# Machine Learning Augmented Branch and Bound for Mixed Integer Linear Programming

arXiv: https://arxiv.org/abs/2402.05501 · HTML: https://mlsanity.com/paper/2402.05501/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 109 references that are in the map.
- First posted on arXiv 8 Feb 2024.

## Builds on (most cited first, 30 of 38)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizon](https://mlsanity.com/paper/1811.06128/) (2018)
- [Exact Combinatorial Optimization with Graph Convolutional Neural Networks](https://mlsanity.com/paper/1906.01629/) (2019)
- [Combinatorial optimization and reasoning with graph neural networks](https://mlsanity.com/paper/2102.09544/) (2021)
- [Solving Mixed Integer Programs Using Neural Networks](https://mlsanity.com/paper/2012.13349/) (2020)
- [A Survey of Zero-shot Generalisation in Deep Reinforcement Learning](https://mlsanity.com/paper/2111.09794/) (2021)
- [Reinforcement Learning for Integer Programming: Learning to Cut](https://mlsanity.com/paper/1906.04859/) (2019)
- [Hybrid Models for Learning to Branch](https://mlsanity.com/paper/2006.15212/) (2020)
- [ParamILS: An Automatic Algorithm Configuration Framework](https://mlsanity.com/paper/1401.3492/) (2014)
- [Learning to Branch](https://mlsanity.com/paper/1803.10150/) (2018)
- [Parameterizing Branch-and-Bound Search Trees to Learn Branching Policies](https://mlsanity.com/paper/2002.05120/) (2020)
- [Learning To Cut By Looking Ahead: Cutting Plane Selection via Imitation Learning](https://mlsanity.com/paper/2206.13414/) (2022)
- [MIP-GNN: A Data-Driven Framework for Guiding Combinatorial Solvers](https://mlsanity.com/paper/2205.14210/) (2022)
- [Learning to Schedule Heuristics in Branch-and-Bound](https://mlsanity.com/paper/2103.10294/) (2021)
- [Learning to branch with Tree MDPs](https://mlsanity.com/paper/2205.11107/) (2022)
- [Learning Cut Selection for Mixed-Integer Linear Programming via Hierarchical Sequence Model](https://mlsanity.com/paper/2302.00244/) (2023)
- [Ecole: A Gym-like Library for Machine Learning in Combinatorial Optimization Solvers](https://mlsanity.com/paper/2011.06069/) (2020)
- [Learning a Large Neighborhood Search Algorithm for Mixed Integer Programs](https://mlsanity.com/paper/2107.10201/) (2021)
- [The Machine Learning for Combinatorial Optimization Competition (ML4CO): Results and Insights](https://mlsanity.com/paper/2203.02433/) (2022)
- [On Representing Linear Programs by Graph Neural Networks](https://mlsanity.com/paper/2209.12288/) (2022)
- [Searching Large Neighborhoods for Integer Linear Programs with Contrastive Learning](https://mlsanity.com/paper/2302.01578/) (2023)
- [Learning Large Neighborhood Search Policy for Integer Programming](https://mlsanity.com/paper/2111.03466/) (2021)
- [Sample Complexity of Tree Search Configuration: Cutting Planes and Beyond](https://mlsanity.com/paper/2106.04033/) (2021)
- [Learning to Compare Nodes in Branch and Bound with Graph Neural Networks](https://mlsanity.com/paper/2210.16934/) (2022)
- [Reinforcement Learning for Variable Selection in a Branch and Bound Algorithm](https://mlsanity.com/paper/2005.10026/) (2020)
- [Lookback for Learning to Branch](https://mlsanity.com/paper/2206.14987/) (2022)
- [Adaptive Cut Selection in Mixed-Integer Linear Programming](https://mlsanity.com/paper/2202.10962/) (2022)
- [Exploring the Power of Graph Neural Networks in Solving Linear Optimization Problems](https://mlsanity.com/paper/2310.10603/) (2023)
- [Machine Learning for Cutting Planes in Integer Programming: A Survey](https://mlsanity.com/paper/2302.09166/) (2023)
- [Theoretical challenges towards cutting-plane selection](https://mlsanity.com/paper/1805.02782/) (2018)

