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A Machine Learning-Based Approximation of Strong Branching

Author

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  • 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
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    References listed on IDEAS

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    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.
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    Cited by:

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    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.
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    4. 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.
    5. 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.
    6. 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.
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    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. Gerdus Benadè & John N. Hooker, 2020. "Optimization Bounds from the Branching Dual," INFORMS Journal on Computing, INFORMS, vol. 32(1), pages 3-15, January.
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