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Logic-Based Benders Decomposition for Large-Scale Optimization

In: Large Scale Optimization in Supply Chains and Smart Manufacturing

Author

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  • John N. Hooker

    (Carnegie Mellon University)

Abstract

Logic-based Benders decomposition (LBBD) is a substantial generalization of classical Benders decomposition that, in principle, allows the subproblem to be any optimization problem rather than specifically a linear or nonlinear programming problem. It is amenable to a wide variety of large-scale problems that decouple or otherwise simplify when certain decision variables are fixed. This chapter presents the basic theory of LBBD and explains how classical Benders decomposition is a special case. It also describes branch and check, a variant of LBBD that solves the master problem only once. It illustrates in detail how Benders cuts and subproblem relaxations can be developed for some planning and scheduling problems. It then describes the role of LBBD in three large-scale case studies. The chapter concludes with an extensive survey of the LBBD literature, organized by problem domain, to allow the reader to explore how Benders cuts have been developed for a wide range of applications.

Suggested Citation

  • John N. Hooker, 2019. "Logic-Based Benders Decomposition for Large-Scale Optimization," Springer Optimization and Its Applications, in: Jesús M. Velásquez-Bermúdez & Marzieh Khakifirooz & Mahdi Fathi (ed.), Large Scale Optimization in Supply Chains and Smart Manufacturing, pages 1-26, Springer.
    • Handle: RePEc:spr:spochp:978-3-030-22788-3_1
    DOI: 10.1007/978-3-030-22788-3_1
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    Citations

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    Cited by:

    1. Liu, Bingqian & Bissuel, Côme & Courtot, François & Gicquel, Céline & Quadri, Dominique, 2024. "A generalized Benders decomposition approach for the optimal design of a local multi-energy system," European Journal of Operational Research, Elsevier, vol. 318(1), pages 43-54.
    2. Aigerim Saken & Emil Karlsson & Stephen J. Maher & Elina Rönnberg, 2023. "Computational Evaluation of Cut-Strengthening Techniques in Logic-Based Benders’ Decomposition," SN Operations Research Forum, Springer, vol. 4(3), pages 1-53, September.
    3. Defeng Sun & Lixin Tang & Roberto Baldacci & Zihan Chen, 2024. "A Decomposition Method for the Group-Based Quay Crane Scheduling Problem," INFORMS Journal on Computing, INFORMS, vol. 36(2), pages 543-570, March.
    4. Özgün Elçi & John Hooker, 2022. "Stochastic Planning and Scheduling with Logic-Based Benders Decomposition," INFORMS Journal on Computing, INFORMS, vol. 34(5), pages 2428-2442, September.
    5. Forbes, M.A. & Harris, M.G. & Jansen, H.M. & van der Schoot, F.A. & Taimre, T., 2024. "Combining optimisation and simulation using logic-based Benders decomposition," European Journal of Operational Research, Elsevier, vol. 312(3), pages 840-854.
    6. Nascimento, Paulo Jorge & Silva, Cristóvão & Antunes, Carlos Henggeler & Moniz, Samuel, 2024. "Optimal decomposition approach for solving large nesting and scheduling problems of additive manufacturing systems," European Journal of Operational Research, Elsevier, vol. 317(1), pages 92-110.
    7. Guo, Penghui & Zhu, Jianjun, 2023. "Capacity reservation for humanitarian relief: A logic-based Benders decomposition method with subgradient cut," European Journal of Operational Research, Elsevier, vol. 311(3), pages 942-970.
    8. Yantong Li & Jean-François Côté & Leandro Callegari-Coelho & Peng Wu, 2022. "Novel Formulations and Logic-Based Benders Decomposition for the Integrated Parallel Machine Scheduling and Location Problem," INFORMS Journal on Computing, INFORMS, vol. 34(2), pages 1048-1069, March.
    9. Ben Mohamed, Imen & Klibi, Walid & Sadykov, Ruslan & Şen, Halil & Vanderbeck, François, 2023. "The two-echelon stochastic multi-period capacitated location-routing problem," European Journal of Operational Research, Elsevier, vol. 306(2), pages 645-667.
    10. Caglar Gencosman, Burcu & Begen, Mehmet A., 2022. "Exact optimization and decomposition approaches for shelf space allocation," European Journal of Operational Research, Elsevier, vol. 299(2), pages 432-447.

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