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• W2158102350 abstract "The imposition of general disjunctions of the form “$pi xleqpi_0veepi xgeqpi_0+1$,” where $pi,pi_0$ 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 cutting-plane algorithm. We 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 $mathcal{NP}$-hard. We further show that the problem remains $mathcal{NP}$-hard even for binary programs or when considering certain restricted classes of disjunctions. We 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 $mathcal{NP}$-complete." @default.
• W2158102350 created "2016-06-24" @default.
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• W2158102350 date "2010-01-01" @default.
• W2158102350 modified "2023-09-27" @default.
• W2158102350 title "On the Complexity of Selecting Disjunctions in Integer Programming" @default.
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• W2158102350 doi "https://doi.org/10.1137/080737587" @default.
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