发表机构
University of Virginia; MIT; Los Alamos National Laboratory（弗吉尼亚大学; 麻省理工学院; 洛斯阿拉莫斯国家实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出Constrained Graph Diffusion（CGD）框架，结合图扩散模型与可行性投影算子求解混合整数规划，在两类任务上较基线方法提升可行性与质量，且最高加速425倍。
AI 中文摘要
本文提出一种新颖的基于学习的方法，用于近似求解混合整数优化问题实例。这类问题计算极具挑战性，因为需要联合确定离散和连续决策，同时满足复杂的组合约束。所提方法依赖于一种基于图的生成扩散模型，该模型学习混合整数优化问题的离散分量，同时将无需训练的可行性投影算子直接整合到反向扩散过程中，以在生成过程中引导中间样本趋向可行集。离散决策生成后，剩余优化问题简化为连续问题，可利用现有数值方法高效求解（相较于原问题）。所得框架命名为Constrained Graph Diffusion（CGD，约束图扩散），与问题无关，可通过合适的投影算子适配广泛类别的混合整数优化问题。我们在最优传输切换（针对ACOPF）和离散投资组合优化任务上评估CGD，结果显示，与基于学习的基线方法相比，其可行性和求解质量有显著提升，且相较于MINLP的最先进数值求解器，加速比最高达425倍。
英文摘要
This paper proposes a novel learning-based approach to approximately solve instances of mixed-integer optimization problems. These problems are computationally challenging, as they require jointly determining discrete and continuous decisions while satisfying complex combinatorial constraints. problem-agnostic and can accommodate a broad class of mixed-integer optimization problems through suitable projection operators. We introduce Constrained Graph Diffusion (CGD), a learning-based framework that approximately solves recurring instances of such problems by learning a conditional distribution over their discrete decisions. CGD uses a graph-based diffusion model and incorporates constraint information directly into the reverse diffusion process, steering intermediate predictions toward the feasible region throughout generation. By operating on continuous relaxations of the discrete variables, CGD defines a differentiable constrained generation pathway up to terminal discrete recovery. Once the discrete decision is recovered and fixed, a numerical optimizer solves the remaining continuous problem, avoiding online combinatorial search over the binary variables while retaining numerical optimization for continuous completion. We evaluate CGD on AC-OPF with branch switching and discrete portfolio optimization, demonstrating substantial improvements in feasibility and solution quality over learning-based baselines while achieving speedups of up to $543\times$ over state-of-the-art MIP solvers on large instances.
