IDEAS home Printed from https://ideas.repec.org/a/spr/joheur/v27y2021i4d10.1007_s10732-021-09467-z.html
   My bibliography  Save this article

Enhancing large neighbourhood search heuristics for Benders’ decomposition

Author

Listed:
  • Stephen J. Maher

    (Lancaster University
    University of Exeter)

Abstract

A general enhancement of the Benders’ decomposition (BD) algorithm can be achieved through the improved use of large neighbourhood search heuristics within mixed-integer programming solvers. While mixed-integer programming solvers are endowed with an array of large neighbourhood search heuristics, few, if any, have been designed for BD. Further, typically the use of large neighbourhood search heuristics is limited to finding solutions to the BD master problem. Given the lack of general frameworks for BD, only ad hoc approaches have been developed to enhance the ability of BD to find high quality primal feasible solutions through the use of large neighbourhood search heuristics. The general BD framework of SCIP has been extended with a trust region based heuristic and a general enhancement for large neighbourhood search heuristics. The general enhancement employs BD to solve the auxiliary problems of all large neighbourhood search heuristics to improve the quality of the identified solutions. The computational results demonstrate that the trust region heuristic and a general large neighbourhood search enhancement technique accelerate the improvement in the primal bound when applying BD.

Suggested Citation

  • Stephen J. Maher, 2021. "Enhancing large neighbourhood search heuristics for Benders’ decomposition," Journal of Heuristics, Springer, vol. 27(4), pages 615-648, August.
    • Handle: RePEc:spr:joheur:v:27:y:2021:i:4:d:10.1007_s10732-021-09467-z
    DOI: 10.1007/s10732-021-09467-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10732-021-09467-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10732-021-09467-z?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Jean-François Cordeau & Goran Stojković & François Soumis & Jacques Desrosiers, 2001. "Benders Decomposition for Simultaneous Aircraft Routing and Crew Scheduling," Transportation Science, INFORMS, vol. 35(4), pages 375-388, November.
    2. Raidl, Günther R., 2015. "Decomposition based hybrid metaheuristics," European Journal of Operational Research, Elsevier, vol. 244(1), pages 66-76.
    3. Maher, Stephen J. & Murray, John M., 2016. "The unrooted set covering connected subgraph problem differentiating between HIV envelope sequences," European Journal of Operational Research, Elsevier, vol. 248(2), pages 668-680.
    4. Edward Rothberg, 2007. "An Evolutionary Algorithm for Polishing Mixed Integer Programming Solutions," INFORMS Journal on Computing, INFORMS, vol. 19(4), pages 534-541, November.
    5. T. L. Magnanti & R. T. Wong, 1981. "Accelerating Benders Decomposition: Algorithmic Enhancement and Model Selection Criteria," Operations Research, INFORMS, vol. 29(3), pages 464-484, June.
    6. Merve Bodur & Sanjeeb Dash & Oktay Günlük & James Luedtke, 2017. "Strengthened Benders Cuts for Stochastic Integer Programs with Continuous Recourse," INFORMS Journal on Computing, INFORMS, vol. 29(1), pages 77-91, February.
    7. George B. Dantzig & Philip Wolfe, 1960. "Decomposition Principle for Linear Programs," Operations Research, INFORMS, vol. 8(1), pages 101-111, February.
    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. 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.
    10. Canto, Salvador Perez, 2008. "Application of Benders' decomposition to power plant preventive maintenance scheduling," European Journal of Operational Research, Elsevier, vol. 184(2), pages 759-777, January.
    11. Maher, Stephen J., 2021. "Implementing the branch-and-cut approach for a general purpose Benders’ decomposition framework," European Journal of Operational Research, Elsevier, vol. 290(2), pages 479-498.
    12. Santoso, Tjendera & Ahmed, Shabbir & Goetschalckx, Marc & Shapiro, Alexander, 2005. "A stochastic programming approach for supply chain network design under uncertainty," European Journal of Operational Research, Elsevier, vol. 167(1), pages 96-115, November.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. Maher, Stephen J., 2021. "Implementing the branch-and-cut approach for a general purpose Benders’ decomposition framework," European Journal of Operational Research, Elsevier, vol. 290(2), pages 479-498.
