Hybrid Models for Learning to Branch
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Abstract (arXiv)
A recent Graph Neural Network (GNN) approach for learning to branch has been shown to successfully reduce the running time of branch-and-bound algorithms for Mixed Integer Linear Programming (MILP). While the GNN relies on a GPU for inference, MILP solvers are purely CPU-based. This severely limits its application as many practitioners may not have access to high-end GPUs. In this work, we ask two key questions. First, in a more realistic setting where only a CPU is available, is the GNN model still competitive? Second, can we devise an alternate computationally inexpensive model that retains the predictive power of the GNN architecture? We answer the first question in the negative, and address the second question by proposing a new hybrid architecture for efficient branching on CPU machines. The proposed architecture combines the expressive power of GNNs with computationally inexpensive multi-layer perceptrons (MLP) for branching. We evaluate our methods on four classes of MILP problems, and show that they lead to up to 26% reduction in solver running time compared to state-of-the-art methods without a GPU, while extrapolating to harder problems than it was trained on. The code for this project is publicly available at https://github.com/pg2455/Hybrid-learn2branch.
Key facts. Cited by 95 papers in the map (data through 14 Oct 2026). First posted on arXiv 26 Jun 2020.
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Citing papers per year: 2021: 8; 2022: 24; 2023: 18; 2024: 20; 2025: 10; 2026: 15.
95 papers.
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- 2021Combinatorial optimization and reasoning with graph neural networkscited by 268
- 2021End-to-End Constrained Optimization Learning: A Surveycited by 157
- 2022MIP-GNN: A Data-Driven Framework for Guiding Combinatorial Solverscited by 49
- 2022Learning to branch with Tree MDPscited by 45
- 2022A Survey for Solving Mixed Integer Programming via Machine Learningcited by 44
- 2021Learning a Large Neighborhood Search Algorithm for Mixed Integer Programscited by 43
- 2023Let the Flows Tell: Solving Graph Combinatorial Optimization Problems with GFlowNetscited by 40
- 2022The Machine Learning for Combinatorial Optimization Competition (ML4CO): Results and Insightscited by 39
- 2022On Representing Linear Programs by Graph Neural Networkscited by 39
- 2023Searching Large Neighborhoods for Integer Linear Programs with Contrastive Learningcited by 37
- 2022Learning to Compare Nodes in Branch and Bound with Graph Neural Networkscited by 31
- 2024Towards Foundation Models for Mixed Integer Linear Programmingcited by 31
38 more
- 2022Lookback for Learning to Branchcited by 27
- 2023Exploring the Power of Graph Neural Networks in Solving Linear Optimization Problemscited by 24
- 2024Machine Learning Augmented Branch and Bound for Mixed Integer Linear Programmingcited by 24
- 2022On Representing Mixed-Integer Linear Programs by Graph Neural Networkscited by 23
- 2022Reinforcement Learning for Branch-and-Bound Optimisation using Retrospective Trajectoriescited by 20
- 2024PDHG-Unrolled Learning-to-Optimize Method for Large-Scale Linear Programmingcited by 17
- 2024MILP-StuDio: MILP Instance Generation via Block Structure Decompositioncited by 17
- 2024Expressive Power of Graph Neural Networks for (Mixed-Integer) Quadratic Programscited by 16
- 2025Apollo-MILP: An Alternating Prediction-Correction Neural Solving Framework for Mixed-Integer Linear Programmingcited by 16
- 2024Distributional MIPLIB: a Multi-Domain Library for Advancing ML-Guided MILP Methodscited by 15
