# A Deep Instance Generative Framework for MILP Solvers Under Limited Data Availability

arXiv: https://arxiv.org/abs/2310.02807 · HTML: https://mlsanity.com/paper/2310.02807/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 60 references that are in the map.
- First posted on arXiv 4 Oct 2023.

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

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Automatic chemical design using a data-driven continuous representation of molecules](https://mlsanity.com/paper/1610.02415/) (2016)
- [Junction Tree Variational Autoencoder for Molecular Graph Generation](https://mlsanity.com/paper/1802.04364/) (2018)
- [Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizon](https://mlsanity.com/paper/1811.06128/) (2018)
- [Generating Sentences from a Continuous Space](https://mlsanity.com/paper/1511.06349/) (2015)
- [Exact Combinatorial Optimization with Graph Convolutional Neural Networks](https://mlsanity.com/paper/1906.01629/) (2019)
- [GuacaMol: Benchmarking Models for De Novo Molecular Design](https://mlsanity.com/paper/1811.09621/) (2018)
- [Solving Mixed Integer Programs Using Neural Networks](https://mlsanity.com/paper/2012.13349/) (2020)
- [A Systematic Survey on Deep Generative Models for Graph Generation](https://mlsanity.com/paper/2007.06686/) (2020)
- [Generative Diffusion Models on Graphs: Methods and Applications](https://mlsanity.com/paper/2302.02591/) (2023)
- [A Survey on Deep Graph Generation: Methods and Applications](https://mlsanity.com/paper/2203.06714/) (2022)
- [MIP-GNN: A Data-Driven Framework for Guiding Combinatorial Solvers](https://mlsanity.com/paper/2205.14210/) (2022)
- [De Novo Molecular Generation via Connection-aware Motif Mining](https://mlsanity.com/paper/2302.01129/) (2023)
- [Learning Cut Selection for Mixed-Integer Linear Programming via Hierarchical Sequence Model](https://mlsanity.com/paper/2302.00244/) (2023)
- [A Survey for Solving Mixed Integer Programming via Machine Learning](https://mlsanity.com/paper/2203.02878/) (2022)
- [Ecole: A Gym-like Library for Machine Learning in Combinatorial Optimization Solvers](https://mlsanity.com/paper/2011.06069/) (2020)
- [A GNN-Guided Predict-and-Search Framework for Mixed-Integer Linear Programming](https://mlsanity.com/paper/2302.05636/) (2023)
- [On Representing Mixed-Integer Linear Programs by Graph Neural Networks](https://mlsanity.com/paper/2210.10759/) (2022)
- [G2SAT: Learning to Generate SAT Formulas](https://mlsanity.com/paper/1910.13445/) (2019)
- [An Improved Reinforcement Learning Algorithm for Learning to Branch](https://mlsanity.com/paper/2201.06213/) (2022)
- [HardSATGEN: Understanding the Difficulty of Hard SAT Formula Generation and A Strong Structure-Hardness-Aware Baseline](https://mlsanity.com/paper/2302.02104/) (2023)

## Built on by (most cited first, 21 of 21)

- [OptMATH: A Scalable Bidirectional Data Synthesis Framework for Optimization Modeling](https://mlsanity.com/paper/2502.11102/) (2025)
- [Towards Foundation Models for Mixed Integer Linear Programming](https://mlsanity.com/paper/2410.08288/) (2024)
- [Large Language Models for Constructing and Optimizing Machine Learning Workflows: A Survey](https://mlsanity.com/paper/2411.10478/) (2024)
- [MILP-StuDio: MILP Instance Generation via Block Structure Decomposition](https://mlsanity.com/paper/2410.22806/) (2024)
- [Apollo-MILP: An Alternating Prediction-Correction Neural Solving Framework for Mixed-Integer Linear Programming](https://mlsanity.com/paper/2503.01129/) (2025)
- [Distributional MIPLIB: a Multi-Domain Library for Advancing ML-Guided MILP Methods](https://mlsanity.com/paper/2406.06954/) (2024)
- [Large Language Models are Good Multi-lingual Learners : When LLMs Meet Cross-lingual Prompts](https://mlsanity.com/paper/2409.11056/) (2024)
- [Generative AI and Process Systems Engineering: The Next Frontier](https://mlsanity.com/paper/2402.10977/) (2024)
- [DIG-MILP: a Deep Instance Generator for Mixed-Integer Linear Programming with Feasibility Guarantee](https://mlsanity.com/paper/2310.13261/) (2023)
- [Machine Learning Insides OptVerse AI Solver: Design Principles and Applications](https://mlsanity.com/paper/2401.05960/) (2024)
- [CoCo-MILP: Inter-Variable Contrastive and Intra-Constraint Competitive MILP Solution Prediction](https://mlsanity.com/paper/2511.09209/) (2025)
- [Accurate and Scalable Graph Neural Networks via Message Invariance](https://mlsanity.com/paper/2502.19693/) (2025)
- [RoME: Domain-Robust Mixture-of-Experts for MILP Solution Prediction across Domains](https://mlsanity.com/paper/2511.02331/) (2025)
- [Are Your Generated Instances Truly Useful? GenBench-MILP: A Benchmark Suite for MILP Instance Generation](https://mlsanity.com/paper/2505.24779/) (2025)
- [Principled Data Augmentation for Learning to Solve Quadratic Programming Problems](https://mlsanity.com/paper/2506.01728/) (2025)
- [Code Retrieval for MILP Instance Generation](https://mlsanity.com/paper/2505.11526/) (2025)
- [Surrogate Interpretable Graph for Random Decision Forests](https://mlsanity.com/paper/2506.01988/) (2025)
- [HardCore Generation: Generating Hard UNSAT Problems for Data Augmentation](https://mlsanity.com/paper/2409.18778/) (2024)
- [EvoOptiGraph: Weakness-Driven Coevolution via Graph-Based Structural Generation for Optimization Modeling](https://mlsanity.com/paper/2606.26578/) (2026)
- [GraphBU: MILP Instance Generation with Graph-Native Block Units](https://mlsanity.com/paper/2607.06532/) (2026)
- [Teaching LLMs to Generate Challenging MILP Instances via Solver Feedback](https://mlsanity.com/paper/2609.37356/) (2026)

## Abstract (arXiv)

In the past few years, there has been an explosive surge in the use of machine learning (ML) techniques to address combinatorial optimization (CO) problems, especially mixed-integer linear programs (MILPs). Despite the achievements, the limited availability of real-world instances often leads to sub-optimal decisions and biased solver assessments, which motivates a suite of synthetic MILP instance generation techniques. However, existing methods either rely heavily on expert-designed formulations or struggle to capture the rich features of real-world instances. To tackle this problem, we propose G2MILP, the first deep generative framework for MILP instances. Specifically, G2MILP represents MILP instances as bipartite graphs, and applies a masked variational autoencoder to iteratively corrupt and replace parts of the original graphs to generate new ones. The appealing feature of G2MILP is that it can learn to generate novel and realistic MILP instances without prior expert-designed formulations, while preserving the structures and computational hardness of real-world datasets, simultaneously. Thus the generated instances can facilitate downstream tasks for enhancing MILP solvers under limited data availability. We design a suite of benchmarks to evaluate the quality of the generated MILP instances. Experiments demonstrate that our method can produce instances that closely resemble real-world datasets in terms of both structures and computational hardness. The deliverables are released at https://miralab-ustc.github.io/L2O-G2MILP.