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Machine Learning Techniques for Branch-and-Cut Methods: The Selection of Cutting Planes

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Numerical Computations: Theory and Algorithms (NUMTA 2023)

Abstract

The selection of cuts to be added to the current LP relaxation is one of the most critical task in Branch-and-Cut methods, since it strongly affects the performances of the algorithm. Recently, machine learning techniques have become popular to define effective cut selection strategies. In this paper we explore the possibility of selecting cuts by ranking them via support vector regression.

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References

  1. Berthold, T., Francobaldi, M., Hendel, G.: Learning to use local cuts: arXiv:2206.11618v1 (2022)

  2. Fan, R.-E., Chang, K.-W., Hsieh, C.-J., Wang, X.-R., Lin, C.-J.: LIBLINEAR: a library for large linear classification. J. Mach. Learn. Res. 9, 1871–1874 (2008)

    MATH  Google Scholar 

  3. Huang, Z., et al.: Learning to select cuts for efficient mixed-integer programming. Pattern Recogn. 123, 108353 (2022)

    Article  MATH  Google Scholar 

  4. Gomory, R.: Outline of an algorithm for integer solutions to linear programs. Bull. Am. Math. Soc. 64, 275–278 (1958)

    Article  MathSciNet  MATH  Google Scholar 

  5. Lodi, A., Zarpellon, G.: On learning and branching: a survey. TOP 25(2), 207–236 (2017). https://doi.org/10.1007/s11750-017-0451-6

    Article  MathSciNet  MATH  Google Scholar 

  6. Paulus, MB., Zarpellon, G., Krause, A., Charlin, L., Maddison CJ.: Learning to cut by looking ahead: cutting plane selection via imitation learning. In: Proceedings of the \(39\)th International Conference on Machine Learning, Baltimore, Maryland, USA, PMLR, 162, arXiv:2206.13414v1 (2022)

  7. Schölkopf, B., Smola, A.J.: Learning with Kernels. The MIT press, Cambridge, Massachusetts (2002)

    MATH  Google Scholar 

  8. Tang, Y., Agrawal, S., Faenza, Y.: Reinforcement learning for integer programming: learning to cut. In: Proceedings of the 37th International Conference on Machine Learning, Article 868, pp. 9367–9376 (2020). arXiv:1906.04859

  9. Turner M., Koch T., Serrano F., Winkler M.: Adaptive cut selection in mixed-integer linear programming. Open J. Mathe. Optim. 4 Article 5 (2023)

    Google Scholar 

  10. Wolsey, L.A.: Integer Programming. Wiley-Interscience, New York (1998)

    MATH  Google Scholar 

  11. Zhang, J., Liu, C., Li, X., Zhen, H.L., Yuan, M., Li, Y.: A survey for solving mixed integer programming via machine learning. Neurocomputing 519, 205–217 (2023)

    Article  MATH  Google Scholar 

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Correspondence to Giovanni Giallombardo .

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Giallombardo, G., Miglionico, G., Sammarra, M. (2025). Machine Learning Techniques for Branch-and-Cut Methods: The Selection of Cutting Planes. In: Sergeyev, Y.D., Kvasov, D.E., Astorino, A. (eds) Numerical Computations: Theory and Algorithms. NUMTA 2023. Lecture Notes in Computer Science, vol 14476. Springer, Cham. https://doi.org/10.1007/978-3-031-81241-5_25

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  • DOI: https://doi.org/10.1007/978-3-031-81241-5_25

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-81240-8

  • Online ISBN: 978-3-031-81241-5

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