# Collab-Solver: Collaborative Solving Policy Learning for Mixed-Integer Linear Programming

arXiv: https://arxiv.org/abs/2508.03030 · HTML: https://mlsanity.com/paper/2508.03030/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 66 references that are in the map.
- First posted on arXiv 5 Aug 2025.

## Builds on (most cited first, 22 of 22)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [Evolution of Heuristics: Towards Efficient Automatic Algorithm Design Using Large Language Model](https://mlsanity.com/paper/2401.02051/) (2024)
- [Order Matters: Sequence to sequence for sets](https://mlsanity.com/paper/1511.06391/) (2015)
- [SMAC3: A Versatile Bayesian Optimization Package for Hyperparameter Optimization](https://mlsanity.com/paper/2109.09831/) (2021)
- [Cross Attention Network for Few-shot Classification](https://mlsanity.com/paper/1910.07677/) (2019)
- [Solving Mixed Integer Programs Using Neural Networks](https://mlsanity.com/paper/2012.13349/) (2020)
- [Learning To Cut By Looking Ahead: Cutting Plane Selection via Imitation Learning](https://mlsanity.com/paper/2206.13414/) (2022)
- [Learning to branch with Tree MDPs](https://mlsanity.com/paper/2205.11107/) (2022)
- [A Survey for Solving Mixed Integer Programming via Machine Learning](https://mlsanity.com/paper/2203.02878/) (2022)
- [The Machine Learning for Combinatorial Optimization Competition (ML4CO): Results and Insights](https://mlsanity.com/paper/2203.02433/) (2022)
- [Adaptive Cut Selection in Mixed-Integer Linear Programming](https://mlsanity.com/paper/2202.10962/) (2022)
- [Machine Learning Augmented Branch and Bound for Mixed Integer Linear Programming](https://mlsanity.com/paper/2402.05501/) (2024)
- [Distributional MIPLIB: a Multi-Domain Library for Advancing ML-Guided MILP Methods](https://mlsanity.com/paper/2406.06954/) (2024)
- [Learning to Cut via Hierarchical Sequence/Set Model for Efficient Mixed-Integer Programming](https://mlsanity.com/paper/2404.12638/) (2024)
- [Learning To Dive In Branch And Bound](https://mlsanity.com/paper/2301.09943/) (2023)
- [Multi-task Representation Learning for Mixed Integer Linear Programming](https://mlsanity.com/paper/2412.14409/) (2024)
- [An Existence Result for Hierarchical Stackelberg v/s Stackelberg Games](https://mlsanity.com/paper/1401.0186/) (2013)
- [Yordle: An Efficient Imitation Learning for Branch and Bound](https://mlsanity.com/paper/2202.01896/) (2022)
- [Energy System Optimisation using (Mixed Integer) Linear Programming](https://mlsanity.com/paper/2308.01882/) (2023)
- [How hard is learning to cut? Trade-offs and sample complexity](https://mlsanity.com/paper/2506.00252/) (2025)

## Abstract (arXiv)

Mixed-integer linear programming (MILP) has been a fundamental problem in combinatorial optimization. Conventional MILP solving mainly relies on carefully designed heuristics embedded in the branch-and-bound framework. Driven by the strong capabilities of neural networks, recent research is exploring the value of machine learning alongside conventional MILP solving. Although learning-based MILP methods have shown great promise, existing works typically learn policies for individual modules in MILP solvers in isolation, without considering their interdependence, which limits both solving efficiency and solution quality. To address this limitation, we propose Collab-Solver, a novel multi-agent-based policy learning framework for MILP that enables collaborative policy optimization for multiple modules. Specifically, we formulate the collaboration between cut selection and branching in MILP solving as a Stackelberg game. Under this formulation, we develop a two-phase learning paradigm to stabilize collaborative policy learning: the first phase performs data-communicated policy pretraining, and the second phase further orchestrates the policy learning for various modules. Extensive experiments on both synthetic and large-scale real-world MILP datasets demonstrate that the jointly learned policies significantly improve solving performance. Moreover, the policies learned by Collab-Solver have also demonstrated excellent generalization abilities across different instance sets.