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Information-based branching schemes for binary linear mixed integer problems

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Abstract

Branching variable selection can greatly affect the effectiveness and efficiency of a branch-and-bound algorithm. Traditional approaches to branching variable selection rely on estimating the effect of the candidate variables on the objective function. We propose an approach which is empowered by exploiting the information contained in a family of fathomed subproblems, collected beforehand from an incomplete branch-and-bound tree. In particular, we use this information to define new branching rules that reduce the risk of incurring inappropriate branchings. We provide computational results that demonstrate the effectiveness of the new branching rules on various benchmark instances.

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Authors and Affiliations

  1. H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, 765 Ferst Drive, NW, Atlanta, GA, 30332-0205, USA

    Fatma Kılınç Karzan, George L. Nemhauser & Martin W. P. Savelsbergh

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  1. Fatma Kılınç Karzan
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  2. George L. Nemhauser
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  3. Martin W. P. Savelsbergh
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Correspondence to Fatma Kılınç Karzan.

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Kılınç Karzan, F., Nemhauser, G.L. & Savelsbergh, M.W.P. Information-based branching schemes for binary linear mixed integer problems. Math. Prog. Comp. 1, 249–293 (2009). https://doi.org/10.1007/s12532-009-0009-1

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  • DOI: https://doi.org/10.1007/s12532-009-0009-1

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