A combinatorial approach for small and strong formulations of disjunctive constraints

TL;DR

This paper introduces a general framework for creating small, strong mixed-integer programming formulations for disjunctive constraints, extending previous work and applying it to various complex constraints.

Contribution

It generalizes existing formulations for SOS2 constraints and provides a complete characterization of the framework's expressive power, enabling new formulations for diverse disjunctive constraints.

Findings

Developed a unified framework for disjunctive constraints

Produced novel small, strong formulations for multiple constraint types

Extended the logarithmic-sized formulations to broader classes of problems

Abstract

We present a framework for constructing strong mixed-integer programming formulations for logical 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.