mlsanityData to 7 Oct 2026

Machine Learning Augmented Branch and Bound for Mixed Integer Linear Programming

arXiv 2402.05501 ↗First posted 8 Feb 2024math.OC cs.LGcited by 24

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Abstract (arXiv)

Mixed Integer Linear Programming (MILP) is a pillar of mathematical optimization that offers a powerful modeling language for a wide range of applications. During the past decades, enormous algorithmic progress has been made in solving MILPs, and many commercial and academic software packages exist. Nevertheless, the availability of data, both from problem instances and from solvers, and the desire to solve new problems and larger (real-life) instances, trigger the need for continuing algorithmic development. MILP solvers use branch and bound as their main component. In recent years, there has been an explosive development in the use of machine learning algorithms for enhancing all main tasks involved in the branch-and-bound algorithm, such as primal heuristics, branching, cutting planes, node selection and solver configuration decisions. This paper presents a survey of such approaches, addressing the vision of integration of machine learning and mathematical optimization as complementary technologies, and how this integration can benefit MILP solving. In particular, we give detailed attention to machine learning algorithms that automatically optimize some metric of branch-and-bound efficiency. We also address how to represent MILPs in the context of applying learning algorithms, MILP benchmarks and software.

Key facts. Cited by 24 papers in the map (data through 7 Oct 2026). Builds on 38 of its 109 references that are in the map. First posted on arXiv 8 Feb 2024.

Builds on

38 of 109 references.

References · 38

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  3. 2019Exact Combinatorial Optimization with Graph Convolutional Neural Networkscited by 313
  4. 2021Combinatorial optimization and reasoning with graph neural networkscited by 267
  5. 2020Solving Mixed Integer Programs Using Neural Networkscited by 178
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  11. 2020Parameterizing Branch-and-Bound Search Trees to Learn Branching Policiescited by 62
  12. 2022Learning To Cut By Looking Ahead: Cutting Plane Selection via Imitation Learningcited by 58
26 more
  1. 2022MIP-GNN: A Data-Driven Framework for Guiding Combinatorial Solverscited by 48
  2. 2021Learning to Schedule Heuristics in Branch-and-Boundcited by 45
  3. 2022Learning to branch with Tree MDPscited by 45
  4. 2023Learning Cut Selection for Mixed-Integer Linear Programming via Hierarchical Sequence Modelcited by 44
  5. 2020Ecole: A Gym-like Library for Machine Learning in Combinatorial Optimization Solverscited by 43
  6. 2021Learning a Large Neighborhood Search Algorithm for Mixed Integer Programscited by 41
  7. 2022The Machine Learning for Combinatorial Optimization Competition (ML4CO): Results and Insightscited by 39
  8. 2022On Representing Linear Programs by Graph Neural Networkscited by 39
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  10. 2021Learning Large Neighborhood Search Policy for Integer Programmingcited by 35
  11. 2021Sample Complexity of Tree Search Configuration: Cutting Planes and Beyondcited by 33
  12. 2022Learning to Compare Nodes in Branch and Bound with Graph Neural Networkscited by 30
  13. 2020Reinforcement Learning for Variable Selection in a Branch and Bound Algorithmcited by 28
  14. 2022Lookback for Learning to Branchcited by 26
  15. 2022Adaptive Cut Selection in Mixed-Integer Linear Programmingcited by 25
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  18. 2018Theoretical challenges towards cutting-plane selectioncited by 16
  19. 2020A Study of Learning Search Approximation in Mixed Integer Branch and Bound: Node Selection in SCIPcited by 16
  20. 2023Learning to Configure Separators in Branch-and-Cutcited by 14
  21. 2021Finding Backdoors to Integer Programs: A Monte Carlo Tree Search Frameworkcited by 12
  22. 2022Learning to Use Local Cutscited by 11
  23. 2023Online Learning for Scheduling MIP Heuristicscited by 6
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 7; 2025: 11; 2026: 6.

24 papers.

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  1. 2024Towards Foundation Models for Mixed Integer Linear Programmingcited by 30
  2. 2025Apollo-MILP: An Alternating Prediction-Correction Neural Solving Framework for Mixed-Integer Linear Programmingcited by 16
  3. 2024Distributional MIPLIB: a Multi-Domain Library for Advancing ML-Guided MILP Methodscited by 15
  4. 2024Multi-task Representation Learning for Mixed Integer Linear Programmingcited by 6
  5. 2024Learning Cut Generating Functions for Integer Programmingcited by 5
  6. 2024Leveraging Constraint Programming in a Deep Learning Approach for Dynamically Solving the Flexible Job-Shop Scheduling Problemcited by 4
  7. 2025Towards graph neural networks for provably solving convex optimization problemscited by 4
  8. 2025Understanding Generalization in Node and Link Predictioncited by 2
  9. 2025A Fair OR-ML Framework for Resource Substitution in Large-Scale Networkscited by 2
  10. 2024Learning optimal objective values for MILPcited by 1
  11. 2025Coherent Local Explanations for Mathematical Optimizationcited by 1
  12. 2025A Denoising Diffusion-Based Evolutionary Algorithm Framework: Application to the Maximum Independent Set Problemcited by 1
12 more
  1. 2026A General Neural Backbone for Mixed-Integer Linear Optimization via Dual Attentioncited by 1
  2. 2026Batched First-Order Methods for Parallel LP Solving in MIPcited by 1
  3. 2024Supplementary Materials to Graph Convolutional Branch and Boundcited by 0
  4. 2025A Distance Metric for Mixed Integer Programming Instancescited by 0
  5. 2025Collab-Solver: Collaborative Solving Policy Learning for Mixed-Integer Linear Programmingcited by 0
  6. 2025HyP-ASO: A Hybrid Policy-based Adaptive Search Optimization Framework for Large-Scale Integer Linear Programscited by 0
  7. 2025A Markov Decision Process for Variable Selection in Branch & Boundcited by 0
  8. 2025Machine Learning Guided Optimal Transmission Switching to Mitigate Wildfire Ignition Riskcited by 0
  9. 2026Imitation Learning for Combinatorial Optimisation under Uncertaintycited by 0
  10. 2026Graph Learning Should Move Beyond Restrictive Views of Spectral and Message-Passing GNNscited by 0
  11. 2026Learning to Approximate Uniform Facility Location via Graph Neural Networkscited by 0
  12. 2026Solving Max-Cut to Global Optimality via Feasibility-Preserving Graph Neural Networkscited by 0