首个支持多任务的机器学习求解混合整数规划框架，提升通用性与效率。
Multi-task Representation Learning for Mixed Integer Linear Programming
- 设计多任务学习框架，统一生成适用于不同求解器和任务的MILP嵌入
- 在三个基准上表现媲美专用模型，在跨规模和跨任务时显著更优
- 适合需要通用求解器、跨场景优化的研究者和工业应用
混合整数线性规划（MILP）是建模和求解复杂组合优化问题的强大工具。近年来，机器学习（ML）引导的方法在提升MILP求解效率方面展现出巨大潜力。然而，这些方法通常依赖独立的离线数据收集与训练流程，限制了其可扩展性和适应性。本文首次提出基于多任务学习的ML引导MILP求解框架。该框架生成的MILP嵌入可有效指导不同求解器（如Gurobi和SCIP）及不同任务（如分支策略和求解器配置）。在三个广泛使用的MILP基准上的大量实验表明，所提模型在同分布下性能与专用模型相当，且在跨问题规模和跨任务的泛化能力上显著优于后者。
原文摘要 · Abstract (English)
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.
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