10732-015-9306-1
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    References listed on IDEAS

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    1. Walter Rei & Jean-François Cordeau & Michel Gendreau & Patrick Soriano, 2009. "Accelerating Benders Decomposition by Local Branching," INFORMS Journal on Computing, INFORMS, vol. 21(2), pages 333-345, May.
    2. Tobias Achterberg & Timo Berthold & Gregor Hendel, 2012. "Rounding and Propagation Heuristics for Mixed Integer Programming," Operations Research Proceedings, in: Diethard Klatte & Hans-Jakob Lüthi & Karl Schmedders (ed.), Operations Research Proceedings 2011, edition 127, pages 71-76, Springer.
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    Citations

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    Cited by:

    1. Stephen J. Maher, 2021. "Enhancing large neighbourhood search heuristics for Benders’ decomposition," Journal of Heuristics, Springer, vol. 27(4), pages 615-648, August.
    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. 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.
    4. Vahdani, Behnam & Mohammadi, Mehrdad & Thevenin, Simon & Gendreau, Michel & Dolgui, Alexandre & Meyer, Patrick, 2023. "Fair-split distribution of multi-dose vaccines with prioritized age groups and dynamic demand: The case study of COVID-19," European Journal of Operational Research, Elsevier, vol. 310(3), pages 1249-1272.
    5. Daniel Baena & Jordi Castro & Antonio Frangioni, 2020. "Stabilized Benders Methods for Large-Scale Combinatorial Optimization, with Application to Data Privacy," Management Science, INFORMS, vol. 66(7), pages 3051-3068, July.
    6. Filipe Rodrigues & Agostinho Agra & Lars Magnus Hvattum & Cristina Requejo, 2021. "Weighted proximity search," Journal of Heuristics, Springer, vol. 27(3), pages 459-496, June.
    7. Ragheb Rahmaniani & Shabbir Ahmed & Teodor Gabriel Crainic & Michel Gendreau & Walter Rei, 2020. "The Benders Dual Decomposition Method," Operations Research, INFORMS, vol. 68(3), pages 878-895, May.

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