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Speed-up Benders decomposition using maximum density cut (MDC) generation

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  • Georgios Saharidis
  • Marianthi Ierapetritou

Abstract

The classical implementation of Benders decomposition in some cases results in low density Benders cuts. Covering Cut Bundle (CCB) generation addresses this issue with a novel way generating a bundle of cuts which could cover more decision variables of the Benders master problem than the classical Benders cut. Our motivation to improve further CCB generation led to a new cut generation strategy. This strategy is referred to as the Maximum Density Cut (MDC) generation strategy. MDC is based on the observation that in some cases CCB generation is computational expensive to cover all decision variables of the master problem than to cover part of them. Thus MDC strategy addresses this issue by generating the cut that involves the rest of the decision variables of the master problem which are not covered in the Benders cut and/or in the CCB. MDC strategy can be applied as a complimentary step to the CCB generation as well as a standalone strategy. In this work the approach is applied to two case studies: the scheduling of crude oil and the scheduling of multi-product, multi-purpose batch plants. In both cases, MDC strategy significant decreases the number of iterations of the Benders decomposition algorithm, leading to improved CPU solution times. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • Georgios Saharidis & Marianthi Ierapetritou, 2013. "Speed-up Benders decomposition using maximum density cut (MDC) generation," Annals of Operations Research, Springer, vol. 210(1), pages 101-123, November.
    • Handle: RePEc:spr:annopr:v:210:y:2013:i:1:p:101-123:10.1007/s10479-012-1237-8
    DOI: 10.1007/s10479-012-1237-8
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    Cited by:

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    2. Hooshmand, F. & Mirarabrazi, F. & MirHassani, S.A., 2020. "Efficient Benders decomposition for distance-based critical node detection problem," Omega, Elsevier, vol. 93(C).
    3. Fausto Errico & Teodor Gabriel Crainic & Federico Malucelli & Maddalena Nonato, 2017. "A Benders Decomposition Approach for the Symmetric TSP with Generalized Latency Arising in the Design of Semiflexible Transit Systems," Transportation Science, INFORMS, vol. 51(2), pages 706-722, May.
    4. M. Jenabi & S. Fatemi Ghomi & S. Torabi & S. Hosseinian, 2015. "Acceleration strategies of Benders decomposition for the security constraints power system expansion planning," Annals of Operations Research, Springer, vol. 235(1), pages 337-369, December.
    5. 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.
    6. Tolga Bektaş & Alper Hamzadayı & Rubén Ruiz, 2020. "Benders decomposition for the mixed no-idle permutation flowshop scheduling problem," Journal of Scheduling, Springer, vol. 23(4), pages 513-523, August.
    7. Jose L. Andrade-Pineda & David Canca & Pedro L. Gonzalez-R, 2017. "On modelling non-linear quantity discounts in a supplier selection problem by mixed linear integer optimization," Annals of Operations Research, Springer, vol. 258(2), pages 301-346, November.
    8. Emilia Grass & Kathrin Fischer & Antonia Rams, 2020. "An accelerated L-shaped method for solving two-stage stochastic programs in disaster management," Annals of Operations Research, Springer, vol. 284(2), pages 557-582, January.
    9. N. Beheshti Asl & S. A. MirHassani, 2019. "Accelerating benders decomposition: multiple cuts via multiple solutions," Journal of Combinatorial Optimization, Springer, vol. 37(3), pages 806-826, April.

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