- 2022An Improved Reinforcement Learning Algorithm for Learning to Branchcited by 14
- 2022Learning to Solve Combinatorial Graph Partitioning Problems via Efficient Explorationcited by 14
- 2023Learning to Configure Separators in Branch-and-Cutcited by 14
- 2021Improved Sample Complexity Bounds for Branch-and-Cutcited by 13
- 2023Promoting Generalization for Exact Solvers via Adversarial Instance Augmentationcited by 12
- 2024Rethinking the Capacity of Graph Neural Networks for Branching Strategycited by 12
- 2023Are Graph Neural Networks Optimal Approximation Algorithms?cited by 11
- 2024Artificial Intelligence for Operations Research: Revolutionizing the Operations Research Processcited by 11
- 2022Learning to Reformulate for Linear Programmingcited by 10
- 2023Learning To Dive In Branch And Boundcited by 10
- 2024CAMBranch: Contrastive Learning with Augmented MILPs for Branchingcited by 10
- 2021Learning to Sparsify Travelling Salesman Problem Instancescited by 9
- 2021Branch and Bound in Mixed Integer Linear Programming Problems: A Survey of Techniques and Trendscited by 9
- 2024SORREL: Suboptimal-Demonstration-Guided Reinforcement Learning for Learning to Branchcited by 9
- 2024Learning to Stop Cut Generation for Efficient Mixed-Integer Linear Programmingcited by 8
- 2024Machine Learning Insides OptVerse AI Solver: Design Principles and Applicationscited by 7
- 2024Optimization by Parallel Quasi-Quantum Annealing with Gradient-Based Samplingcited by 7
- 2022Learning for Spatial Branching: An Algorithm Selection Approachcited by 6
- 2022DOGE-Train: Discrete Optimization on GPU with End-to-end Trainingcited by 6
- 2023NN-Steiner: A Mixed Neural-algorithmic Approach for the Rectilinear Steiner Minimum Tree Problemcited by 6
- 2024Metric Learning to Accelerate Convergence of Operator Splitting Methods for Differentiable Parametric Programmingcited by 6
- 2022Confidence Threshold Neural Divingcited by 5
- 2023Taking the human out of decomposition-based optimization via artificial intelligence: Part II. Learning to initializecited by 5
- 2024Learning Backdoors for Mixed Integer Linear Programs with Contrastive Learningcited by 5
- 2021ML4CO: Is GCNN All You Need? Graph Convolutional Neural Networks Produce Strong Baselines For Combinatorial Optimization Problems, If Tuned and Trained Properly, on Appropriate Datacited by 4
- 2023A Neural Separation Algorithm for the Rounded Capacity Inequalitiescited by 4
- 2023Learning to Branch in Combinatorial Optimization with Graph Pointer Networkscited by 4
- 2024Learning to Remove Cuts in Integer Linear Programmingcited by 4
50 most cited of 95 All 95 (JSON)
- 2026Reformulation-Contrastive Learning for Mixed Integer Programs30 Sep 2026
- 2026BiFE: Search-Efficient Discovery of CPU-Only Branching Policies via LLM-based Bi-Fidelity Evolution29 Sep 2026
- 2026SHSP: Structure-Aware Hierarchical Solution Prediction for Mixed-Integer Linear Programming26 Aug 2026
- 2026Constrained Graph Diffusion for Mixed Integer Optimization13 Aug 2026
- 2026A Weisfeiler-Leman Characterization of Global-Attention Graph Transformers for Mixed-Integer Linear Programs20 Jul 2026
- 2026Fusing Backdoors, Machine Learning, and Optimization for Large-Scale Parametric Mixed-Integer Programs19 Jun 2026
- 2026MILP-Evo: Closed-Loop Fully Automatic Design of MILP Solvers12 May 2026
- 2026LLM4Branch: Large Language Model for Discovering Efficient Branching Policies of Integer Programs11 May 2026
- 2026Agentic MIP Research: Accelerated Constraint Handler Generation9 May 2026
- 2026Speeding Up Mixed-Integer Programming Solvers with Sparse Learning for Branching31 Mar 2026
