Binary extended formulations of polyhedral mixed-integer sets

We analyze different ways of constructing binary extended formulations of polyhedral mixed-integer sets with bounded integer variables and compare their relative strength with respect to split cuts. We show that among all binary extended formulations where each bounded integer variable is represente...

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Veröffentlicht in:Mathematical programming Jg. 170; H. 1; S. 207 - 236
Hauptverfasser: Dash, Sanjeeb, Günlük, Oktay, Hildebrand, Robert
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2018
Springer Nature B.V
Schlagworte:
Calculus of Variations and Optimal Control; Optimization
Combinatorics
Enumeration
Formulations
Full Length Paper
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Mathematics of Computing
Numerical Analysis
Theoretical
Variables
Branch-and-bound
Extended formulations
Cutting planes
90C57
Mixed-integer programming
90C11
Binarization
ISSN:0025-5610, 1436-4646
Online-Zugang:Volltext
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Abstract We analyze different ways of constructing binary extended formulations of polyhedral mixed-integer sets with bounded integer variables and compare their relative strength with respect to split cuts. We show that among all binary extended formulations where each bounded integer variable is represented by a distinct collection of binary variables, what we call “unimodular” extended formulations are the strongest. We also compare the strength of some binary extended formulations from the literature. Finally, we study the behavior of branch-and-bound on such extended formulations and show that branching on the new binary variables leads to significantly smaller enumeration trees in some cases.
AbstractList We analyze different ways of constructing binary extended formulations of polyhedral mixed-integer sets with bounded integer variables and compare their relative strength with respect to split cuts. We show that among all binary extended formulations where each bounded integer variable is represented by a distinct collection of binary variables, what we call “unimodular” extended formulations are the strongest. We also compare the strength of some binary extended formulations from the literature. Finally, we study the behavior of branch-and-bound on such extended formulations and show that branching on the new binary variables leads to significantly smaller enumeration trees in some cases.
Author Günlük, Oktay
Dash, Sanjeeb
Hildebrand, Robert
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  fullname: Günlük, Oktay
  email: gunluk@us.ibm.com
  organization: IBM T. J. Watson Research Center
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  givenname: Robert
  surname: Hildebrand
  fullname: Hildebrand, Robert
  organization: Grado Department of Industrial and Systems Engineering, Virginia Tech
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CitedBy_id crossref_primary_10_1007_s00500_023_08379_3
crossref_primary_10_1007_s10107_025_02220_5
crossref_primary_10_1137_19M1291145
crossref_primary_10_1287_moor_2021_0129
crossref_primary_10_1016_j_orl_2024_107119
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ContentType Journal Article
Copyright Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society 2018
Mathematical Programming is a copyright of Springer, (2018). All Rights Reserved.
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Issue 1
Keywords Branch-and-bound
Extended formulations
Cutting planes
90C57
Mixed-integer programming
90C11
Binarization
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Snippet We analyze different ways of constructing binary extended formulations of polyhedral mixed-integer sets with bounded integer variables and compare their...
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SubjectTerms Calculus of Variations and Optimal Control; Optimization
Combinatorics
Enumeration
Formulations
Full Length Paper
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Mathematics of Computing
Numerical Analysis
Theoretical
Variables
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Title Binary extended formulations of polyhedral mixed-integer sets
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