发表机构
State Key Laboratory of Novel Software Technology, Nanjing University; School of Artificial Intelligence, Nanjing University; State Key Laboratory of Technology and Equipment for Defense Against Power System Operational Risks, Nari Technology Co., Ltd.（南京大学 现代软件工程国家重点实验室; 南京大学 人工智能学院; 南瑞科技股份有限公司 电力系统运行风险防御技术与装备国家重点实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对混合整数线性规划（MILP）解预测的一次性范式缺陷，提出SHSP框架，采用分层条件解码与置信度掩码修复机制，在四个基准上使解间隙平均降低54%，性能优于现有方法。
AI 中文摘要
混合整数线性规划（Mixed-Integer Linear Programming，MILP）是组合优化领域的基础优化范式，已广泛应用于现实世界的各类场景。由于其具有NP难特性，为大规模或高约束MILP实例获取最优解在计算上仍难以实现。因此，基于学习的解预测方法应运而生，成为为求解器提供高质量变量分配以加速求解的有前景的途径。然而，现有方法通常采用一次性预测范式，同时预测所有变量的边际概率。结果是，变量间的条件依赖关系仅通过消息传递被隐式捕捉，而对组合结构的建模负担完全落在图神经网络的表征能力上。为解决这一局限，我们提出结构感知分层解预测（Structure-Aware Hierarchical Solution Prediction，SHSP）框架，该框架用一种新颖的分层条件解码机制替代一次性方法的并行边际解码。具体而言，SHSP从约束结构构建变量耦合图，沿耦合强度递增的层级顺序解码变量，并将每个层级的条件建立在先前预测的分配之上。为缓解解码过程中的误差累积，SHSP进一步引入了感知置信度的掩码修复机制，以识别并修正不可靠的中间预测。我们将SHSP与多种学习引导的搜索方法集成，并在四个标准MILP基准上对其进行评估。实验结果表明，SHSP显著优于现有的一次性预测基线，实现了解间隙平均降低54%。
英文摘要
Mixed-Integer Linear Programming (MILP) is a fundamental optimization paradigm in combinatorial optimization and has been widely applied across real-world domains. Due to its NP-hard nature, obtaining optimal solutions for large-scale or highly constrained MILP instances remains computationally prohibitive. Learning-based solution prediction has therefore emerged as a promising approach to provide high-quality variable assignment for solver acceleration. However, existing methods typically adopt a one-shot prediction paradigm that predicts the marginal probabilities of all variables simultaneously. As a result, the conditional dependencies among variables are only implicitly captured through message passing, with the burden of modeling the combinatorial structure falling entirely on the representational capacity of graph neural networks. To address this limitation, we propose the Structure-Aware Hierarchical Solution Prediction (SHSP) framework that replaces the parallel marginal decoding of one-shot methods with a novel hierarchical conditional decoding mechanism. Specifically, SHSP constructs a variable coupling graph from the constraint structure, decodes variables sequentially along a hierarchy of increasing coupling strength, and conditions each hierarchy on previously predicted assignments. To mitigate error accumulation during the decoding process, SHSP further incorporates a confidence-aware mask-and-repair mechanism to identify and correct unreliable intermediate predictions. We integrate SHSP with multiple learning-guided search methods, and evaluate it on four standard MILP benchmarks. Experimental results demonstrate that SHSP significantly outperforms existing one-shot prediction baselines, achieving a 54% average reduction in solution gap.