- 2026SRG: Score-based Relaxation-guided Generation for Mixed Integer Linear Programming25 Mar 2026
- 2026Towards Solving Polynomial-Objective Integer Programming with Hypergraph Neural Networks16 Mar 2026
38 more
- 2026Learning Structural Hardness for Combinatorial Auctions: Instance-Dependent Algorithm Selection via Graph Neural Networks16 Feb 2026
- 2026Batched First-Order Methods for Parallel LP Solving in MIP29 Jan 2026
- 2026A General Neural Backbone for Mixed-Integer Linear Optimization via Dual Attention8 Jan 2026
- 2025Branching Strategies Based on Subgraph GNNs: A Study on Theoretical Promise versus Practical Reality10 Dec 2025
- 2025Dynamic Stratified Contrastive Learning with Upstream Augmentation for MILP Branching26 Nov 2025
- 2025A Neural Network Framework for Discovering Closed-form Solutions to Quadratic Programs with Linear Constraints27 Oct 2025
- 2025Edge-Selector Model Applied for Local Search Neighborhood for Solving Vehicle Routing Problems12 Aug 2025
- 2025FMIP: Joint Continuous-Integer Flow For Mixed-Integer Linear Programming31 Jul 2025
- 2025DualSchool: How Reliable are LLMs for Optimization Education?27 May 2025
- 2025Towards VM Rescheduling Optimization Through Deep Reinforcement Learning23 May 2025
- 2025Code Retrieval for MILP Instance Generation11 May 2025
- 2025PROPEL: Supervised and Reinforcement Learning for Large-Scale Supply Chain Planning10 Apr 2025
- 2025Apollo-MILP: An Alternating Prediction-Correction Neural Solving Framework for Mixed-Integer Linear Programming3 Mar 2025
- 2024SORREL: Suboptimal-Demonstration-Guided Reinforcement Learning for Learning to Branch20 Dec 2024
- 2024RL-SPH: Learning to Achieve Feasible Solutions for Integer Linear Programs29 Nov 2024
- 2024MILP-StuDio: MILP Instance Generation via Block Structure Decomposition30 Oct 2024
- 2024Towards Foundation Models for Mixed Integer Linear Programming10 Oct 2024
- 2024Optimization by Parallel Quasi-Quantum Annealing with Gradient-Based Sampling2 Sep 2024
- 2024Robotic warehousing operations: a learn-then-optimize approach to large-scale neighborhood search29 Aug 2024
- 2024Learning to Remove Cuts in Integer Linear Programming26 Jun 2024
- 2024Distributional MIPLIB: a Multi-Domain Library for Advancing ML-Guided MILP Methods11 Jun 2024
- 2024Expressive Power of Graph Neural Networks for (Mixed-Integer) Quadratic Programs9 Jun 2024
- 2024PDHG-Unrolled Learning-to-Optimize Method for Large-Scale Linear Programming4 Jun 2024
- 2024Metric Learning to Accelerate Convergence of Operator Splitting Methods for Differentiable Parametric Programming1 Apr 2024
- 2024Machina Economicus: A New Paradigm for Prosumers in the Energy Internet of Smart Cities28 Feb 2024
- 2024Accelerating data-driven algorithm selection for combinatorial partitioning problems22 Feb 2024
- 2024Rethinking the Capacity of Graph Neural Networks for Branching Strategy11 Feb 2024
- 2024Machine Learning Augmented Branch and Bound for Mixed Integer Linear Programming8 Feb 2024
- 2024CAMBranch: Contrastive Learning with Augmented MILPs for Branching6 Feb 2024
- 2024Learning to Stop Cut Generation for Efficient Mixed-Integer Linear Programming31 Jan 2024
- 2024Learning Backdoors for Mixed Integer Linear Programs with Contrastive Learning19 Jan 2024
- 2024Machine Learning Insides OptVerse AI Solver: Design Principles and Applications11 Jan 2024
- 2024Artificial Intelligence for Operations Research: Revolutionizing the Operations Research Process6 Jan 2024
- 2023NN-Steiner: A Mixed Neural-algorithmic Approach for the Rectilinear Steiner Minimum Tree Problem17 Dec 2023
