mlsanityData to 14 Oct 2026

MIP-GNN: A Data-Driven Framework for Guiding Combinatorial Solvers

arXiv 2205.14210 ↗First posted 27 May 2022cs.LG cs.NE math.OCcited by 49

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Abstract (arXiv)

Mixed-integer programming (MIP) technology offers a generic way of formulating and solving combinatorial optimization problems. While generally reliable, state-of-the-art MIP solvers base many crucial decisions on hand-crafted heuristics, largely ignoring common patterns within a given instance distribution of the problem of interest. Here, we propose MIP-GNN, a general framework for enhancing such solvers with data-driven insights. By encoding the variable-constraint interactions of a given mixed-integer linear program (MILP) as a bipartite graph, we leverage state-of-the-art graph neural network architectures to predict variable biases, i.e., component-wise averages of (near) optimal solutions, indicating how likely a variable will be set to 0 or 1 in (near) optimal solutions of binary MILPs. In turn, the predicted biases stemming from a single, once-trained model are used to guide the solver, replacing heuristic components. We integrate MIP-GNN into a state-of-the-art MIP solver, applying it to tasks such as node selection and warm-starting, showing significant improvements compared to the default setting of the solver on two classes of challenging binary MILPs.

Key facts. Cited by 49 papers in the map (data through 14 Oct 2026). Builds on 35 of its 70 references that are in the map. First posted on arXiv 27 May 2022.

Builds on

35 of 70 references.

References · 35

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 4; 2023: 7; 2024: 14; 2025: 15; 2026: 9.

49 papers.

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  1. 2022On Representing Linear Programs by Graph Neural Networkscited by 39
  2. 2022Lookback for Learning to Branchcited by 27
  3. 2023Exploring the Power of Graph Neural Networks in Solving Linear Optimization Problemscited by 24
  4. 2024Machine Learning Augmented Branch and Bound for Mixed Integer Linear Programmingcited by 24
  5. 2022On Representing Mixed-Integer Linear Programs by Graph Neural Networkscited by 23
  6. 2023A Deep Instance Generative Framework for MILP Solvers Under Limited Data Availabilitycited by 21
  7. 2023Machine Learning for Cutting Planes in Integer Programming: A Surveycited by 20
  8. 2024Graph Reinforcement Learning for Combinatorial Optimization: A Survey and Unifying Perspectivecited by 16
  9. 2024Expressive Power of Graph Neural Networks for (Mixed-Integer) Quadratic Programscited by 16
  10. 2025Apollo-MILP: An Alternating Prediction-Correction Neural Solving Framework for Mixed-Integer Linear Programmingcited by 16
  11. 2024Distributional MIPLIB: a Multi-Domain Library for Advancing ML-Guided MILP Methodscited by 15
  12. 2024Rethinking the Capacity of Graph Neural Networks for Branching Strategycited by 12
37 more
  1. 2024From Large Language Models and Optimization to Decision Optimization CoPilot: A Research Manifestocited by 11
  2. 2024Effective Generation of Feasible Solutions for Integer Programming via Guided Diffusioncited by 8
  3. 2024Learning to Optimize for Mixed-Integer Non-linear Programming with Feasibility Guaranteescited by 8
  4. 2024LLMs for Cold-Start Cutting Plane Separator Configurationcited by 8
  5. 2024Multi-task Representation Learning for Mixed Integer Linear Programmingcited by 7
  6. 2025Towards graph neural networks for provably solving convex optimization problemscited by 4
  7. 2025PROPEL: Supervised and Reinforcement Learning for Large-Scale Supply Chain Planningcited by 4
  8. 2025Learning from Algorithm Feedback: One-Shot SAT Solver Guidance with GNNscited by 4
  9. 2025CoCo-MILP: Inter-Variable Contrastive and Intra-Constraint Competitive MILP Solution Predictioncited by 4
  10. 2025When GNNs meet symmetry in ILPs: an orbit-based feature augmentation approachcited by 3
  11. 2025STRCMP: Integrating Graph Structural Priors with Language Models for Combinatorial Optimizationcited by 3
  12. 2025RoME: Domain-Robust Mixture-of-Experts for MILP Solution Prediction across Domainscited by 3
  13. 2022Machine Learning for K-adaptability in Two-stage Robust Optimizationcited by 2
  14. 2025Principled Data Augmentation for Learning to Solve Quadratic Programming Problemscited by 2
  15. 2025Constraint Matters: Multi-Modal Representation for Reducing Mixed-Integer Linear programmingcited by 2
  16. 2023Graph Neural Networks for the Offline Nanosatellite Task Scheduling Problemcited by 1
  17. 2023Data-driven Mixed Integer Optimization through Probabilistic Multi-variable Branchingcited by 1
  18. 2023Threshold-aware Learning to Generate Feasible Solutions for Mixed Integer Programscited by 1
  19. 2024Learning optimal objective values for MILPcited by 1
  20. 2025BenLOC: A Benchmark for Learning to Configure MIP Optimizerscited by 1
  21. 2025Unsupervised Learning for the Elementary Shortest Path Problemcited by 1
  22. 2025Dynamic Stratified Contrastive Learning with Upstream Augmentation for MILP Branchingcited by 1
  23. 2026A General Neural Backbone for Mixed-Integer Linear Optimization via Dual Attentioncited by 1
  24. 2026On the Expressive Power of GNNs to Solve Linear SDPscited by 1
  25. 2026Solving Max-Cut to Global Optimality via Feasibility-Preserving Graph Neural Networkscited by 1
  26. 2023The logic of rational graph neural networkscited by 0
  27. 2024Supplementary Materials to Graph Convolutional Branch and Boundcited by 0
  28. 2024An Unsupervised Learning Framework Combined with Heuristics for the Maximum Minimal Cut Problemcited by 0
  29. 2024Learn2Aggregate: Supervised Generation of Chv'atal-Gomory Cuts Using Graph Neural Networkscited by 0
  30. 2025BIPNN: Learning to Solve Binary Integer Programming via Hypergraph Neural Networkscited by 0
  31. 2025Feature Augmentation of GNNs for ILPs: Local Uniqueness Sufficescited by 0
  32. 2026Imitation Learning for Combinatorial Optimisation under Uncertaintycited by 0
  33. 2026Learning to Approximate Uniform Facility Location via Graph Neural Networkscited by 0
  34. 2026Deep Learning for Sequential Decision Making under Uncertainty: Foundations, Frameworks, and Frontierscited by 0
  35. 2026Target-Aware Data Augmentation for SAT Predictioncited by 0
  36. 2026Fusing Backdoors, Machine Learning, and Optimization for Large-Scale Parametric Mixed-Integer Programscited by 0
  37. 2026Autoregressive Differentiable Method for Integer Programmingcited by 0