    4. 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.
    5. Rodríguez, Jesús A. & Anjos, Miguel F. & Côté, Pascal & Desaulniers, Guy, 2021. "Accelerating Benders decomposition for short-term hydropower maintenance scheduling," European Journal of Operational Research, Elsevier, vol. 289(1), pages 240-253.
    6. M. Jenabi & S. M. T. Fatemi Ghomi & S. A. Torabi & Moeen Sammak Jalali, 2022. "An accelerated Benders decomposition algorithm for stochastic power system expansion planning using sample average approximation," OPSEARCH, Springer;Operational Research Society of India, vol. 59(4), pages 1304-1336, December.
    7. Lim, Gino J. & Bard, Jonathan F., 2016. "Benders decomposition and an IP-based heuristic for selecting IMRT treatment beam anglesAuthor-Name: Lin, Sifeng," European Journal of Operational Research, Elsevier, vol. 251(3), pages 715-726.
    8. Gary Froyland & Stephen J. Maher & Cheng-Lung Wu, 2014. "The Recoverable Robust Tail Assignment Problem," Transportation Science, INFORMS, vol. 48(3), pages 351-372, August.
    9. 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.
    10. Wakui, Tetsuya & Hashiguchi, Moe & Yokoyama, Ryohei, 2021. "Structural design of distributed energy networks by a hierarchical combination of variable- and constraint-based decomposition methods," Energy, Elsevier, vol. 224(C).
    11. Jeihoonian, Mohammad & Kazemi Zanjani, Masoumeh & Gendreau, Michel, 2016. "Accelerating Benders decomposition for closed-loop supply chain network design: Case of used durable products with different quality levels," European Journal of Operational Research, Elsevier, vol. 251(3), pages 830-845.
    12. Vedat Bayram & Hande Yaman, 2018. "Shelter Location and Evacuation Route Assignment Under Uncertainty: A Benders Decomposition Approach," Transportation Science, INFORMS, vol. 52(2), pages 416-436, March.
    13. Belieres, Simon & Hewitt, Mike & Jozefowiez, Nicolas & Semet, Frédéric, 2022. "Meta partial benders decomposition for the logistics service network design problem," European Journal of Operational Research, Elsevier, vol. 300(2), pages 473-489.
    14. Placido dos Santos, Felipe Silva & Oliveira, Fabricio, 2019. "An enhanced L-Shaped method for optimizing periodic-review inventory control problems modeled via two-stage stochastic programming," European Journal of Operational Research, Elsevier, vol. 275(2), pages 677-693.
    15. Vahab Vahdat & Mohammad Ali Vahdatzad, 2017. "Accelerated Benders’ Decomposition for Integrated Forward/Reverse Logistics Network Design under Uncertainty," Logistics, MDPI, vol. 1(2), pages 1-21, December.
    16. Hanif Sherali & Ki-Hwan Bae & Mohamed Haouari, 2013. "A benders decomposition approach for an integrated airline schedule design and fleet assignment problem with flight retiming, schedule balance, and demand recapture," Annals of Operations Research, Springer, vol. 210(1), pages 213-244, November.
    17. Hanif Sherali & Brian Lunday, 2013. "On generating maximal nondominated Benders cuts," Annals of Operations Research, Springer, vol. 210(1), pages 57-72, November.
    18. Anne Mercier, 2008. "A Theoretical Comparison of Feasibility Cuts for the Integrated Aircraft-Routing and Crew-Pairing Problem," Transportation Science, INFORMS, vol. 42(1), pages 87-104, February.
    19. Keyvanshokooh, Esmaeil & Ryan, Sarah M. & Kabir, Elnaz, 2016. "Hybrid robust and stochastic optimization for closed-loop supply chain network design using accelerated Benders decomposition," European Journal of Operational Research, Elsevier, vol. 249(1), pages 76-92.
    20. Shengzhi Shao & Hanif D. Sherali & Mohamed Haouari, 2017. "A Novel Model and Decomposition Approach for the Integrated Airline Fleet Assignment, Aircraft Routing, and Crew Pairing Problem," Transportation Science, INFORMS, vol. 51(1), pages 233-249, February.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joheur:v:27:y:2021:i:4:d:10.1007_s10732-021-09467-z. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.