- 2023Solve Large-scale Unit Commitment Problems by Physics-informed Graph Learning26 Nov 2023
- 2023Exact Combinatorial Optimization with Temporo-Attentional Graph Neural Networks23 Nov 2023
- 2023Learning to Configure Separators in Branch-and-Cut8 Nov 2023
- 2023Promoting Generalization for Exact Solvers via Adversarial Instance Augmentation22 Oct 2023
50 newest of 95 All 95 (JSON)
- 2022An Improved Reinforcement Learning Algorithm for Learning to Branchcited by 14
- 2024CAMBranch: Contrastive Learning with Augmented MILPs for Branchingcited by 10
- 2024SORREL: Suboptimal-Demonstration-Guided Reinforcement Learning for Learning to Branchcited by 9
- 2022Yordle: An Efficient Imitation Learning for Branch and Boundcited by 2
- 2022Branch Ranking for Efficient Mixed-Integer Programming via Offline Ranking-based Policy Learningcited by 2
- 2024SORREL: Suboptimal-Demonstration-Guided Reinforcement Learning for Learning to Branch20 Dec 2024
- 2024CAMBranch: Contrastive Learning with Augmented MILPs for Branching6 Feb 2024
- 2022Branch Ranking for Efficient Mixed-Integer Programming via Offline Ranking-based Policy Learning26 Jul 2022
- 2022Yordle: An Efficient Imitation Learning for Branch and Bound2 Feb 2022
- 2022An Improved Reinforcement Learning Algorithm for Learning to Branch17 Jan 2022
- 2021Combinatorial optimization and reasoning with graph neural networkscited by 268
- 2021End-to-End Constrained Optimization Learning: A Surveycited by 157
- 2022MIP-GNN: A Data-Driven Framework for Guiding Combinatorial Solverscited by 49
- 2022Learning to branch with Tree MDPscited by 45
- 2022A Survey for Solving Mixed Integer Programming via Machine Learningcited by 44
- 2021Learning a Large Neighborhood Search Algorithm for Mixed Integer Programscited by 43
- 2023Let the Flows Tell: Solving Graph Combinatorial Optimization Problems with GFlowNetscited by 40
- 2022The Machine Learning for Combinatorial Optimization Competition (ML4CO): Results and Insightscited by 39
- 2022On Representing Linear Programs by Graph Neural Networkscited by 39
- 2023Searching Large Neighborhoods for Integer Linear Programs with Contrastive Learningcited by 37
- 2022Learning to Compare Nodes in Branch and Bound with Graph Neural Networkscited by 31
- 2024Towards Foundation Models for Mixed Integer Linear Programmingcited by 31
12 most cited of 87 All 87 (JSON)
- 2026Reformulation-Contrastive Learning for Mixed Integer Programs30 Sep 2026
- 2026BiFE: Search-Efficient Discovery of CPU-Only Branching Policies via LLM-based Bi-Fidelity Evolution29 Sep 2026
- 2026SHSP: Structure-Aware Hierarchical Solution Prediction for Mixed-Integer Linear Programming26 Aug 2026
- 2026Constrained Graph Diffusion for Mixed Integer Optimization13 Aug 2026
- 2026A Weisfeiler-Leman Characterization of Global-Attention Graph Transformers for Mixed-Integer Linear Programs20 Jul 2026
- 2026Fusing Backdoors, Machine Learning, and Optimization for Large-Scale Parametric Mixed-Integer Programs19 Jun 2026
- 2026MILP-Evo: Closed-Loop Fully Automatic Design of MILP Solvers12 May 2026
- 2026LLM4Branch: Large Language Model for Discovering Efficient Branching Policies of Integer Programs11 May 2026
- 2026Speeding Up Mixed-Integer Programming Solvers with Sparse Learning for Branching31 Mar 2026
- 2026SRG: Score-based Relaxation-guided Generation for Mixed Integer Linear Programming25 Mar 2026
- 2026Towards Solving Polynomial-Objective Integer Programming with Hypergraph Neural Networks16 Mar 2026
- 2026Learning Structural Hardness for Combinatorial Auctions: Instance-Dependent Algorithm Selection via Graph Neural Networks16 Feb 2026
12 newest of 87 All 87 (JSON)