# Distributional MIPLIB: a Multi-Domain Library for Advancing ML-Guided MILP Methods

arXiv: https://arxiv.org/abs/2406.06954 · HTML: https://mlsanity.com/paper/2406.06954/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 77 references that are in the map.
- First posted on arXiv 11 Jun 2024.

## Builds on (most cited first, 30 of 31)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [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)
- [OR-Gym: A Reinforcement Learning Library for Operations Research Problems](https://mlsanity.com/paper/2008.06319/) (2020)
- [MIP-GNN: A Data-Driven Framework for Guiding Combinatorial Solvers](https://mlsanity.com/paper/2205.14210/) (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)
- [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)
- [A GNN-Guided Predict-and-Search Framework for Mixed-Integer Linear Programming](https://mlsanity.com/paper/2302.05636/) (2023)
- [The Machine Learning for Combinatorial Optimization Competition (ML4CO): Results and Insights](https://mlsanity.com/paper/2203.02433/) (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)
- [Learning to Compare Nodes in Branch and Bound with Graph Neural Networks](https://mlsanity.com/paper/2210.16934/) (2022)
- [Lookback for Learning to Branch](https://mlsanity.com/paper/2206.14987/) (2022)
- [Machine Learning Augmented Branch and Bound for Mixed Integer Linear Programming](https://mlsanity.com/paper/2402.05501/) (2024)
- [A Deep Instance Generative Framework for MILP Solvers Under Limited Data Availability](https://mlsanity.com/paper/2310.02807/) (2023)
- [Finding Backdoors to Integer Programs: A Monte Carlo Tree Search Framework](https://mlsanity.com/paper/2110.08423/) (2021)
- [Promoting Generalization for Exact Solvers via Adversarial Instance Augmentation](https://mlsanity.com/paper/2310.14161/) (2023)
- [CAMBranch: Contrastive Learning with Augmented MILPs for Branching](https://mlsanity.com/paper/2402.03647/) (2024)
- [Distributional Learning of Variational AutoEncoder: Application to Synthetic Data Generation](https://mlsanity.com/paper/2302.11294/) (2023)
- [Learning Pseudo-Backdoors for Mixed Integer Programs](https://mlsanity.com/paper/2106.05080/) (2021)
- [Optimizing Transmission Infrastructure Investments to Support Line De-energization for Mitigating Wildfire Ignition Risk](https://mlsanity.com/paper/2203.10176/) (2022)
- [Reinforcement Learning for Node Selection in Branch-and-Bound](https://mlsanity.com/paper/2310.00112/) (2023)
- [Lower bound on size of branch-and-bound trees for solving lot-sizing problem](https://mlsanity.com/paper/2112.03965/) (2021)

## Built on by (most cited first, 15 of 15)

- [Towards Foundation Models for Mixed Integer Linear Programming](https://mlsanity.com/paper/2410.08288/) (2024)
- [LLMs for Cold-Start Cutting Plane Separator Configuration](https://mlsanity.com/paper/2412.12038/) (2024)
- [Multi-task Representation Learning for Mixed Integer Linear Programming](https://mlsanity.com/paper/2412.14409/) (2024)
- [Balans: Multi-Armed Bandits-based Adaptive Large Neighborhood Search for Mixed-Integer Programming Problem](https://mlsanity.com/paper/2412.14382/) (2024)
- [Constraint Matters: Multi-Modal Representation for Reducing Mixed-Integer Linear programming](https://mlsanity.com/paper/2508.18742/) (2025)
- [FORGE: Foundational Optimization Representations from Graph Embeddings](https://mlsanity.com/paper/2508.20330/) (2025)
- [ParBalans: Parallel Multi-Armed Bandits-based Adaptive Large Neighborhood Search](https://mlsanity.com/paper/2508.06736/) (2025)
- [ID-PaS+ : Identity-Aware Predict-and-Search for General Mixed-Integer Linear Programs](https://mlsanity.com/paper/2512.10211/) (2025)
- [Collab-Solver: Collaborative Solving Policy Learning for Mixed-Integer Linear Programming](https://mlsanity.com/paper/2508.03030/) (2025)
- [Machine Learning Guided Optimal Transmission Switching to Mitigate Wildfire Ignition Risk](https://mlsanity.com/paper/2510.25147/) (2025)
- [ML-Guided Primal Heuristics for Mixed Binary Quadratic Programs](https://mlsanity.com/paper/2604.23053/) (2026)
- [Fusing Backdoors, Machine Learning, and Optimization for Large-Scale Parametric Mixed-Integer Programs](https://mlsanity.com/paper/2606.21440/) (2026)
- [Teaching LLMs to Generate Challenging MILP Instances via Solver Feedback](https://mlsanity.com/paper/2609.37356/) (2026)
- [Reformulation-Contrastive Learning for Mixed Integer Programs](https://mlsanity.com/paper/2610.00730/) (2026)
- [ORDO: Operation-level Round-aware Dynamic Ordering for MIP Presolve](https://mlsanity.com/paper/2610.11294/) (2026)

## Abstract (arXiv)

Mixed Integer Linear Programming (MILP) is a fundamental tool for modeling combinatorial optimization problems. Recently, a growing body of research has used machine learning to accelerate MILP solving. Despite the increasing popularity of this approach, there is a lack of a common repository that provides distributions of similar MILP instances across different domains, at different hardness levels, with standardized test sets. In this paper, we introduce Distributional MIPLIB, a multi-domain library of problem distributions for advancing ML-guided MILP methods. We curate MILP distributions from existing work in this area as well as real-world problems that have not been used, and classify them into different hardness levels. It will facilitate research in this area by enabling comprehensive evaluation on diverse and realistic domains. We empirically illustrate the benefits of using Distributional MIPLIB as a research vehicle in two ways. We evaluate the performance of ML-guided variable branching on previously unused distributions to identify potential areas for improvement. Moreover, we propose to learn branching policies from a mix of distributions, demonstrating that mixed distributions achieve better performance compared to homogeneous distributions when there is limited data and generalize well to larger instances. The dataset is publicly available at https://sites.google.com/usc.edu/distributional-miplib/home.