mlsanityData to 14 Oct 2026

A GNN-Guided Predict-and-Search Framework for Mixed-Integer Linear Programming

arXiv 2302.05636 ↗First posted 11 Feb 2023math.OCcited by 41

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Abstract (arXiv)

Mixed-integer linear programming (MILP) is widely employed for modeling combinatorial optimization problems. In practice, similar MILP instances with only coefficient variations are routinely solved, and machine learning (ML) algorithms are capable of capturing common patterns across these MILP instances. In this work, we combine ML with optimization and propose a novel predict-and-search framework for efficiently identifying high-quality feasible solutions. Specifically, we first utilize graph neural networks to predict the marginal probability of each variable, and then search for the best feasible solution within a properly defined ball around the predicted solution. We conduct extensive experiments on public datasets, and computational results demonstrate that our proposed framework achieves 51.1% and 9.9% performance improvements to MILP solvers SCIP and Gurobi on primal gaps, respectively.

Key facts. Cited by 41 papers in the map (data through 14 Oct 2026). First posted on arXiv 11 Feb 2023.

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 4; 2024: 8; 2025: 16; 2026: 13.

41 papers.

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  1. 2023A Deep Instance Generative Framework for MILP Solvers Under Limited Data Availabilitycited by 21
  2. 2024MILP-StuDio: MILP Instance Generation via Block Structure Decompositioncited by 17
  3. 2025Apollo-MILP: An Alternating Prediction-Correction Neural Solving Framework for Mixed-Integer Linear Programmingcited by 16
  4. 2024Distributional MIPLIB: a Multi-Domain Library for Advancing ML-Guided MILP Methodscited by 15
  5. 2024Learning to Optimize for Mixed-Integer Non-linear Programming with Feasibility Guaranteescited by 8
  6. 2024Multi-task Representation Learning for Mixed Integer Linear Programmingcited by 7
  7. 2024Learning Backdoors for Mixed Integer Linear Programs with Contrastive Learningcited by 5
  8. 2025Towards graph neural networks for provably solving convex optimization problemscited by 4
  9. 2025PROPEL: Supervised and Reinforcement Learning for Large-Scale Supply Chain Planningcited by 4
  10. 2025When GNNs meet symmetry in ILPs: an orbit-based feature augmentation approachcited by 3
  11. 2025RoME: Domain-Robust Mixture-of-Experts for MILP Solution Prediction across Domainscited by 3
  12. 2023Graph-SCP: Accelerating Set Cover Problems with Graph Neural Networkscited by 2
29 more
  1. 2025Constraint Matters: Multi-Modal Representation for Reducing Mixed-Integer Linear programmingcited by 2
  2. 2025FORGE: Foundational Optimization Representations from Graph Embeddingscited by 2
  3. 2025Enforcing convex constraints in Graph Neural Networkscited by 2
  4. 2023Graph Neural Networks for the Offline Nanosatellite Task Scheduling Problemcited by 1
  5. 2023Data-driven Mixed Integer Optimization through Probabilistic Multi-variable Branchingcited by 1
  6. 2024Network Interdiction Goes Neuralcited by 1
  7. 2024Learning optimal objective values for MILPcited by 1
  8. 2024RL-SPH: Learning to Achieve Feasible Solutions for Integer Linear Programscited by 1
  9. 2025ASAP: Exploiting the Satisficing Generalization Edge in Neural Combinatorial Optimizationcited by 1
  10. 2025Code Retrieval for MILP Instance Generationcited by 1
  11. 2025ID-PaS+ : Identity-Aware Predict-and-Search for General Mixed-Integer Linear Programscited by 1
  12. 2026A General Neural Backbone for Mixed-Integer Linear Optimization via Dual Attentioncited by 1
  13. 2025FMIP: Joint Continuous-Integer Flow For Mixed-Integer Linear Programmingcited by 0
  14. 2025HyP-ASO: A Hybrid Policy-based Adaptive Search Optimization Framework for Large-Scale Integer Linear Programscited by 0
  15. 2025Feature Augmentation of GNNs for ILPs: Local Uniqueness Sufficescited by 0
  16. 2025Machine Learning Guided Optimal Transmission Switching to Mitigate Wildfire Ignition Riskcited by 0
  17. 2025Neural Tractability via Structure: Learning-Augmented Algorithms for Graph Combinatorial Optimizationcited by 0
  18. 2026Imitation Learning for Combinatorial Optimisation under Uncertaintycited by 0
  19. 2026Enhancing Genetic Algorithms with Graph Neural Networks: A Timetabling Case Studycited by 0
  20. 2026Learning to Solve Orienteering Problem with Time Windows and Variable Profitscited by 0
  21. 2026Towards Solving Polynomial-Objective Integer Programming with Hypergraph Neural Networkscited by 0
  22. 2026SRG: Score-based Relaxation-guided Generation for Mixed Integer Linear Programmingcited by 0
  23. 2026Differentiable Initialization-Accelerated CPU-GPU Hybrid Combinatorial Schedulingcited by 0
  24. 2026Solving Integer Linear Programming with Parallel Temperingcited by 0
  25. 2026Fusing Backdoors, Machine Learning, and Optimization for Large-Scale Parametric Mixed-Integer Programscited by 0
  26. 2026Graph4BiLO: Graph Neural Network Approximation for Bilevel Mixed-Integer Linear Optimizationcited by 0
  27. 2026Autoresearch in Mixed-Integer Linear and Nonlinear Programmingcited by 0
  28. 2026Reformulation-Contrastive Learning for Mixed Integer Programscited by 0
  29. 2026Autoregressive Differentiable Method for Integer Programmingcited by 0