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Random sampling and machine learning to understand good decompositions

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  • S. Basso

    (Università degli Studi di Milano)

  • A. Ceselli

    (Università degli Studi di Milano)

  • A. Tettamanzi

    (Université Côte d’Azur - INRIA)

Abstract

Motivated by its implications in the development of general purpose solvers for decomposable Mixed Integer Programs (MIPs), we address a fundamental research question, that is how to exploit data-driven techniques to obtain automatic decomposition methods. We preliminary investigate the link between static properties of MIP input instances and good decomposition patterns. We devise a random sampling algorithm, considering a set of generic MIP base instances, and generate a large, balanced and well diversified set of decomposition patterns, that we analyze with machine learning tools. We also propose and test a minimal proof of concept framework performing data-driven automatic decomposition. The use of supervised techniques highlights interesting structures of random decompositions, as well as proving (under certain conditions) that data-driven methods are fruitful in our context, triggering at the same time perspectives for future research.

Suggested Citation

  • S. Basso & A. Ceselli & A. Tettamanzi, 2020. "Random sampling and machine learning to understand good decompositions," Annals of Operations Research, Springer, vol. 284(2), pages 501-526, January.
    • Handle: RePEc:spr:annopr:v:284:y:2020:i:2:d:10.1007_s10479-018-3067-9
    DOI: 10.1007/s10479-018-3067-9
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    References listed on IDEAS

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    1. J. Brooks & Eva Lee, 2010. "Analysis of the consistency of a mixed integer programming-based multi-category constrained discriminant model," Annals of Operations Research, Springer, vol. 174(1), pages 147-168, February.
    2. Alberto Ceselli & Federico Liberatore & Giovanni Righini, 2009. "A computational evaluation of a general branch-and-price framework for capacitated network location problems," Annals of Operations Research, Springer, vol. 167(1), pages 209-251, March.
    3. Delorme, Maxence & Iori, Manuel & Martello, Silvano, 2016. "Bin packing and cutting stock problems: Mathematical models and exact algorithms," European Journal of Operational Research, Elsevier, vol. 255(1), pages 1-20.
    4. VANDERBECK, François & WOLSEY, Laurence A., 2010. "Reformulation and decomposition of integer programs," LIDAM Reprints CORE 2188, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Andrea Bettinelli & Alberto Ceselli & Giovanni Righini, 2010. "A branch-and-price algorithm for the variable size bin packing problem with minimum filling constraint," Annals of Operations Research, Springer, vol. 179(1), pages 221-241, September.
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    Cited by:

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    2. 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.

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