IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v210y2013i1p33-5510.1007-s10479-010-0806-y.html
   My bibliography  Save this article

An interior-point Benders based branch-and-cut algorithm for mixed integer programs

Author

Listed:
  • Joe Naoum-Sawaya
  • Samir Elhedhli

Abstract

We present an interior-point branch-and-cut algorithm for structured integer programs based on Benders decomposition and the analytic center cutting plane method (ACCPM). We show that the ACCPM based Benders cuts are both pareto-optimal and valid for any node of the branch-and-bound tree. The valid cuts are added to a pool of cuts that is used to warm-start the solution of the nodes after branching. The algorithm is tested on two classes of problems: the capacitated facility location problem and the multicommodity capacitated fixed charge network design problem. For the capacitated facility location problem, the proposed approach was on average 2.5 times faster than Benders-branch-and-cut and 11 times faster than classical Benders decomposition. For the multicommodity capacitated fixed charge network design problem, the proposed approach was 4 times faster than Benders-branch-and-cut while classical Benders decomposition failed to solve the majority of the tested instances. Copyright Springer Science+Business Media, LLC 2013

Suggested Citation

  • Joe Naoum-Sawaya & Samir Elhedhli, 2013. "An interior-point Benders based branch-and-cut algorithm for mixed integer programs," Annals of Operations Research, Springer, vol. 210(1), pages 33-55, November.
    • Handle: RePEc:spr:annopr:v:210:y:2013:i:1:p:33-55:10.1007/s10479-010-0806-y
    DOI: 10.1007/s10479-010-0806-y
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-010-0806-y
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-010-0806-y?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. Cote, Gilles & Laughton, Michael A., 1984. "Large-scale mixed integer programming: Benders-type heuristics," European Journal of Operational Research, Elsevier, vol. 16(3), pages 327-333, June.
    2. 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.
    3. Nesterov, Y., 1995. "Complexity estimates of some cutting plane methods based on the analytic barrier," LIDAM Reprints CORE 1167, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Dale McDaniel & Mike Devine, 1977. "A Modified Benders' Partitioning Algorithm for Mixed Integer Programming," Management Science, INFORMS, vol. 24(3), pages 312-319, November.
    5. A. M. Geoffrion & G. W. Graves, 1974. "Multicommodity Distribution System Design by Benders Decomposition," Management Science, INFORMS, vol. 20(5), pages 822-844, January.
    6. Cynthia Barnhart & Ellis L. Johnson & George L. Nemhauser & Martin W. P. Savelsbergh & Pamela H. Vance, 1998. "Branch-and-Price: Column Generation for Solving Huge Integer Programs," Operations Research, INFORMS, vol. 46(3), pages 316-329, June.
    7. 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.
    8. J. L. Goffin & A. Haurie & J. P. Vial, 1992. "Decomposition and Nondifferentiable Optimization with the Projective Algorithm," Management Science, INFORMS, vol. 38(2), pages 284-302, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ljubić, Ivana & Pozo, Miguel A. & Puerto, Justo & Torrejón, Alberto, 2024. "Benders decomposition for the discrete ordered median problem," European Journal of Operational Research, Elsevier, vol. 317(3), pages 858-874.
    2. Elisangela Martins de Sá & Ivan Contreras & Jean-François Cordeau & Ricardo Saraiva de Camargo & Gilberto de Miranda, 2015. "The Hub Line Location Problem," Transportation Science, INFORMS, vol. 49(3), pages 500-518, August.
    3. Joe Naoum-Sawaya & Christoph Buchheim, 2016. "Robust Critical Node Selection by Benders Decomposition," INFORMS Journal on Computing, INFORMS, vol. 28(1), pages 162-174, February.
    4. Kiho Seo & Seulgi Joung & Chungmok Lee & Sungsoo Park, 2022. "A Closest Benders Cut Selection Scheme for Accelerating the Benders Decomposition Algorithm," INFORMS Journal on Computing, INFORMS, vol. 34(5), pages 2804-2827, September.
    5. Matteo Fischetti & Ivana Ljubić & Markus Sinnl, 2017. "Redesigning Benders Decomposition for Large-Scale Facility Location," Management Science, INFORMS, vol. 63(7), pages 2146-2162, July.
    6. 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.
    7. Domínguez, Concepción & Labbé, Martine & Marín, Alfredo, 2021. "The rank pricing problem with ties," European Journal of Operational Research, Elsevier, vol. 294(2), pages 492-506.
    8. Su, Chengguo & Wang, Peilin & Yuan, Wenlin & Wu, Yang & Jiang, Feng & Wu, Zening & Yan, Denghua, 2022. "Short-term optimal scheduling of cascade hydropower plants with reverse-regulating effects," Renewable Energy, Elsevier, vol. 199(C), pages 395-406.
    9. Yossiri Adulyasak & Jean-François Cordeau & Raf Jans, 2015. "Benders Decomposition for Production Routing Under Demand Uncertainty," Operations Research, INFORMS, vol. 63(4), pages 851-867, August.
    10. 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.
    11. Fischetti, Matteo & Ljubić, Ivana & Sinnl, Markus, 2016. "Benders decomposition without separability: A computational study for capacitated facility location problems," European Journal of Operational Research, Elsevier, vol. 253(3), pages 557-569.
    12. 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.
    13. Zhang, Qihuan & Wang, Ziteng & Huang, Min & Yu, Yang & Fang, Shu-Cherng, 2022. "Heterogeneous multi-depot collaborative vehicle routing problem," Transportation Research Part B: Methodological, Elsevier, vol. 160(C), pages 1-20.
    14. 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.
    15. 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.
    16. Nathan Sudermann‐Merx & Steffen Rebennack & Christian Timpe, 2021. "Crossing Minimal Edge‐Constrained Layout Planning using Benders Decomposition," Production and Operations Management, Production and Operations Management Society, vol. 30(10), pages 3429-3447, October.
    17. Gendron, Bernard & Scutellà, Maria Grazia & Garroppo, Rosario G. & Nencioni, Gianfranco & Tavanti, Luca, 2016. "A branch-and-Benders-cut method for nonlinear power design in green wireless local area networks," European Journal of Operational Research, Elsevier, vol. 255(1), pages 151-162.
    18. 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.
    19. Elhedhli, Samir & Naoum-Sawaya, Joe, 2015. "Improved branching disjunctions for branch-and-bound: An analytic center approach," European Journal of Operational Research, Elsevier, vol. 247(1), pages 37-45.
    20. 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.