## Built on by (most cited first, 24 of 24)

- [Towards Foundation Models for Mixed Integer Linear Programming](https://mlsanity.com/paper/2410.08288/) (2024)
- [Apollo-MILP: An Alternating Prediction-Correction Neural Solving Framework for Mixed-Integer Linear Programming](https://mlsanity.com/paper/2503.01129/) (2025)
- [Distributional MIPLIB: a Multi-Domain Library for Advancing ML-Guided MILP Methods](https://mlsanity.com/paper/2406.06954/) (2024)
- [Multi-task Representation Learning for Mixed Integer Linear Programming](https://mlsanity.com/paper/2412.14409/) (2024)
- [Learning Cut Generating Functions for Integer Programming](https://mlsanity.com/paper/2405.13992/) (2024)
- [Leveraging Constraint Programming in a Deep Learning Approach for Dynamically Solving the Flexible Job-Shop Scheduling Problem](https://mlsanity.com/paper/2403.09249/) (2024)
- [Towards graph neural networks for provably solving convex optimization problems](https://mlsanity.com/paper/2502.02446/) (2025)
- [Understanding Generalization in Node and Link Prediction](https://mlsanity.com/paper/2507.00927/) (2025)
- [A Fair OR-ML Framework for Resource Substitution in Large-Scale Networks](https://mlsanity.com/paper/2511.18269/) (2025)
- [Learning optimal objective values for MILP](https://mlsanity.com/paper/2411.18321/) (2024)
- [Coherent Local Explanations for Mathematical Optimization](https://mlsanity.com/paper/2502.04840/) (2025)
- [A Denoising Diffusion-Based Evolutionary Algorithm Framework: Application to the Maximum Independent Set Problem](https://mlsanity.com/paper/2510.08627/) (2025)
- [A General Neural Backbone for Mixed-Integer Linear Optimization via Dual Attention](https://mlsanity.com/paper/2601.04509/) (2026)
- [Batched First-Order Methods for Parallel LP Solving in MIP](https://mlsanity.com/paper/2601.21990/) (2026)
- [Solving Max-Cut to Global Optimality via Feasibility-Preserving Graph Neural Networks](https://mlsanity.com/paper/2605.07113/) (2026)
- [Supplementary Materials to Graph Convolutional Branch and Bound](https://mlsanity.com/paper/2406.03099/) (2024)
- [A Distance Metric for Mixed Integer Programming Instances](https://mlsanity.com/paper/2507.11063/) (2025)
- [Collab-Solver: Collaborative Solving Policy Learning for Mixed-Integer Linear Programming](https://mlsanity.com/paper/2508.03030/) (2025)
- [HyP-ASO: A Hybrid Policy-based Adaptive Search Optimization Framework for Large-Scale Integer Linear Programs](https://mlsanity.com/paper/2509.15828/) (2025)
- [A Markov Decision Process for Variable Selection in Branch & Bound](https://mlsanity.com/paper/2510.19348/) (2025)
- [Machine Learning Guided Optimal Transmission Switching to Mitigate Wildfire Ignition Risk](https://mlsanity.com/paper/2510.25147/) (2025)
- [Imitation Learning for Combinatorial Optimisation under Uncertainty](https://mlsanity.com/paper/2601.05383/) (2026)
- [Graph Learning Should Move Beyond Restrictive Views of Spectral and Message-Passing GNNs](https://mlsanity.com/paper/2602.10031/) (2026)
- [Learning to Approximate Uniform Facility Location via Graph Neural Networks](https://mlsanity.com/paper/2602.13155/) (2026)

## 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.