学习早期至最终解的一致性以加速混合整数线性规划（MILP）
Learning Early-to-Final Solution Consistency for MILP Acceleration
浏览论文内容
中文总结 AI 辅助
本文针对MILP求解难的问题，提出学习早期至最终解一致性的新范式，通过预测变量赋值的一致性引导搜索，在Gurobi和SCIP上均实现了原差距的显著降低。
中文摘要 AI 辅助
混合整数线性规划（MILP）是运筹学与组合优化领域的基础问题类，广泛应用于工业决策。然而由于其NP-难特性，现代求解器可能无法在实际时间限制内为具有挑战性的MILP实例找到高质量解。近期的基于学习的方法试图通过从静态实例级特征（如变量-约束二分图）直接预测高质量解来加速MILP求解，但仅从实例特征准确预测解较为困难，且这些方法大多忽略了求解器搜索过程中揭示的信息。本文发现，MILP求解器在搜索早期阶段生成的解计算成本低，且通常在结构上接近全预算搜索后找到的解。受此观察启发，我们提出一种新的求解器感知范式，将学习目标从变量赋值转移到早期至最终的一致性：对于每个变量，我们预测其早期阶段的赋值是否应保留在全预算解中。预测的一致性自然引导下游搜索，例如通过固定被判定为一致的赋值。在推理时，我们进一步整合多个早期阶段解的一致性预测以提升鲁棒性。在四个MILP基准上的实验表明，我们的方法可在不同下游流程中提升预测引导的搜索效果。结合Gurobi，我们提出的方法平均将原差距降低56.9%，并在组合拍卖实例上完全消除了该差距。此外，我们将在Gurobi上训练的模型零样本迁移到SCIP而无需适配，在基准上实现了平均36.4%的差距降低。
英文摘要
Mixed-Integer Linear Programming (MILP) is a fundamental problem class in operations research and combinatorial optimization, with broad applications to industrial decision-making. Owing to their NP-hardness, however, modern solvers may struggle to find high-quality solutions for challenging MILP instances within practical time limits. Recent learning-based approaches seek to accelerate MILP solving by directly predicting high-quality solutions from static instance-level features, such as variable-constraint bipartite graphs. Yet accurate solution prediction from instance features alone is difficult, and these methods largely overlook the information revealed during the solver's search process. In this paper, we find that solutions produced at the early search stage of MILP solvers, which are computationally cheap to obtain, are often structurally close to the solutions found after full-budget search. Motivated by this observation, we propose a new solver-informed paradigm that shifts the learning target from variable assignment to early-to-final consistency: for each variable, we predict whether its early-stage assignment should persist in full-budget solutions. The predicted consistency naturally guides downstream search, for instance by fixing the assignments deemed consistent. At inference time, we further ensemble consistency predictions across multiple early-stage solutions to improve robustness. Experiments across four MILP benchmarks show our method improves prediction-guided search across diverse downstream pipelines. With Gurobi, our proposed method reduces the primal gap by 56.9% on average and closes it completely on combinatorial auction instances. Besides, we transferred the Gurobi-trained model zero-shot to SCIP without adaptation, achieving a 36.4% average gap reduction across benchmarks.
