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...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:SIAM journal on optimization Jg. 20; H. 5; S. 2181 - 2198
Hauptverfasser: Mahajan, Ashutosh, Ralphs, Ted
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Philadelphia Society for Industrial and Applied Mathematics 01.01.2010
Schlagworte:
Algorithms
Criteria
Imposition
Inequalities
Integer programming
Linear programming
Mixed integer
Optimization
Optimization algorithms
Ratios
Studies
Symbols
ISSN:1052-6234, 1095-7189
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung: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.)
Bibliographie: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