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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Bibliographic Details
Published in:Mathematical programming Vol. 170; no. 1; pp. 207 - 236
Main Authors: Dash, Sanjeeb, Günlük, Oktay, Hildebrand, Robert
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2018
Springer Nature B.V
Subjects:
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 Access:Get full text
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Summary: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.
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ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-018-1294-0