# A Survey for Solving Mixed Integer Programming via Machine Learning

arXiv: https://arxiv.org/abs/2203.02878 · HTML: https://mlsanity.com/paper/2203.02878/

## Key facts

- Cited by 44 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 85 references that are in the map.
- First posted on arXiv 6 Mar 2022.

## Builds on (most cited first, 26 of 26)

- [Generative Adversarial Imitation Learning](https://mlsanity.com/paper/1606.03476/) (2016)
- [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)
- [Learning to Perform Local Rewriting for Combinatorial Optimization](https://mlsanity.com/paper/1810.00337/) (2018)
- [Solving Mixed Integer Programs Using Neural Networks](https://mlsanity.com/paper/2012.13349/) (2020)
- [Generalize a Small Pre-trained Model to Arbitrarily Large TSP Instances](https://mlsanity.com/paper/2012.10658/) (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)
- [Exploratory Combinatorial Optimization with Reinforcement Learning](https://mlsanity.com/paper/1909.04063/) (2019)
- [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)
- [OR-Gym: A Reinforcement Learning Library for Operations Research Problems](https://mlsanity.com/paper/2008.06319/) (2020)
- [CombOptNet: Fit the Right NP-Hard Problem by Learning Integer Programming Constraints](https://mlsanity.com/paper/2105.02343/) (2021)
- [Learning to Select Cuts for Efficient Mixed-Integer Programming](https://mlsanity.com/paper/2105.13645/) (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)
- [Learning to Solve Large-Scale Security-Constrained Unit Commitment Problems](https://mlsanity.com/paper/1902.01697/) (2019)
- [Learning Large Neighborhood Search Policy for Integer Programming](https://mlsanity.com/paper/2111.03466/) (2021)
- [Best arm identification in multi-armed bandits with delayed feedback](https://mlsanity.com/paper/1803.10937/) (2018)
- [Reinforcement Learning for Variable Selection in a Branch and Bound Algorithm](https://mlsanity.com/paper/2005.10026/) (2020)
- [Learning Primal Heuristics for Mixed Integer Programs](https://mlsanity.com/paper/2107.00866/) (2021)
- [DASH: Dynamic Approach for Switching Heuristics](https://mlsanity.com/paper/1307.4689/) (2013)
- [Branch and Bound in Mixed Integer Linear Programming Problems: A Survey of Techniques and Trends](https://mlsanity.com/paper/2111.06257/) (2021)
- [Smart Feasibility Pump: Reinforcement Learning for (Mixed) Integer Programming](https://mlsanity.com/paper/2102.09663/) (2021)
- [Co-training for Policy Learning](https://mlsanity.com/paper/1907.04484/) (2019)
- [Accelerating Primal Solution Findings for Mixed Integer Programs Based on Solution Prediction](https://mlsanity.com/paper/1906.09575/) (2019)

