Title: HTS-Adapt: A Hybrid Training Strategy with Adaptive Search Region Adjustment for MILPs
Primary area: optimization
Keywords: Mixed Integer Linear Programming, Machine Learning, Predict-and-Search

Abstract: Mixed Integer Linear Programming (MILP) problems are essential for optimizing complex systems but are NP-hard, posing significant challenges as the problem scale and complexity increase. Recent advances have integrated machine learning to predict partial solutions by exploiting structural patterns in MILP instances. However, existing methods often suffer from inaccurate and infeasible predictions, limiting their practical utility. In this work, we improve the Contrastive Predict-and-Search (ConPaS) framework by introducing a Hybrid Training Strategy with Adaptive Search Region Adjustment mechanism (HTS-Adapt). HTS selectively applies label-based learning and contrastive learning based on the structural properties of variables, improving prediction accuracy. Adapt dynamically adjusts the search space to mitigate infeasible predictions, thereby reducing computational overhead. Experiments demonstrate that our approach achieves a notable performance enhancement by improving prediction accuracy and reducing the search space, proving its effectiveness in addressing real-world MILP challenges. Compared to the MILP solver SCIP, our method achieves an average reduction of more than 50\% in the solution gap across four MILP datasets.