IDEAS home Printed from https://ideas.repec.org/a/inm/orijoc/v29y2017i1p185-195.html
   My bibliography  Save this article

A Machine Learning-Based Approximation of Strong Branching

Author

Listed:
  • Alejandro Marcos Alvarez

    (Department of Electrical Engineering and Computer Science, Université de Liège, Sart-Tilman B28, Liège, Belgium)

  • Quentin Louveaux

    (Department of Electrical Engineering and Computer Science, Université de Liège, Sart-Tilman B28, Liège, Belgium)

  • Louis Wehenkel

    (Department of Electrical Engineering and Computer Science, Université de Liège, Sart-Tilman B28, Liège, Belgium)

Abstract

We present in this paper a new generic approach to variable branching in branch and bound for mixed-integer linear problems. Our approach consists in imitating the decisions taken by a good branching strategy, namely strong branching, with a fast approximation. This approximated function is created by a machine learning technique from a set of observed branching decisions taken by strong branching. The philosophy of the approach is similar to reliability branching. However, our approach can catch more complex aspects of observed previous branchings to take a branching decision. The experiments performed on randomly generated and MIPLIB problems show promising results.

Suggested Citation

  • Alejandro Marcos Alvarez & Quentin Louveaux & Louis Wehenkel, 2017. "A Machine Learning-Based Approximation of Strong Branching," INFORMS Journal on Computing, INFORMS, vol. 29(1), pages 185-195, February.
  • Handle: RePEc:inm:orijoc:v:29:y:2017:i:1:p:185-195
    DOI: 10.1287/ijoc.2016.0723
    as

    Download full text from publisher

    File URL: https://doi.org/10.1287/ijoc.2016.0723
    Download Restriction: no

    File URL: https://libkey.io/10.1287/ijoc.2016.0723?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. Norman J. Driebeek, 1966. "An Algorithm for the Solution of Mixed Integer Programming Problems," Management Science, INFORMS, vol. 12(7), pages 576-587, March.
    2. Liberto, Giovanni Di & Kadioglu, Serdar & Leo, Kevin & Malitsky, Yuri, 2016. "DASH: Dynamic Approach for Switching Heuristics," European Journal of Operational Research, Elsevier, vol. 248(3), pages 943-953.
    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. Yang, Yu & Boland, Natashia & Dilkina, Bistra & Savelsbergh, Martin, 2022. "Learning generalized strong branching for set covering, set packing, and 0–1 knapsack problems," European Journal of Operational Research, Elsevier, vol. 301(3), pages 828-840.
    2. Nikolaus Furian & Michael O’Sullivan & Cameron Walker & Eranda Çela, 2021. "A machine learning-based branch and price algorithm for a sampled vehicle routing problem," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 43(3), pages 693-732, September.
    3. Yu Yang & Natashia Boland & Martin Savelsbergh, 2021. "Multivariable Branching: A 0-1 Knapsack Problem Case Study," INFORMS Journal on Computing, INFORMS, vol. 33(4), pages 1354-1367, October.
    4. Bissan Ghaddar & Ignacio Gómez-Casares & Julio González-Díaz & Brais González-Rodríguez & Beatriz Pateiro-López & Sofía Rodríguez-Ballesteros, 2023. "Learning for Spatial Branching: An Algorithm Selection Approach," INFORMS Journal on Computing, INFORMS, vol. 35(5), pages 1024-1043, September.
    5. Bengio, Yoshua & Lodi, Andrea & Prouvost, Antoine, 2021. "Machine learning for combinatorial optimization: A methodological tour d’horizon," European Journal of Operational Research, Elsevier, vol. 290(2), pages 405-421.
    6. Andrea Lodi & Giulia Zarpellon, 2017. "On learning and branching: a survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(2), pages 207-236, July.
    7. Atefeh Rajabalizadeh & Danial Davarnia, 2024. "Solving a Class of Cut-Generating Linear Programs via Machine Learning," INFORMS Journal on Computing, INFORMS, vol. 36(3), pages 708-722, May.
    8. Dimitris Bertsimas & Cheol Woo Kim, 2023. "A Prescriptive Machine Learning Approach to Mixed-Integer Convex Optimization," INFORMS Journal on Computing, INFORMS, vol. 35(6), pages 1225-1241, November.
    9. Xiangyi Zhang & Lu Chen & Michel Gendreau & André Langevin, 2022. "Learning-Based Branch-and-Price Algorithms for the Vehicle Routing Problem with Time Windows and Two-Dimensional Loading Constraints," INFORMS Journal on Computing, INFORMS, vol. 34(3), pages 1419-1436, May.
    10. Gregor Hendel & Daniel Anderson & Pierre Le Bodic & Marc E. Pfetsch, 2022. "Estimating the Size of Branch-and-Bound Trees," INFORMS Journal on Computing, INFORMS, vol. 34(2), pages 934-952, March.
    11. Álinson S. Xavier & Feng Qiu & Shabbir Ahmed, 2021. "Learning to Solve Large-Scale Security-Constrained Unit Commitment Problems," INFORMS Journal on Computing, INFORMS, vol. 33(2), pages 739-756, May.
    12. Francisco Jara-Moroni & John E. Mitchell & Jong-Shi Pang & Andreas Wächter, 2020. "An enhanced logical benders approach for linear programs with complementarity constraints," Journal of Global Optimization, Springer, vol. 77(4), pages 687-714, August.
    13. Sebastian Kraul & Markus Seizinger & Jens O. Brunner, 2023. "Machine Learning–Supported Prediction of Dual Variables for the Cutting Stock Problem with an Application in Stabilized Column Generation," INFORMS Journal on Computing, INFORMS, vol. 35(3), pages 692-709, May.
    14. Kandula, Shanthan & Krishnamoorthy, Srikumar & Roy, Debjit, 2021. "Learning to Play the Box-Sizing Game: A Machine Learning Approach for Solving the E-commerce Packaging Problem," IIMA Working Papers WP 2021-11-02, Indian Institute of Management Ahmedabad, Research and Publication Department.
    15. Gerdus Benadè & John N. Hooker, 2020. "Optimization Bounds from the Branching Dual," INFORMS Journal on Computing, INFORMS, vol. 32(1), pages 3-15, January.
    16. Dimitris Bertsimas & Bartolomeo Stellato, 2022. "Online Mixed-Integer Optimization in Milliseconds," INFORMS Journal on Computing, INFORMS, vol. 34(4), pages 2229-2248, July.
    17. Sidhant Misra & Line Roald & Yeesian Ng, 2022. "Learning for Constrained Optimization: Identifying Optimal Active Constraint Sets," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 463-480, January.

