# Cutting Plane Selection with Analytic Centers and Multiregression

arXiv: https://arxiv.org/abs/2212.07231 · HTML: https://mlsanity.com/paper/2212.07231/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 32 references that are in the map.
- First posted on arXiv 14 Dec 2022.

## Builds on (most cited first, 7 of 7)

- [Reinforcement Learning for Integer Programming: Learning to Cut](https://mlsanity.com/paper/1906.04859/) (2019)
- [Learning To Cut By Looking Ahead: Cutting Plane Selection via Imitation Learning](https://mlsanity.com/paper/2206.13414/) (2022)
- [Learning to Select Cuts for Efficient Mixed-Integer Programming](https://mlsanity.com/paper/2105.13645/) (2021)
- [Sample Complexity of Tree Search Configuration: Cutting Planes and Beyond](https://mlsanity.com/paper/2106.04033/) (2021)
- [Adaptive Cut Selection in Mixed-Integer Linear Programming](https://mlsanity.com/paper/2202.10962/) (2022)
- [Theoretical challenges towards cutting-plane selection](https://mlsanity.com/paper/1805.02782/) (2018)
- [On the depth of cutting planes](https://mlsanity.com/paper/1903.05304/) (2019)

## Built on by (most cited first, 4 of 4)

- [Machine Learning for Cutting Planes in Integer Programming: A Survey](https://mlsanity.com/paper/2302.09166/) (2023)
- [Differentiable Cutting-plane Layers for Mixed-integer Linear Optimization](https://mlsanity.com/paper/2311.03350/) (2023)
- [Beyond Local Selection: Global Cut Selection for Enhanced Mixed-Integer Programming](https://mlsanity.com/paper/2503.15847/) (2025)
- [A Context-Aware Cutting Plane Selection Algorithm for Mixed-Integer Programming](https://mlsanity.com/paper/2307.07322/) (2023)

## Abstract (arXiv)

Cutting planes are a crucial component of state-of-the-art mixed-integer programming solvers, with the choice of which subset of cuts to add being vital for solver performance. We propose new distance-based measures to qualify the value of a cut by quantifying the extent to which it separates relevant parts of the relaxed feasible set. For this purpose, we use the analytic centers of the relaxation polytope or of its optimal face, as well as alternative optimal solutions of the linear programming relaxation. We assess the impact of the choice of distance measure on root node performance and throughout the whole branch-and-bound tree, comparing our measures against those prevalent in the literature. Finally, by a multi-output regression, we predict the relative performance of each measure, using static features readily available before the separation process. Our results indicate that analytic center-based methods help to significantly reduce the number of branch-and-bound nodes needed to explore the search space and that our multiregression approach can further improve on any individual method.