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International Conference on Integration of Constraint Programming, Artificial Intelligence, and Operations Research

CPAIOR 2015: Integration of AI and OR Techniques in Constraint Programming pp 199–214Cite as

Enhancing MIP Branching Decisions by Using the Sample Variance of Pseudo Costs

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9075))

Abstract

The selection of a good branching variable is crucial for small search trees in Mixed Integer Programming. Most modern solvers employ a strategy guided by history information, mainly the variable pseudo-costs, which are used to estimate the objective gain. At the beginning of the search, such information is usually collected via an expensive look-ahead strategy called strong branching until variables are considered reliable.

The reliability notion is thereby mostly based on fixed-number thresholds, which may lead to ineffective branching decisions on problems with highly varying objective gains.

We suggest two new notions of reliability motivated by mathematical statistics that take into account the sample variance of the past observations on each variable individually. The first method prioritizes additional strong branching look-aheads on variables whose pseudo-costs show a large variance by measuring the relative error of a pseudo-cost confidence interval. The second method performs a specialized version of a two-sample Student’s \(t\)-test for filtering branching candidates with a high probability to be better than the best history candidate.

Both methods were implemented in the MIP-solver SCIP and computational results on standard MIP test sets are presented.

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Authors and Affiliations

  1. Konrad Zuse Zentrum für Informationstechnologie, Berlin, Germany

    Gregor Hendel

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  1. Gregor Hendel
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Correspondence to Gregor Hendel .

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Editors and Affiliations

  1. University of Connecticut, Storrs, Connecticut, USA

    Laurent Michel

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Hendel, G. (2015). Enhancing MIP Branching Decisions by Using the Sample Variance of Pseudo Costs. In: Michel, L. (eds) Integration of AI and OR Techniques in Constraint Programming. CPAIOR 2015. Lecture Notes in Computer Science(), vol 9075. Springer, Cham. https://doi.org/10.1007/978-3-319-18008-3_14

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  • DOI: https://doi.org/10.1007/978-3-319-18008-3_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-18007-6

  • Online ISBN: 978-3-319-18008-3

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