mlsanityData to 7 Oct 2026

Machine Learning for Cutting Planes in Integer Programming: A Survey

arXiv 2302.09166 ↗First posted 17 Feb 2023math.OC cs.AI cs.LGcited by 19

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Abstract (arXiv)

We survey recent work on machine learning (ML) techniques for selecting cutting planes (or cuts) in mixed-integer linear programming (MILP). Despite the availability of various classes of cuts, the task of choosing a set of cuts to add to the linear programming (LP) relaxation at a given node of the branch-and-bound (B&B) tree has defied both formal and heuristic solutions to date. ML offers a promising approach for improving the cut selection process by using data to identify promising cuts that accelerate the solution of MILP instances. This paper presents an overview of the topic, highlighting recent advances in the literature, common approaches to data collection, evaluation, and ML model architectures. We analyze the empirical results in the literature in an attempt to quantify the progress that has been made and conclude by suggesting avenues for future research.

Key facts. Cited by 19 papers in the map (data through 7 Oct 2026). Builds on 27 of its 61 references that are in the map. First posted on arXiv 17 Feb 2023.

Builds on

27 of 61 references.

References · 27

  1. 2018Attention-based Deep Multiple Instance Learningcited by 1,077
  2. 2015Pointer Networkscited by 882
  3. 2018Attention, Learn to Solve Routing Problems!cited by 646
  4. 2018Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizoncited by 612
  5. 2016Neural Combinatorial Optimization with Reinforcement Learningcited by 600
  6. 2019Exact Combinatorial Optimization with Graph Convolutional Neural Networkscited by 313
  7. 2021Combinatorial optimization and reasoning with graph neural networkscited by 267
  8. 2020Reinforcement Learning for Combinatorial Optimization: A Surveycited by 235
  9. 2021SMAC3: A Versatile Bayesian Optimization Package for Hyperparameter Optimizationcited by 229
  10. 2020Solving Mixed Integer Programs Using Neural Networkscited by 178
  11. 2021End-to-End Constrained Optimization Learning: A Surveycited by 154
  12. 2019Reinforcement Learning for Integer Programming: Learning to Cutcited by 108
15 more
  1. 2020Parameterizing Branch-and-Bound Search Trees to Learn Branching Policiescited by 62
  2. 2022Learning To Cut By Looking Ahead: Cutting Plane Selection via Imitation Learningcited by 58
  3. 2021Learning to Select Cuts for Efficient Mixed-Integer Programmingcited by 48
  4. 2022MIP-GNN: A Data-Driven Framework for Guiding Combinatorial Solverscited by 48
  5. 2021Learning to Schedule Heuristics in Branch-and-Boundcited by 45
  6. 2023Learning Cut Selection for Mixed-Integer Linear Programming via Hierarchical Sequence Modelcited by 44
  7. 2021Sample Complexity of Tree Search Configuration: Cutting Planes and Beyondcited by 33
  8. 2019How much data is sufficient to learn high-performing algorithms? Generalization guarantees for data-driven algorithm designcited by 27
  9. 2022Adaptive Cut Selection in Mixed-Integer Linear Programmingcited by 25
  10. 2022Structural Analysis of Branch-and-Cut and the Learnability of Gomory Mixed Integer Cutscited by 19
  11. 2018Theoretical challenges towards cutting-plane selectioncited by 16
  12. 2022Learning to Use Local Cutscited by 11
  13. 2019Benders Cut Classification via Support Vector Machines for Solving Two-stage Stochastic Programscited by 7
  14. 2020On a reduction for a class of resource allocation problemscited by 6
  15. 2022Cutting Plane Selection with Analytic Centers and Multiregressioncited by 4

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 4; 2024: 9; 2025: 2; 2026: 4.

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  1. 2023Exploring the Power of Graph Neural Networks in Solving Linear Optimization Problemscited by 24
  2. 2024Machine Learning Augmented Branch and Bound for Mixed Integer Linear Programmingcited by 24
  3. 2024Learning to optimize: A tutorial for continuous and mixed-integer optimizationcited by 8
  4. 2024Learning to Optimize for Mixed-Integer Non-linear Programming with Feasibility Guaranteescited by 8
  5. 2024Sample Complexity of Algorithm Selection Using Neural Networks and Its Applications to Branch-and-Cutcited by 7
  6. 2024Metric Learning to Accelerate Convergence of Operator Splitting Methods for Differentiable Parametric Programmingcited by 6
  7. 2023Predict-Then-Optimize by Proxy: Learning Joint Models of Prediction and Optimizationcited by 4
  8. 2024Learning to Remove Cuts in Integer Linear Programmingcited by 4
  9. 2023Differentiable Cutting-plane Layers for Mixed-integer Linear Optimizationcited by 3
  10. 2024Adaptive Stabilization Based on Machine Learning for Column Generationcited by 3
  11. 2025How hard is learning to cut? Trade-offs and sample complexitycited by 1
  12. 2023A Context-Aware Cutting Plane Selection Algorithm for Mixed-Integer Programmingcited by 0
7 more
  1. 2024Subsampled Ensemble Can Improve Generalization Tail Exponentiallycited by 0
  2. 2024Towards An Unsupervised Learning Scheme for Efficiently Solving Parameterized Mixed-Integer Programscited by 0
  3. 2025Quantum-Inspired DRL Approach with LSTM and OU Noise for Cut Order Planning Optimizationcited by 0
  4. 2026Imitation Learning for Combinatorial Optimisation under Uncertaintycited by 0
  5. 2026Designing faster mixed integer linear programming algorithm via learning the optimal pathcited by 0
  6. 2026Towards Solving Polynomial-Objective Integer Programming with Hypergraph Neural Networkscited by 0
  7. 2026Solving Max-Cut to Global Optimality via Feasibility-Preserving Graph Neural Networkscited by 0