# Experiments with two-row cuts from degenerate tableaux

## TL;DR

This paper investigates the effectiveness of two-row cuts from degenerate tableaux in mixed-integer programming, comparing their performance to GMI cuts through experiments that consider reliability and aggressiveness of cut generation.

## Contribution

It provides an empirical analysis of two-row cuts' impact on MIP instances, highlighting the importance of experimental setup and cut generator parameters.

## Key findings

- Two-row cuts can dominate split closures in some cases.
- The competitiveness of these cuts relative to GMI cuts depends on experimental conditions.
- Reliability and aggressiveness settings significantly influence cut effectiveness.

## Abstract

There has been a recent interest in cutting planes generated from two or more rows of the optimal simplex tableau. One can construct examples of integer programs for which a single cutting plane generated from two rows dominates the entire split closure. Motivated by these theoretical results, we study the effect of adding a family of cutting planes generated from two rows on a set of instances from the MIPLIB library. The conclusion of whether these cuts are competitive with GMI cuts is very sensitive to the experimental setup. In particular, we consider the issue of reliability versus aggressiveness of the cut generators, an issue that is usually not addressed in the literature.