# CLCR: Contrastive Learning-based Constraint Reordering for Efficient MILP Solving

arXiv: https://arxiv.org/abs/2504.03688 · HTML: https://mlsanity.com/paper/2504.03688/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 32 references that are in the map.
- First posted on arXiv 23 Mar 2025.

## Builds on (most cited first, 11 of 11)

- [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)
- [Pointer Networks](https://mlsanity.com/paper/1506.03134/) (2015)
- [Exact Combinatorial Optimization with Graph Convolutional Neural Networks](https://mlsanity.com/paper/1906.01629/) (2019)
- [Learning to Schedule Heuristics in Branch-and-Bound](https://mlsanity.com/paper/2103.10294/) (2021)
- [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)
- [Adaptive Cut Selection in Mixed-Integer Linear Programming](https://mlsanity.com/paper/2202.10962/) (2022)
- [Learning to Reformulate for Linear Programming](https://mlsanity.com/paper/2201.06216/) (2022)
- [PySCIPOpt-ML: Embedding Trained Machine Learning Models into Mixed-Integer Programs](https://mlsanity.com/paper/2312.08074/) (2023)
- [From an Interior Point to a Corner Point: Smart Crossover](https://mlsanity.com/paper/2102.09420/) (2021)

## Built on by (most cited first, 2 of 2)

- [Principled Data Augmentation for Learning to Solve Quadratic Programming Problems](https://mlsanity.com/paper/2506.01728/) (2025)
- [ORDO: Operation-level Round-aware Dynamic Ordering for MIP Presolve](https://mlsanity.com/paper/2610.11294/) (2026)

## Abstract (arXiv)

Constraint ordering plays a critical role in the efficiency of Mixed-Integer Linear Programming (MILP) solvers, particularly for large-scale problems where poorly ordered constraints trigger increased LP iterations and suboptimal search trajectories. This paper introduces CLCR (Contrastive Learning-based Constraint Reordering), a novel framework that systematically optimizes constraint ordering to accelerate MILP solving. CLCR first clusters constraints based on their structural patterns and then employs contrastive learning with a pointer network to optimize their sequence, preserving problem equivalence while improving solver efficiency. Experiments on benchmarks show CLCR reduces solving time by 30% and LP iterations by 25% on average, without sacrificing solution accuracy. This work demonstrates the potential of data-driven constraint ordering to enhance optimization models, offering a new paradigm for bridging mathematical programming with machine learning.