## Built on by (most cited first, 30 of 44)

- [A Deep Instance Generative Framework for MILP Solvers Under Limited Data Availability](https://mlsanity.com/paper/2310.02807/) (2023)
- [A Survey of Optimization-based Task and Motion Planning: From Classical To Learning Approaches](https://mlsanity.com/paper/2404.02817/) (2024)
- [Generative Models in Decision Making: A Survey](https://mlsanity.com/paper/2502.17100/) (2025)
- [Artificial Intelligence for Operations Research: Revolutionizing the Operations Research Process](https://mlsanity.com/paper/2401.03244/) (2024)
- [Learning To Dive In Branch And Bound](https://mlsanity.com/paper/2301.09943/) (2023)
- [CAMBranch: Contrastive Learning with Augmented MILPs for Branching](https://mlsanity.com/paper/2402.03647/) (2024)
- [Leveraging Large Language Models for Solving Rare MIP Challenges](https://mlsanity.com/paper/2409.04464/) (2024)
- [Learning to Optimize for Mixed-Integer Non-linear Programming with Feasibility Guarantees](https://mlsanity.com/paper/2410.11061/) (2024)
- [Accelerate Presolve in Large-Scale Linear Programming via Reinforcement Learning](https://mlsanity.com/paper/2310.11845/) (2023)
- [Machine Learning Insides OptVerse AI Solver: Design Principles and Applications](https://mlsanity.com/paper/2401.05960/) (2024)
- [Learning Backdoors for Mixed Integer Linear Programs with Contrastive Learning](https://mlsanity.com/paper/2401.10467/) (2024)
- [Learning Solution-Aware Transformers for Efficiently Solving Quadratic Assignment Problem](https://mlsanity.com/paper/2406.09899/) (2024)
- [Abstract Operations Research Modeling Using Natural Language Inputs](https://mlsanity.com/paper/2408.07272/) (2024)
- [Symbol-Equivariant Recurrent Reasoning Models](https://mlsanity.com/paper/2603.02193/) (2026)
- [Metaheuristics for (Variable-Size) Mixed Optimization Problems: A Unified Taxonomy and Survey](https://mlsanity.com/paper/2401.03880/) (2024)
- [Data-driven Prediction of Relevant Scenarios for Robust Combinatorial Optimization](https://mlsanity.com/paper/2203.16642/) (2022)
- [Physics-Informed Graph Neural Network for Dynamic Reconfiguration of Power Systems](https://mlsanity.com/paper/2310.00728/) (2023)
- [Deep Learning for Two-Stage Robust Integer Optimization](https://mlsanity.com/paper/2310.04345/) (2023)
- [CLCR: Contrastive Learning-based Constraint Reordering for Efficient MILP Solving](https://mlsanity.com/paper/2504.03688/) (2025)
- [Are Your Generated Instances Truly Useful? GenBench-MILP: A Benchmark Suite for MILP Instance Generation](https://mlsanity.com/paper/2505.24779/) (2025)
- [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)
- [Grid-SiPhyR: An end-to-end learning to optimize framework for combinatorial problems in power systems](https://mlsanity.com/paper/2206.06789/) (2022)
- [Graph Neural Networks for the Offline Nanosatellite Task Scheduling Problem](https://mlsanity.com/paper/2303.13773/) (2023)
- [Deep learning enhanced mixed integer optimization: Learning to reduce model dimensionality](https://mlsanity.com/paper/2401.09556/) (2024)
- [Deep Sensitivity Analysis for Objective-Oriented Combinatorial Optimization](https://mlsanity.com/paper/2403.00016/) (2024)
- [Towards Interpreting Multi-Objective Feature Associations](https://mlsanity.com/paper/2403.00017/) (2024)
- [Integrating Reinforcement Learning and Model Predictive Control with Applications to Microgrids](https://mlsanity.com/paper/2409.11267/) (2024)
- [Boosting Cross-problem Generalization in Diffusion-Based Neural Combinatorial Solver via Inference Time Adaptation](https://mlsanity.com/paper/2502.12188/) (2025)
- [MILP-SAT-GNN: Yet Another Neural SAT Solver](https://mlsanity.com/paper/2507.01825/) (2025)

## Abstract (arXiv)

This paper surveys the trend of leveraging machine learning to solve mixed integer programming (MIP) problems. Theoretically, MIP is an NP-hard problem, and most of the combinatorial optimization (CO) problems can be formulated as the MIP. Like other CO problems, the human-designed heuristic algorithms for MIP rely on good initial solutions and cost a lot of computational resources. Therefore, we consider applying machine learning methods to solve MIP, since ML-enhanced approaches can provide the solution based on the typical patterns from the historical data. In this paper, we first introduce the formulation and preliminaries of MIP and several traditional algorithms to solve MIP. Then, we advocate further promoting the different integration of machine learning and MIP and introducing related learning-based methods, which can be classified into exact algorithms and heuristic algorithms. Finally, we propose the outlook for learning-based MIP solvers, direction towards more combinatorial optimization problems beyond MIP, and also the mutual embrace of traditional solvers and machine learning components.