IDEAS home Printed from https://ideas.repec.org/a/inm/orijoc/v31y2019i2p285-301.html
   My bibliography  Save this article

Target Cuts from Relaxed Decision Diagrams

Author

Listed:
  • Christian Tjandraatmadja

    (Tepper School of Business, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213)

  • Willem-Jan van Hoeve

    (Tepper School of Business, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213)

Abstract

The most common approach to generate cuts in integer programming is to derive them from the linear programming relaxation. We study an alternative approach that extracts cuts from discrete relaxations known as relaxed decision diagrams. Through a connection between decision diagrams and polarity, the algorithm generates cuts that are facet defining for the convex hull of a decision diagram relaxation. As proof of concept, we provide computational evidence that this algorithm generates strong cuts for the maximum independent set problem and the minimum set covering problem.

Suggested Citation

  • Christian Tjandraatmadja & Willem-Jan van Hoeve, 2019. "Target Cuts from Relaxed Decision Diagrams," INFORMS Journal on Computing, INFORMS, vol. 31(2), pages 285-301, April.
  • Handle: RePEc:inm:orijoc:v:31:y:2019:i:2:p:285-301
    DOI: 10.1287/ijoc.2018.0830
    as

    Download full text from publisher

    File URL: https://doi.org/10.1287/ijoc.2018.0830
    Download Restriction: no

    File URL: https://libkey.io/10.1287/ijoc.2018.0830?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
    ---><---

    References listed on IDEAS

    as
    1. R. Kipp Martin & Ronald L. Rardin & Brian A. Campbell, 1990. "Polyhedral Characterization of Discrete Dynamic Programming," Operations Research, INFORMS, vol. 38(1), pages 127-138, February.
    2. Andre A. Cire & Willem-Jan van Hoeve, 2013. "Multivalued Decision Diagrams for Sequencing Problems," Operations Research, INFORMS, vol. 61(6), pages 1411-1428, December.
    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. Guopeng Song & Roel Leus, 2022. "Parallel Machine Scheduling Under Uncertainty: Models and Exact Algorithms," INFORMS Journal on Computing, INFORMS, vol. 34(6), pages 3059-3079, November.
    2. Margarita P. Castro & Andre A. Cire & J. Christopher Beck, 2022. "Decision Diagrams for Discrete Optimization: A Survey of Recent Advances," INFORMS Journal on Computing, INFORMS, vol. 34(4), pages 2271-2295, July.

    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. Amin Hosseininasab & Willem-Jan van Hoeve, 2021. "Exact Multiple Sequence Alignment by Synchronized Decision Diagrams," INFORMS Journal on Computing, INFORMS, vol. 33(2), pages 721-738, May.
    2. David Bergman & Andre A. Cire, 2018. "Discrete Nonlinear Optimization by State-Space Decompositions," Management Science, INFORMS, vol. 64(10), pages 4700-4720, October.
    3. David Bergman & Andre A. Cire & Willem-Jan van Hoeve & J. N. Hooker, 2016. "Discrete Optimization with Decision Diagrams," INFORMS Journal on Computing, INFORMS, vol. 28(1), pages 47-66, February.
    4. de Lima, Vinícius L. & Alves, Cláudio & Clautiaux, François & Iori, Manuel & Valério de Carvalho, José M., 2022. "Arc flow formulations based on dynamic programming: Theoretical foundations and applications," European Journal of Operational Research, Elsevier, vol. 296(1), pages 3-21.
    5. Daniel Kowalczyk & Roel Leus, 2018. "A Branch-and-Price Algorithm for Parallel Machine Scheduling Using ZDDs and Generic Branching," INFORMS Journal on Computing, INFORMS, vol. 30(4), pages 768-782, November.
    6. STEPHAN, Rüdiger, 2010. "An extension of disjunctive programming and its impact for compact tree formulations," LIDAM Discussion Papers CORE 2010045, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. Michele Conforti & Gérard Cornuéjols & Giacomo Zambelli, 2013. "Extended formulations in combinatorial optimization," Annals of Operations Research, Springer, vol. 204(1), pages 97-143, April.
    8. Johannes Maschler & Günther R. Raidl, 2021. "Multivalued decision diagrams for prize-collecting job sequencing with one common and multiple secondary resources," Annals of Operations Research, Springer, vol. 302(2), pages 507-531, July.
    9. David Bergman & Merve Bodur & Carlos Cardonha & Andre A. Cire, 2022. "Network Models for Multiobjective Discrete Optimization," INFORMS Journal on Computing, INFORMS, vol. 34(2), pages 990-1005, March.
    10. Christopher Hojny & Tristan Gally & Oliver Habeck & Hendrik Lüthen & Frederic Matter & Marc E. Pfetsch & Andreas Schmitt, 2020. "Knapsack polytopes: a survey," Annals of Operations Research, Springer, vol. 292(1), pages 469-517, September.
    11. Margarita P. Castro & Andre A. Cire & J. Christopher Beck, 2020. "An MDD-Based Lagrangian Approach to the Multicommodity Pickup-and-Delivery TSP," INFORMS Journal on Computing, INFORMS, vol. 32(2), pages 263-278, April.
    12. Steven Harrod, 2011. "Modeling Network Transition Constraints with Hypergraphs," Transportation Science, INFORMS, vol. 45(1), pages 81-97, February.
    13. Kinable, Joris & Cire, Andre A. & van Hoeve, Willem-Jan, 2017. "Hybrid optimization methods for time-dependent sequencing problems," European Journal of Operational Research, Elsevier, vol. 259(3), pages 887-897.
    14. de Weerdt, Mathijs & Baart, Robert & He, Lei, 2021. "Single-machine scheduling with release times, deadlines, setup times, and rejection," European Journal of Operational Research, Elsevier, vol. 291(2), pages 629-639.
    15. Arvind U. Raghunathan & David Bergman & John N. Hooker & Thiago Serra & Shingo Kobori, 2024. "Seamless Multimodal Transportation Scheduling," INFORMS Journal on Computing, INFORMS, vol. 36(2), pages 336-358, March.
    16. Khachai, Daniil & Sadykov, Ruslan & Battaia, Olga & Khachay, Michael, 2023. "Precedence constrained generalized traveling salesman problem: Polyhedral study, formulations, and branch-and-cut algorithm," European Journal of Operational Research, Elsevier, vol. 309(2), pages 488-505.
    17. François Clautiaux & Ruslan Sadykov & François Vanderbeck & Quentin Viaud, 2019. "Pattern-based diving heuristics for a two-dimensional guillotine cutting-stock problem with leftovers," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 7(3), pages 265-297, September.
    18. Bahman Naderi & Vahid Roshanaei & Mehmet A. Begen & Dionne M. Aleman & David R. Urbach, 2021. "Increased Surgical Capacity without Additional Resources: Generalized Operating Room Planning and Scheduling," Production and Operations Management, Production and Operations Management Society, vol. 30(8), pages 2608-2635, August.
    19. Salii, Yaroslav, 2019. "Revisiting dynamic programming for precedence-constrained traveling salesman problem and its time-dependent generalization," European Journal of Operational Research, Elsevier, vol. 272(1), pages 32-42.
    20. Yuri Faenza & Volker Kaibel, 2009. "Extended Formulations for Packing and Partitioning Orbitopes," Mathematics of Operations Research, INFORMS, vol. 34(3), pages 686-697, August.

    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:inm:orijoc:v:31:y:2019:i:2:p:285-301. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.