Embedding Formulations and Complexity for Unions of Polyhedra
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1506.01417.pdf
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Author(s)
Vielma Centeno, Juan Pablo
Date Issued
November 2017
Journal
Management Science
Publisher
Institute for Operations Research and the Management Sciences (INFORMS)
Citation
Vielma, Juan Pablo. “Embedding Formulations and Complexity for Unions of Polyhedra.” Management Science 64, 10 (October 2018): 4721–4734. doi:10.1287/mnsc.2017.2856. © 2017 The Author
Version
Author's final manuscript
Abstract
It is well known that selecting a good Mixed Integer Programming (MIP) formulation is crucial for an effective solution with state-of-the art solvers. While best practices and guidelines for constructing good formulations abound, there is rarely a systematic construction leading to the best possible formulation. We introduce embedding formulations and complexity as a new MIP formulation paradigm for systematically constructing formulations for disjunctive constraints that are optimal with respect to size. More specifically,
they yield the smallest possible ideal formulation (i.e. one whose LP relaxation has integral extreme points) among all formulations that only use 0-1 auxiliary variables. We use the paradigm to characterize optimal
formulations for SOS2 constraints and certain piecewise linear functions of two variables. We also show that the resulting formulations can provide a significant computational advantage over all known formulations
for piecewise linear functions.
MIT Department
Sloan School of Management
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1287/MNSC.2017.2856
