On the Complexity of Selecting Disjunctions in Integer Programming

The imposition of general disjunctions of the form " ... ," where ... are integer-valued, is a fundamental operation in both the branch-and-bound and cutting-plane algorithms for solving mixed integer linear programs. Such disjunctions can be used for branching at each iteration of the bra...

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Bibliographic Details
Published in:SIAM journal on optimization Vol. 20; no. 5; pp. 2181 - 2198
Main Authors: Mahajan, Ashutosh, Ralphs, Ted
Format: Journal Article
Language:English
Published: Philadelphia Society for Industrial and Applied Mathematics 01.01.2010
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ISSN:1052-6234, 1095-7189
Online Access:Get full text
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Summary:The imposition of general disjunctions of the form " ... ," where ... are integer-valued, is a fundamental operation in both the branch-and-bound and cutting-plane algorithms for solving mixed integer linear programs. Such disjunctions can be used for branching at each iteration of the branch-and-bound algorithm or to generate split inequalities for the cuttingplane algorithm. The authors first consider the problem of selecting a general disjunction and show that the problem of selecting an optimal such disjunction, according to specific criteria described herein, is ... -hard. They further show that the problem remains ... -hard even for binary programs or when considering certain restricted classes of disjunctions. They observe that the problem of deciding whether a given inequality is a split inequality can be reduced to one of the above problems, which leads to a proof that the problem is ... -complete.(ProQuest: ... denotes formulae/symbols omitted.)
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ISSN:1052-6234
1095-7189
DOI:10.1137/080737587