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Home / Proceedings / Proceedings of the AAAI Conference on Artificial Intelligence, 35 / No. 5: AAAI-21 Technical Tracks 5

Learning To Scale Mixed-Integer Programs

February 1, 2023

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Authors

Timo Berthold

FICO


Gregor Hendel

FICO


DOI:

10.1609/aaai.v35i5.16482


Abstract:

Many practical applications require the solution of numerically challenging linear programs (LPs) and mixed integer programs (MIPs). Scaling is a widely used preconditioning technique that aims at reducing the error propagation of the involved linear systems, thereby improving the numerical behavior of the dual simplex algorithm and, consequently, LP-based branch-and-bound. A reliable scaling method often makes the difference whether these problems can be solved correctly or not. In this paper, we investigate the use of machine learning to choose at the beginning of the solution process between two common scaling methods: Standard scaling and Curtis-Reid scaling. The latter often, but not always, leads to a more robust solution process, but may suffer from longer solution times. Rather than training for overall solution time, we propose to use the attention level of a MIP solution process as a learning label. We evaluate the predictive power of a random forest approach and a linear regressor that learns the (square-root of the) difference in attention level. It turns out that the resulting classification not only reduces various types of numerical errors by large margins, but it also improves the performance of the dual simplex algorithm. The learned model has been implemented within the FICO Xpress MIP solver and it is used by default since release 8.9, May 2020, to determine the scaling algorithm Xpress applies before solving an LP or a MIP.

Topics: AAAI

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HOW TO CITE:

Timo Berthold||Gregor Hendel Learning To Scale Mixed-Integer Programs Proceedings of the AAAI Conference on Artificial Intelligence (2021) 3661-3668.

Timo Berthold||Gregor Hendel Learning To Scale Mixed-Integer Programs AAAI 2021, 3661-3668.

Timo Berthold||Gregor Hendel (2021). Learning To Scale Mixed-Integer Programs. Proceedings of the AAAI Conference on Artificial Intelligence, 3661-3668.

Timo Berthold||Gregor Hendel. Learning To Scale Mixed-Integer Programs. Proceedings of the AAAI Conference on Artificial Intelligence 2021 p.3661-3668.

Timo Berthold||Gregor Hendel. 2021. Learning To Scale Mixed-Integer Programs. "Proceedings of the AAAI Conference on Artificial Intelligence". 3661-3668.

Timo Berthold||Gregor Hendel. (2021) "Learning To Scale Mixed-Integer Programs", Proceedings of the AAAI Conference on Artificial Intelligence, p.3661-3668

Timo Berthold||Gregor Hendel, "Learning To Scale Mixed-Integer Programs", AAAI, p.3661-3668, 2021.

Timo Berthold||Gregor Hendel. "Learning To Scale Mixed-Integer Programs". Proceedings of the AAAI Conference on Artificial Intelligence, 2021, p.3661-3668.

Timo Berthold||Gregor Hendel. "Learning To Scale Mixed-Integer Programs". Proceedings of the AAAI Conference on Artificial Intelligence, (2021): 3661-3668.

Timo Berthold||Gregor Hendel. Learning To Scale Mixed-Integer Programs. AAAI[Internet]. 2021[cited 2023]; 3661-3668.


ISSN: 2374-3468


Published by AAAI Press, Palo Alto, California USA
Copyright 2022, Association for the Advancement of
Artificial Intelligence 1900 Embarcadero Road, Suite
101, Palo Alto, California 94303 All Rights Reserved

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