Face Dimensions of General-Purpose Cutting Planes for Mixed-Integer Linear Programs

TL;DR

This paper experimentally investigates the face dimensions of general-purpose cutting planes in mixed-integer linear programming and relates these dimensions to their effectiveness in branch-and-bound algorithms.

Contribution

It provides the first empirical analysis of face dimensions of general-purpose cutting planes and links these dimensions to their practical impact in solving MILPs.

Findings

Face dimensions vary significantly across cutting planes.

Larger face dimensions correlate with stronger cuts.

The study offers insights into the effectiveness of cutting planes in branch-and-bound.

Abstract

Cutting planes are a key ingredient to successfully solve mixed-integer linear programs. For specific problems, their strength is often theoretically assessed by showing that they are facet-defining for the corresponding mixed-integer hull. In this paper we experimentally investigate the dimensions of faces induced by general-purpose cutting planes generated by a state-of-the-art solver. Therefore, we relate the dimension of each cutting plane to its impact in a branch-and-bound algorithm.