# Learning To Dive In Branch And Bound

arXiv: https://arxiv.org/abs/2301.09943 · HTML: https://mlsanity.com/paper/2301.09943/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 50 references that are in the map.
- First posted on arXiv 24 Jan 2023.

## Builds on (most cited first, 21 of 21)

- [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)
- [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)
- [Maximum Resilience of Artificial Neural Networks](https://mlsanity.com/paper/1705.01040/) (2017)
- [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 Select Cuts for Efficient Mixed-Integer Programming](https://mlsanity.com/paper/2105.13645/) (2021)
- [Learning to Schedule Heuristics in Branch-and-Bound](https://mlsanity.com/paper/2103.10294/) (2021)
- [A Survey for Solving Mixed Integer Programming via Machine Learning](https://mlsanity.com/paper/2203.02878/) (2022)
- [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)
- [Learning Large Neighborhood Search Policy for Integer Programming](https://mlsanity.com/paper/2111.03466/) (2021)
- [Adaptive Cut Selection in Mixed-Integer Linear Programming](https://mlsanity.com/paper/2202.10962/) (2022)
- [Augment with Care: Contrastive Learning for Combinatorial Problems](https://mlsanity.com/paper/2202.08396/) (2022)
- [Learning Hard Optimization Problems: A Data Generation Perspective](https://mlsanity.com/paper/2106.02601/) (2021)
- [Learning to Use Local Cuts](https://mlsanity.com/paper/2206.11618/) (2022)
- [Instance-wise algorithm configuration with graph neural networks](https://mlsanity.com/paper/2202.04910/) (2022)
- [Conflict-Driven Heuristics for Mixed Integer Programming](https://mlsanity.com/paper/1902.02615/) (2019)

## Built on by (most cited first, 10 of 10)

- [Apollo-MILP: An Alternating Prediction-Correction Neural Solving Framework for Mixed-Integer Linear Programming](https://mlsanity.com/paper/2503.01129/) (2025)
- [Promoting Generalization for Exact Solvers via Adversarial Instance Augmentation](https://mlsanity.com/paper/2310.14161/) (2023)
- [Leveraging Constraint Programming in a Deep Learning Approach for Dynamically Solving the Flexible Job-Shop Scheduling Problem](https://mlsanity.com/paper/2403.09249/) (2024)
- [Constraint Matters: Multi-Modal Representation for Reducing Mixed-Integer Linear programming](https://mlsanity.com/paper/2508.18742/) (2025)
- [RL-SPH: Learning to Achieve Feasible Solutions for Integer Linear Programs](https://mlsanity.com/paper/2411.19517/) (2024)
- [MILP-Evo: Closed-Loop Fully Automatic Design of MILP Solvers](https://mlsanity.com/paper/2607.18252/) (2026)
- [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)
- [Designing faster mixed integer linear programming algorithm via learning the optimal path](https://mlsanity.com/paper/2601.16056/) (2026)
- [Learning to Solve Orienteering Problem with Time Windows and Variable Profits](https://mlsanity.com/paper/2603.06260/) (2026)

## Abstract (arXiv)

Primal heuristics are important for solving mixed integer linear programs, because they find feasible solutions that facilitate branch and bound search. A prominent group of primal heuristics are diving heuristics. They iteratively modify and resolve linear programs to conduct a depth-first search from any node in the search tree. Existing divers rely on generic decision rules that fail to exploit structural commonality between similar problem instances that often arise in practice. Therefore, we propose L2Dive to learn specific diving heuristics with graph neural networks: We train generative models to predict variable assignments and leverage the duality of linear programs to make diving decisions based on the model's predictions. L2Dive is fully integrated into the open-source solver SCIP. We find that L2Dive outperforms standard divers to find better feasible solutions on a range of combinatorial optimization problems. For real-world applications from server load balancing and neural network verification, L2Dive improves the primal-dual integral by up to 7% (35%) on average over a tuned (default) solver baseline and reduces average solving time by 20% (29%).