    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. Bissan Ghaddar & Ignacio Gómez-Casares & Julio González-Díaz & Brais González-Rodríguez & Beatriz Pateiro-López & Sofía Rodríguez-Ballesteros, 2023. "Learning for Spatial Branching: An Algorithm Selection Approach," INFORMS Journal on Computing, INFORMS, vol. 35(5), pages 1024-1043, September.
    2. Bożena Staruch & Bogdan Staruch, 2021. "Competence-based assignment of tasks to workers in factories with demand-driven manufacturing," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 29(2), pages 553-565, June.
    3. Nikolaus Furian & Michael O’Sullivan & Cameron Walker & Eranda Çela, 2021. "A machine learning-based branch and price algorithm for a sampled vehicle routing problem," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 43(3), pages 693-732, September.
    4. Bengio, Yoshua & Lodi, Andrea & Prouvost, Antoine, 2021. "Machine learning for combinatorial optimization: A methodological tour d’horizon," European Journal of Operational Research, Elsevier, vol. 290(2), pages 405-421.
    5. Gavin J. Bell & Bruce W. Lamar & Chris A. Wallace, 1999. "Capacity improvement, penalties, and the fixed charge transportation problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(4), pages 341-355, June.
    6. Hajra Khan & Imran Fareed Nizami & Saeed Mian Qaisar & Asad Waqar & Moez Krichen & Abdulaziz Turki Almaktoom, 2022. "Analyzing Optimal Battery Sizing in Microgrids Based on the Feature Selection and Machine Learning Approaches," Energies, MDPI, vol. 15(21), pages 1-22, October.
    7. Andrea Lodi & Giulia Zarpellon, 2017. "On learning and branching: a survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(2), pages 207-236, July.
    8. Sun, Minghe, 2002. "The transportation problem with exclusionary side constraints and two branch-and-bound algorithms," European Journal of Operational Research, Elsevier, vol. 140(3), pages 629-647, August.
    9. J. T. Linderoth & M. W. P. Savelsbergh, 1999. "A Computational Study of Search Strategies for Mixed Integer Programming," INFORMS Journal on Computing, INFORMS, vol. 11(2), pages 173-187, May.
    10. Robin Kemminer & Jannick Lange & Jens Peter Kempkes & Kevin Tierney & Dimitri Weiß, 2024. "Configuring Mixed-Integer Programming Solvers for Large-Scale Instances," SN Operations Research Forum, Springer, vol. 5(2), pages 1-14, June.
    11. Yu Yang & Natashia Boland & Martin Savelsbergh, 2021. "Multivariable Branching: A 0-1 Knapsack Problem Case Study," INFORMS Journal on Computing, INFORMS, vol. 33(4), pages 1354-1367, October.
    12. Jawahar, N. & Balaji, A.N., 2009. "A genetic algorithm for the two-stage supply chain distribution problem associated with a fixed charge," European Journal of Operational Research, Elsevier, vol. 194(2), pages 496-537, April.
    13. Kurt M. Bretthauer, 1994. "A penalty for concave minimization derived from the tuy cutting plane," Naval Research Logistics (NRL), John Wiley & Sons, vol. 41(3), pages 455-463, April.
    14. Ellis L. Johnson & George L. Nemhauser & Martin W.P. Savelsbergh, 2000. "Progress in Linear Programming-Based Algorithms for Integer Programming: An Exposition," INFORMS Journal on Computing, INFORMS, vol. 12(1), pages 2-23, February.
    15. Renata Mansini & Roberto Zanotti, 2020. "A Core-Based Exact Algorithm for the Multidimensional Multiple Choice Knapsack Problem," INFORMS Journal on Computing, INFORMS, vol. 32(4), pages 1061-1079, October.
    16. Kurt M. Bretthauer & A. Victor Cabot & M. A. Venkataramanan, 1994. "An algorithm and new penalties for concave integer minimization over a polyhedron," Naval Research Logistics (NRL), John Wiley & Sons, vol. 41(3), pages 435-454, April.
    17. Jeffery L. Kennington & Charles D. Nicholson, 2010. "The Uncapacitated Time-Space Fixed-Charge Network Flow Problem: An Empirical Investigation of Procedures for Arc Capacity Assignment," INFORMS Journal on Computing, INFORMS, vol. 22(2), pages 326-337, May.

    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:29:y:2017:i:1:p:185-195. 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.