# Designing faster mixed integer linear programming algorithm via learning the optimal path

arXiv: https://arxiv.org/abs/2601.16056 · HTML: https://mlsanity.com/paper/2601.16056/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 45 references that are in the map.
- First posted on arXiv 22 Jan 2026.

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

- [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)
- [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)
- [The Machine Learning for Combinatorial Optimization Competition (ML4CO): Results and Insights](https://mlsanity.com/paper/2203.02433/) (2022)
- [Learning to Compare Nodes in Branch and Bound with Graph Neural Networks](https://mlsanity.com/paper/2210.16934/) (2022)
- [Towards Foundation Models for Mixed Integer Linear Programming](https://mlsanity.com/paper/2410.08288/) (2024)
- [Reinforcement Learning for Branch-and-Bound Optimisation using Retrospective Trajectories](https://mlsanity.com/paper/2205.14345/) (2022)
- [Machine Learning for Cutting Planes in Integer Programming: A Survey](https://mlsanity.com/paper/2302.09166/) (2023)
- [A Study of Learning Search Approximation in Mixed Integer Branch and Bound: Node Selection in SCIP](https://mlsanity.com/paper/2007.03948/) (2020)
- [Apollo-MILP: An Alternating Prediction-Correction Neural Solving Framework for Mixed-Integer Linear Programming](https://mlsanity.com/paper/2503.01129/) (2025)
- [Learning to Search via Retrospective Imitation](https://mlsanity.com/paper/1804.00846/) (2018)
- [An Improved Reinforcement Learning Algorithm for Learning to Branch](https://mlsanity.com/paper/2201.06213/) (2022)
- [Learning To Dive In Branch And Bound](https://mlsanity.com/paper/2301.09943/) (2023)
- [Combinatorial Optimization with Automated Graph Neural Networks](https://mlsanity.com/paper/2406.02872/) (2024)
- [A Mixed-Integer Linear Programming Formulation for Human Multi-Robot Task Allocation](https://mlsanity.com/paper/2106.06772/) (2021)
- [Reinforcement Learning for Node Selection in Branch-and-Bound](https://mlsanity.com/paper/2310.00112/) (2023)

## Abstract (arXiv)

Designing faster algorithms for solving Mixed-Integer Linear Programming (MILP) problems is highly desired across numerous practical domains, as a vast array of complex real-world challenges can be effectively modeled as MILP formulations. Solving these problems typically employs the branch-and-bound algorithm, the core of which can be conceived as searching for a path of nodes (or sub-problems) that contains the optimal solution to the original MILP problem. Traditional approaches to finding this path rely heavily on hand-crafted, intuition-based heuristic strategies, which often suffer from unstable and unpredictable performance across different MILP problem instances. To address this limitation, we introduce DeepBound, a deep learning-based node selection algorithm that automates the learning of such human intuition from data. The core of DeepBound lies in learning to prioritize nodes containing the optimal solution, thereby improving solving efficiency. DeepBound introduces a multi-level feature fusion network to capture the node representations. To tackle the inherent node imbalance in branch-and-bound trees, DeepBound employs a pairwise training paradigm that enhances the model's ability to discriminate between nodes. Extensive experiments on three NP-hard MILP benchmarks demonstrate that DeepBound achieves superior solving efficiency over conventional heuristic rules and existing learning-based approaches, obtaining optimal feasible solutions with significantly reduced computation time. Moreover, DeepBound demonstrates strong generalization capability on large and complex instances. The analysis of its learned features reveals that the method can automatically discover more flexible and robust feature selection, which may effectively improve and potentially replace human-designed heuristic rules.