IDEAS home Printed from https://ideas.repec.org/a/spr/topjnl/v25y2017i2d10.1007_s11750-017-0451-6.html
   My bibliography  Save this article

On learning and branching: a survey

Author

Listed:
  • Andrea Lodi

    (École Polytechnique de Montréal)

  • Giulia Zarpellon

    (École Polytechnique de Montréal)

Abstract

This paper surveys learning techniques to deal with the two most crucial decisions in the branch-and-bound algorithm for Mixed-Integer Linear Programming, namely variable and node selections. Because of the lack of deep mathematical understanding on those decisions, the classical and vast literature in the field is inherently based on computational studies and heuristic, often problem-specific, strategies. We will both interpret some of those early contributions in the light of modern (machine) learning techniques, and give the details of the recent algorithms that instead explicitly incorporate machine learning paradigms.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:topjnl:v:25:y:2017:i:2:d:10.1007_s11750-017-0451-6
    DOI: 10.1007/s11750-017-0451-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11750-017-0451-6
    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/s11750-017-0451-6?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. Gérard Cornuéjols & Miroslav Karamanov & Yanjun Li, 2006. "Early Estimates of the Size of Branch-and-Bound Trees," INFORMS Journal on Computing, INFORMS, vol. 18(1), pages 86-96, February.
    2. 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.
    3. 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.
    4. Matteo Fischetti & Michele Monaci, 2014. "Exploiting Erraticism in Search," Operations Research, INFORMS, vol. 62(1), pages 114-122, February.
    5. 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. Christoph Hertrich & Martin Skutella, 2023. "Provably Good Solutions to the Knapsack Problem via Neural Networks of Bounded Size," INFORMS Journal on Computing, INFORMS, vol. 35(5), pages 1079-1097, September.
    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. Eric Larsen & Sébastien Lachapelle & Yoshua Bengio & Emma Frejinger & Simon Lacoste-Julien & Andrea Lodi, 2022. "Predicting Tactical Solutions to Operational Planning Problems Under Imperfect Information," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 227-242, January.
    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.
    7. Bongiovanni, Claudia & Kaspi, Mor & Cordeau, Jean-François & Geroliminis, Nikolas, 2022. "A machine learning-driven two-phase metaheuristic for autonomous ridesharing operations," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 165(C).
    8. Charly Robinson La Rocca & Jean-François Cordeau & Emma Frejinger, 2024. "One-Shot Learning for MIPs with SOS1 Constraints," SN Operations Research Forum, Springer, vol. 5(3), pages 1-28, September.
    9. Juho Lauri & Sourav Dutta & Marco Grassia & Deepak Ajwani, 2023. "Learning fine-grained search space pruning and heuristics for combinatorial optimization," Journal of Heuristics, Springer, vol. 29(2), pages 313-347, June.
    10. 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.
    11. Dogacan Yilmaz & İ. Esra Büyüktahtakın, 2023. "Learning Optimal Solutions via an LSTM-Optimization Framework," SN Operations Research Forum, Springer, vol. 4(2), pages 1-40, June.
    12. 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.
    13. Renke Kuhlmann, 2019. "Learning to steer nonlinear interior-point methods," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 7(4), pages 381-419, December.
    14. 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.
    15. 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.
    16. Brais González-Rodríguez & Joaquín Ossorio-Castillo & Julio González-Díaz & Ángel M. González-Rueda & David R. Penas & Diego Rodríguez-Martínez, 2023. "Computational advances in polynomial optimization: RAPOSa, a freely available global solver," Journal of Global Optimization, Springer, vol. 85(3), pages 541-568, March.
    17. Dimitris Bertsimas & Bartolomeo Stellato, 2022. "Online Mixed-Integer Optimization in Milliseconds," INFORMS Journal on Computing, INFORMS, vol. 34(4), pages 2229-2248, July.
    18. Emilio Carrizosa & Cristina Molero-Río & Dolores Romero Morales, 2021. "Mathematical optimization in classification and regression trees," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(1), pages 5-33, April.
    19. Shen, Yunzhuang & Sun, Yuan & Li, Xiaodong & Eberhard, Andrew & Ernst, Andreas, 2023. "Adaptive solution prediction for combinatorial optimization," European Journal of Operational Research, Elsevier, vol. 309(3), pages 1392-1408.
    20. Quentin Cappart & David Bergman & Louis-Martin Rousseau & Isabeau Prémont-Schwarz & Augustin Parjadis, 2022. "Improving Variable Orderings of Approximate Decision Diagrams Using Reinforcement Learning," INFORMS Journal on Computing, INFORMS, vol. 34(5), pages 2552-2570, September.
    21. Gambella, Claudio & Ghaddar, Bissan & Naoum-Sawaya, Joe, 2021. "Optimization problems for machine learning: A survey," European Journal of Operational Research, Elsevier, vol. 290(3), pages 807-828.

    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. 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.
    3. 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.
    4. 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.
    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. 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.
    7. Gerdus Benadè & John N. Hooker, 2020. "Optimization Bounds from the Branching Dual," INFORMS Journal on Computing, INFORMS, vol. 32(1), pages 3-15, January.
    8. 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.
    9. 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.
    10. 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.
    11. Liang Chen & Wei-Kun Chen & Mu-Ming Yang & Yu-Hong Dai, 2021. "An exact separation algorithm for unsplittable flow capacitated network design arc-set polyhedron," Journal of Global Optimization, Springer, vol. 81(3), pages 659-689, November.
    12. 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.
    13. 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.
    14. Michele Monaci & André Gustavo Santos, 2018. "Minimum tiling of a rectangle by squares," Annals of Operations Research, Springer, vol. 271(2), pages 831-851, December.
    15. Ruslan Sadykov & François Vanderbeck & Artur Pessoa & Issam Tahiri & Eduardo Uchoa, 2019. "Primal Heuristics for Branch and Price: The Assets of Diving Methods," INFORMS Journal on Computing, INFORMS, vol. 31(2), pages 251-267, April.
    16. Kumar Abhishek & Sven Leyffer & Jeff Linderoth, 2010. "FilMINT: An Outer Approximation-Based Solver for Convex Mixed-Integer Nonlinear Programs," INFORMS Journal on Computing, INFORMS, vol. 22(4), pages 555-567, November.
    17. Matteo Fischetti & Michele Monaci, 2014. "Exploiting Erraticism in Search," Operations Research, INFORMS, vol. 62(1), pages 114-122, February.
    18. Alexander Schnell & Richard F. Hartl, 2016. "On the efficient modeling and solution of the multi-mode resource-constrained project scheduling problem with generalized precedence relations," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(2), pages 283-303, March.
    19. Luke Mason & Vicky Mak-Hau & Andreas Ernst, 2015. "A parallel optimisation approach for the realisation problem in intensity modulated radiotherapy treatment planning," Computational Optimization and Applications, Springer, vol. 60(2), pages 441-477, March.
    20. Hejl, Lukáš & Šůcha, Přemysl & Novák, Antonín & Hanzálek, Zdeněk, 2022. "Minimizing the weighted number of tardy jobs on a single machine: Strongly correlated instances," European Journal of Operational Research, Elsevier, vol. 298(2), pages 413-424.

    More about this item

    Keywords

    Branch and bound; Machine learning;

    Statistics

    Access and download statistics

    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:topjnl:v:25:y:2017:i:2:d:10.1007_s11750-017-0451-6. 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.