# Speeding Up Mixed-Integer Programming Solvers with Sparse Learning for Branching

arXiv: https://arxiv.org/abs/2604.00094 · HTML: https://mlsanity.com/paper/2604.00094/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 50 references that are in the map.
- First posted on arXiv 31 Mar 2026.

## Builds on (most cited first, 19 of 19)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Exact Combinatorial Optimization with Graph Convolutional Neural Networks](https://mlsanity.com/paper/1906.01629/) (2019)
- [Solving Mixed Integer Programs Using Neural Networks](https://mlsanity.com/paper/2012.13349/) (2020)
- [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)
- [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)
- [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)
- [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)
- [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)
- [A Study of Learning Search Approximation in Mixed Integer Branch and Bound: Node Selection in SCIP](https://mlsanity.com/paper/2007.03948/) (2020)
- [A Theoretical and Computational Analysis of Full Strong-Branching](https://mlsanity.com/paper/2110.10754/) (2021)
- [Progress in Mathematical Programming Solvers from 2001 to 2020](https://mlsanity.com/paper/2206.09787/) (2022)
- [Learning for Spatial Branching: An Algorithm Selection Approach](https://mlsanity.com/paper/2204.10834/) (2022)
- [An Abstract Model for Branching and its Application to Mixed Integer Programming](https://mlsanity.com/paper/1511.01818/) (2015)
- [Exploiting Instance and Variable Similarity to Improve Learning-Enhanced Branching](https://mlsanity.com/paper/2208.10028/) (2022)

## Abstract (arXiv)

Machine learning is increasingly used to improve decisions within branch-and-bound algorithms for mixed-integer programming. Many existing approaches rely on deep learning, which often requires very large training datasets and substantial computational resources for both training and deployment, typically with GPU parallelization. In this work, we take a different path by developing interpretable models that are simple but effective. We focus on approximating strong branching (SB) scores, a highly effective yet computationally expensive branching rule. Using sparse learning methods, we build models with fewer than 4% of the parameters of a state-of-the-art graph neural network (GNN) while achieving competitive accuracy. Relative to SCIP's built-in branching rules and the GNN-based model, our CPU-only models are faster than the default solver and the GPU-accelerated GNN. The models are simple to train and deploy, and they remain effective with small training sets, which makes them practical in low-resource settings. Extensive experiments across diverse problem classes demonstrate the efficiency of this approach.