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

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.

@article{zeng2025_2504.03688,
  title={ CLCR: Contrastive Learning-based Constraint Reordering for Efficient MILP Solving },
  author={ Shuli Zeng and Mengjie Zhou and Sijia Zhang and Yixiang Hu and Feng Wu and Xiang-Yang Li },
  journal={arXiv preprint arXiv:2504.03688},
  year={ 2025 }
}