# Adaptive Cut Selection in Mixed-Integer Linear Programming arXiv: https://arxiv.org/abs/2202.10962 ยท HTML: https://mlsanity.com/paper/2202.10962/ ## Key facts - Cited by 26 papers in the map (data through 14 Oct 2026). - Builds on 13 of its 35 references that are in the map. - First posted on arXiv 22 Feb 2022. ## Builds on (most cited first, 13 of 13) - [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014) - [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019) - [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016) - [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019) - [Exact Combinatorial Optimization with Graph Convolutional Neural Networks](https://mlsanity.com/paper/1906.01629/) (2019) - [Combinatorial optimization and reasoning with graph neural networks](https://mlsanity.com/paper/2102.09544/) (2021) - [SMAC3: A Versatile Bayesian Optimization Package for Hyperparameter Optimization](https://mlsanity.com/paper/2109.09831/) (2021) - [Solving Mixed Integer Programs Using Neural Networks](https://mlsanity.com/paper/2012.13349/) (2020) - [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) - [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) - [Theoretical challenges towards cutting-plane selection](https://mlsanity.com/paper/1805.02782/) (2018) ## Built on by (most cited first, 26 of 26) - [Learning Cut Selection for Mixed-Integer Linear Programming via Hierarchical Sequence Model](https://mlsanity.com/paper/2302.00244/) (2023) - [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) - [Structural Analysis of Branch-and-Cut and the Learnability of Gomory Mixed Integer Cuts](https://mlsanity.com/paper/2204.07312/) (2022) - [Learning to Configure Separators in Branch-and-Cut](https://mlsanity.com/paper/2311.05650/) (2023) - [Rethinking the Capacity of Graph Neural Networks for Branching Strategy](https://mlsanity.com/paper/2402.07099/) (2024) - [Learning to Cut via Hierarchical Sequence/Set Model for Efficient Mixed-Integer Programming](https://mlsanity.com/paper/2404.12638/) (2024) - [Learning To Dive In Branch And Bound](https://mlsanity.com/paper/2301.09943/) (2023) - [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) - [Cutting Plane Selection with Analytic Centers and Multiregression](https://mlsanity.com/paper/2212.07231/) (2022) - [StriderNET: A Graph Reinforcement Learning Approach to Optimize Atomic Structures on Rough Energy Landscapes](https://mlsanity.com/paper/2301.12477/) (2023) - [Towards graph neural networks for provably solving convex optimization problems](https://mlsanity.com/paper/2502.02446/) (2025) - [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) - [CLCR: Contrastive Learning-based Constraint Reordering for Efficient MILP Solving](https://mlsanity.com/paper/2504.03688/) (2025) - [HGCN2SP: Hierarchical Graph Convolutional Network for Two-Stage Stochastic Programming](https://mlsanity.com/paper/2511.16027/) (2025) - [MILP-Evo: Closed-Loop Fully Automatic Design of MILP Solvers](https://mlsanity.com/paper/2607.18252/) (2026) - [A Context-Aware Cutting Plane Selection Algorithm for Mixed-Integer Programming](https://mlsanity.com/paper/2307.07322/) (2023) - [A Distance Metric for Mixed Integer Programming Instances](https://mlsanity.com/paper/2507.11063/) (2025) - [Collab-Solver: Collaborative Solving Policy Learning for Mixed-Integer Linear Programming](https://mlsanity.com/paper/2508.03030/) (2025) - [Sequence-Structured Decision Learning for Branch-and-Bound in Mixed-Integer Linear Programming](https://mlsanity.com/paper/2610.14835/) (2026) ## Abstract (arXiv) Cutting plane selection is a subroutine used in all modern mixed-integer linear programming solvers with the goal of selecting a subset of generated cuts that induce optimal solver performance. These solvers have millions of parameter combinations, and so are excellent candidates for parameter tuning. Cut selection scoring rules are usually weighted sums of different measurements, where the weights are parameters. We present a parametric family of mixed-integer linear programs together with infinitely many family-wide valid cuts. Some of these cuts can induce integer optimal solutions directly after being applied, while others fail to do so even if an infinite amount are applied. We show for a specific cut selection rule, that any finite grid search of the parameter space will always miss all parameter values, which select integer optimal inducing cuts in an infinite amount of our problems. We propose a variation on the design of existing graph convolutional neural networks, adapting them to learn cut selection rule parameters. We present a reinforcement learning framework for selecting cuts, and train our design using said framework over MIPLIB 2017 and a neural network verification data set. Our framework and design show that adaptive cut selection does substantially improve performance over a diverse set of instances, but that finding a single function describing such a rule is difficult. Code for reproducing all experiments is available at https://github.com/Opt-Mucca/Adaptive-Cutsel-MILP.