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A combinatorial approach for small and strong formulations of disjunctive constraints

Joey Huchette (huchette***at***mit.edu)
Juan Pablo Vielma (jvielma***at***mit.edu)

Abstract: We present a framework for constructing small, strong mixed-integer formulations for disjunctive constraints. Our approach is a generalization of the logarithmically-sized formulations of Vielma and Nemhauser for SOS2 constraints, and we offer a complete characterization of its expressive power. We apply the framework to a variety of disjunctive constraints, producing novel, small, and strong formulations for outer approximations of multilinear terms, generalizations of special ordered sets, piecewise linear functions over a variety of domains, and obstacle avoidance constraints.

Keywords: Integer Programming, Piecewise Linear, Polyhedra

Category 1: Integer Programming ((Mixed) Integer Linear Programming )


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Entry Submitted: 05/20/2016
Entry Accepted: 05/20/2016
Entry Last Modified: 05/24/2018

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