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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| Published in: | SIAM journal on optimization Vol. 20; no. 5; pp. 2181 - 2198 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Philadelphia
Society for Industrial and Applied Mathematics
01.01.2010
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| Subjects: | |
| 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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| Bibliography: | SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-2 content type line 23 |
| ISSN: | 1052-6234 1095-7189 |
| DOI: | 10.1137/080737587 |