# Learning to Reformulate for Linear Programming

arXiv: https://arxiv.org/abs/2201.06216 · HTML: https://mlsanity.com/paper/2201.06216/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 35 references that are in the map.
- First posted on arXiv 17 Jan 2022.

## Builds on (most cited first, 7 of 7)

- [Pointer Networks](https://mlsanity.com/paper/1506.03134/) (2015)
- [Neural Combinatorial Optimization with Reinforcement Learning](https://mlsanity.com/paper/1611.09940/) (2016)
- [Exact Combinatorial Optimization with Graph Convolutional Neural Networks](https://mlsanity.com/paper/1906.01629/) (2019)
- [Learning a SAT Solver from Single-Bit Supervision](https://mlsanity.com/paper/1802.03685/) (2018)
- [Hybrid Models for Learning to Branch](https://mlsanity.com/paper/2006.15212/) (2020)
- [Learning to Branch](https://mlsanity.com/paper/1803.10150/) (2018)
- [From an Interior Point to a Corner Point: Smart Crossover](https://mlsanity.com/paper/2102.09420/) (2021)

## Built on by (most cited first, 10 of 10)

- [Learning Cut Selection for Mixed-Integer Linear Programming via Hierarchical Sequence Model](https://mlsanity.com/paper/2302.00244/) (2023)
- [On Representing Linear Programs by Graph Neural Networks](https://mlsanity.com/paper/2209.12288/) (2022)
- [Exploring the Power of Graph Neural Networks in Solving Linear Optimization Problems](https://mlsanity.com/paper/2310.10603/) (2023)
- [Learning to Cut via Hierarchical Sequence/Set Model for Efficient Mixed-Integer Programming](https://mlsanity.com/paper/2404.12638/) (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)
- [Towards graph neural networks for provably solving convex optimization problems](https://mlsanity.com/paper/2502.02446/) (2025)
- [Taking the human out of decomposition-based optimization via artificial intelligence: Part I. Learning when to decompose](https://mlsanity.com/paper/2310.07068/) (2023)
- [CLCR: Contrastive Learning-based Constraint Reordering for Efficient MILP Solving](https://mlsanity.com/paper/2504.03688/) (2025)
- [HGCN2SP: Hierarchical Graph Convolutional Network for Two-Stage Stochastic Programming](https://mlsanity.com/paper/2511.16027/) (2025)

## Abstract (arXiv)

It has been verified that the linear programming (LP) is able to formulate many real-life optimization problems, which can obtain the optimum by resorting to corresponding solvers such as OptVerse, Gurobi and CPLEX. In the past decades, a serial of traditional operation research algorithms have been proposed to obtain the optimum of a given LP in a fewer solving time. Recently, there is a trend of using machine learning (ML) techniques to improve the performance of above solvers. However, almost no previous work takes advantage of ML techniques to improve the performance of solver from the front end, i.e., the modeling (or formulation). In this paper, we are the first to propose a reinforcement learning-based reformulation method for LP to improve the performance of solving process. Using an open-source solver COIN-OR LP (CLP) as an environment, we implement the proposed method over two public research LP datasets and one large-scale LP dataset collected from practical production planning scenario. The evaluation results suggest that the proposed method can effectively reduce both the solving iteration number (25%downarrow) and the solving time (15%downarrow) over above datasets in average, compared to directly solving the original LP instances.