    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. 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.
    3. de Sá, Elisangela Martins & de Camargo, Ricardo Saraiva & de Miranda, Gilberto, 2013. "An improved Benders decomposition algorithm for the tree of hubs location problem," European Journal of Operational Research, Elsevier, vol. 226(2), pages 185-202.
    4. Lixin Tang & Wei Jiang & Georgios Saharidis, 2013. "An improved Benders decomposition algorithm for the logistics facility location problem with capacity expansions," Annals of Operations Research, Springer, vol. 210(1), pages 165-190, November.
    5. 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.
    6. Hanif Sherali & Brian Lunday, 2013. "On generating maximal nondominated Benders cuts," Annals of Operations Research, Springer, vol. 210(1), pages 57-72, November.
    7. Elisangela Martins de Sá & Ivan Contreras & Jean-François Cordeau & Ricardo Saraiva de Camargo & Gilberto de Miranda, 2015. "The Hub Line Location Problem," Transportation Science, INFORMS, vol. 49(3), pages 500-518, August.
    8. 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.
    9. 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.
    10. 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.
    11. Azad, Nader & Hassini, Elkafi, 2019. "Recovery strategies from major supply disruptions in single and multiple sourcing networks," European Journal of Operational Research, Elsevier, vol. 275(2), pages 481-501.
    12. 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.
    13. Qipeng Zheng & Jianhui Wang & Panos Pardalos & Yongpei Guan, 2013. "A decomposition approach to the two-stage stochastic unit commitment problem," Annals of Operations Research, Springer, vol. 210(1), pages 387-410, November.
    14. Kuthambalayan, Thyagaraj S. & Mehta, Peeyush & Shanker, Kripa, 2014. "Integrating operations and marketing decisions using delayed differentiation of products and guaranteed delivery time under stochastic demand," European Journal of Operational Research, Elsevier, vol. 237(2), pages 617-627.
    15. 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.
    16. Chao Li & Muhong Zhang & Kory Hedman, 2021. "Extreme Ray Feasibility Cuts for Unit Commitment with Uncertainty," INFORMS Journal on Computing, INFORMS, vol. 33(3), pages 1037-1055, July.
    17. 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.
    18. Brech, Claus-Henning & Ernst, Andreas & Kolisch, Rainer, 2019. "Scheduling medical residents’ training at university hospitals," European Journal of Operational Research, Elsevier, vol. 274(1), pages 253-266.
    19. 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.
    20. 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.

    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:annopr:v:210:y:2013:i:1:p:33-55:10.1007/s10479-010-0806-y. 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.