Mixed Integer Linear Programs (MILPs) are highly flexible and powerful tools for modeling and solving complex real-world combinatorial optimization problems. Recently, machine learning (ML)-guided approaches have demonstrated significant potential in improving MILP-solving efficiency. However, these methods typically rely on separate offline data collection and training processes, which limits their scalability and adaptability. This paper introduces the first multi-task learning framework for ML-guided MILP solving. The proposed framework provides MILP embeddings helpful in guiding MILP solving across solvers (e.g., Gurobi and SCIP) and across tasks (e.g., Branching and Solver configuration). Through extensive experiments on three widely used MILP benchmarks, we demonstrate that our multi-task learning model performs similarly to specialized models within the same distribution. Moreover, it significantly outperforms them in generalization across problem sizes and tasks.

本研究解决了现有机器学习指导的混合整数线性规划（MILP）方法在数据收集和训练过程中的独立性问题，从而限制了其可扩展性和适应性。我们提出了一种新的多任务学习框架，能够横向指导多种求解器的MILP求解，并在多个任务中提供MILP嵌入。实验证明，该模型在多样性和任务泛化能力上显著优于传统专用模型。

用于混合整数线性规划的多任务表征学习