# Theoretical challenges towards cutting-plane selection

arXiv: https://arxiv.org/abs/1805.02782 · HTML: https://mlsanity.com/paper/1805.02782/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 May 2018.

## Built on by (most cited first, 16 of 16)

- [Learning To Cut By Looking Ahead: Cutting Plane Selection via Imitation Learning](https://mlsanity.com/paper/2206.13414/) (2022)
- [Learning Cut Selection for Mixed-Integer Linear Programming via Hierarchical Sequence Model](https://mlsanity.com/paper/2302.00244/) (2023)
- [Adaptive Cut Selection in Mixed-Integer Linear Programming](https://mlsanity.com/paper/2202.10962/) (2022)
- [Machine Learning Augmented Branch and Bound for Mixed Integer Linear Programming](https://mlsanity.com/paper/2402.05501/) (2024)
- [Machine Learning for Cutting Planes in Integer Programming: A Survey](https://mlsanity.com/paper/2302.09166/) (2023)
- [Learning to Configure Separators in Branch-and-Cut](https://mlsanity.com/paper/2311.05650/) (2023)
- [Learning to Cut via Hierarchical Sequence/Set Model for Efficient Mixed-Integer Programming](https://mlsanity.com/paper/2404.12638/) (2024)
- [Branch and Bound in Mixed Integer Linear Programming Problems: A Survey of Techniques and Trends](https://mlsanity.com/paper/2111.06257/) (2021)
- [LLMs for Cold-Start Cutting Plane Separator Configuration](https://mlsanity.com/paper/2412.12038/) (2024)
- [Machine Learning Insides OptVerse AI Solver: Design Principles and Applications](https://mlsanity.com/paper/2401.05960/) (2024)
- [Accelerating process control and optimization via machine learning: A review](https://mlsanity.com/paper/2412.18529/) (2024)
- [Cutting Plane Selection with Analytic Centers and Multiregression](https://mlsanity.com/paper/2212.07231/) (2022)
- [Learning to Remove Cuts in Integer Linear Programming](https://mlsanity.com/paper/2406.18781/) (2024)
- [Differentiable Cutting-plane Layers for Mixed-integer Linear Optimization](https://mlsanity.com/paper/2311.03350/) (2023)
- [Predicting Accurate Lagrangian Multipliers for Mixed Integer Linear Programs](https://mlsanity.com/paper/2310.14659/) (2023)
- [An Expansion-Based Approach for Quantified Integer Programming](https://mlsanity.com/paper/2506.04452/) (2025)

## Abstract (arXiv)

While many classes of cutting-planes are at the disposal of integer programming solvers, our scientific understanding is far from complete with regards to cutting-plane selection, i.e., the task of selecting a portfolio of cutting-planes to be added to the LP relaxation at a given node of the branch-and-bound tree. In this paper we review the different classes of cutting-planes available, known theoretical results about their relative strength, important issues pertaining to cut selection, and discuss some possible new directions to be pursued in order to accomplish cutting-plane selection in a more principled manner. Finally, we review some lines of work that we undertook to provide a preliminary theoretical underpinning for some of the issues related to cut selection.