# Learning to Select Cuts for Efficient Mixed-Integer Programming arXiv: https://arxiv.org/abs/2105.13645 ยท HTML: https://mlsanity.com/paper/2105.13645/ ## Key facts - Cited by 48 papers in the map (data through 14 Oct 2026). - Builds on 12 of its 49 references that are in the map. - First posted on arXiv 28 May 2021. ## Builds on (most cited first, 12 of 12) - [Pointer Networks](https://mlsanity.com/paper/1506.03134/) (2015) - [Attention, Learn to Solve Routing Problems!](https://mlsanity.com/paper/1803.08475/) (2018) - [Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizon](https://mlsanity.com/paper/1811.06128/) (2018) - [Neural Combinatorial Optimization with Reinforcement Learning](https://mlsanity.com/paper/1611.09940/) (2016) - [A Brief Survey of Deep Reinforcement Learning](https://mlsanity.com/paper/1708.05866/) (2017) - [Reinforcement Learning for Solving the Vehicle Routing Problem](https://mlsanity.com/paper/1802.04240/) (2018) - [Exact Combinatorial Optimization with Graph Convolutional Neural Networks](https://mlsanity.com/paper/1906.01629/) (2019) - [Solving Mixed Integer Programs Using Neural Networks](https://mlsanity.com/paper/2012.13349/) (2020) - [Multiple Instance Learning: A Survey of Problem Characteristics and Applications](https://mlsanity.com/paper/1612.03365/) (2016) - [Reinforcement Learning for Integer Programming: Learning to Cut](https://mlsanity.com/paper/1906.04859/) (2019) - [Learning to Branch](https://mlsanity.com/paper/1803.10150/) (2018) - [Multiple Instance Learning with Bag Dissimilarities](https://mlsanity.com/paper/1309.5643/) (2013) ## Built on by (most cited first, 30 of 48) - [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) - [A Survey for Solving Mixed Integer Programming via Machine Learning](https://mlsanity.com/paper/2203.02878/) (2022) - [Searching Large Neighborhoods for Integer Linear Programs with Contrastive Learning](https://mlsanity.com/paper/2302.01578/) (2023) - [Sample Complexity of Tree Search Configuration: Cutting Planes and Beyond](https://mlsanity.com/paper/2106.04033/) (2021) - [Lookback for Learning to Branch](https://mlsanity.com/paper/2206.14987/) (2022) - [Adaptive Cut Selection in Mixed-Integer Linear Programming](https://mlsanity.com/paper/2202.10962/) (2022) - [On Representing Mixed-Integer Linear Programs by Graph Neural Networks](https://mlsanity.com/paper/2210.10759/) (2022) - [Machine Learning for Cutting Planes in Integer Programming: A Survey](https://mlsanity.com/paper/2302.09166/) (2023) - [Structural Analysis of Branch-and-Cut and the Learnability of Gomory Mixed Integer Cuts](https://mlsanity.com/paper/2204.07312/) (2022) - [Apollo-MILP: An Alternating Prediction-Correction Neural Solving Framework for Mixed-Integer Linear Programming](https://mlsanity.com/paper/2503.01129/) (2025) - [Distributional MIPLIB: a Multi-Domain Library for Advancing ML-Guided MILP Methods](https://mlsanity.com/paper/2406.06954/) (2024) - [Improved Sample Complexity Bounds for Branch-and-Cut](https://mlsanity.com/paper/2111.11207/) (2021) - [Learning to Cut via Hierarchical Sequence/Set Model for Efficient Mixed-Integer Programming](https://mlsanity.com/paper/2404.12638/) (2024) - [Artificial Intelligence for Operations Research: Revolutionizing the Operations Research Process](https://mlsanity.com/paper/2401.03244/) (2024) - [Learning To Dive In Branch And Bound](https://mlsanity.com/paper/2301.09943/) (2023) - [Branch and Bound in Mixed Integer Linear Programming Problems: A Survey of Techniques and Trends](https://mlsanity.com/paper/2111.06257/) (2021) - [Generative AI and Process Systems Engineering: The Next Frontier](https://mlsanity.com/paper/2402.10977/) (2024) - [Learning to Stop Cut Generation for Efficient Mixed-Integer Linear Programming](https://mlsanity.com/paper/2401.17527/) (2024) - [Learning to optimize: A tutorial for continuous and mixed-integer optimization](https://mlsanity.com/paper/2405.15251/) (2024) - [Machine Learning Insides OptVerse AI Solver: Design Principles and Applications](https://mlsanity.com/paper/2401.05960/) (2024) - [Sample Complexity of Algorithm Selection Using Neural Networks and Its Applications to Branch-and-Cut](https://mlsanity.com/paper/2402.02328/) (2024) - [DOGE-Train: Discrete Optimization on GPU with End-to-end Training](https://mlsanity.com/paper/2205.11638/) (2022) - [Online Learning for Scheduling MIP Heuristics](https://mlsanity.com/paper/2304.03755/) (2023) - [Confidence Threshold Neural Diving](https://mlsanity.com/paper/2202.07506/) (2022) - [Taking the human out of decomposition-based optimization via artificial intelligence: Part II. Learning to initialize](https://mlsanity.com/paper/2310.07082/) (2023) - [ML4CO: Is GCNN All You Need? Graph Convolutional Neural Networks Produce Strong Baselines For Combinatorial Optimization Problems, If Tuned and Trained Properly, on Appropriate Data](https://mlsanity.com/paper/2112.12251/) (2021) - [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) ## Abstract (arXiv) Cutting plane methods play a significant role in modern solvers for tackling mixed-integer programming (MIP) problems. Proper selection of cuts would remove infeasible solutions in the early stage, thus largely reducing the computational burden without hurting the solution accuracy. However, the major cut selection approaches heavily rely on heuristics, which strongly depend on the specific problem at hand and thus limit their generalization capability. In this paper, we propose a data-driven and generalizable cut selection approach, named Cut Ranking, in the settings of multiple instance learning. To measure the quality of the candidate cuts, a scoring function, which takes the instance-specific cut features as inputs, is trained and applied in cut ranking and selection. In order to evaluate our method, we conduct extensive experiments on both synthetic datasets and real-world datasets. Compared with commonly used heuristics for cut selection, the learning-based policy has shown to be more effective, and is capable of generalizing over multiple problems with different properties. Cut Ranking has been deployed in an industrial solver for large-scale MIPs. In the online A/B testing of the product planning problems with more than 107 variables and constraints daily, Cut Ranking has achieved the average speedup ratio of 12.42% over the production solver without any accuracy loss of solution.