用学习优化方法快速求解大规模非线性整数规划问题，保证解的可行性和整数性。
Learning to Optimize for Mixed-Integer Non-linear Programming with Feasibility Guarantees
- 通过整数修正层和梯度投影确保解的整数性与约束可行性
- 在数万变量规模下毫秒级生成高质量可行解，优于传统求解器
- 适合需要反复求解相似参数实例的工程场景，如能源调度
混合整数非线性规划（MINLP）广泛存在于能源系统、过程工程和交通等领域，因其离散决策与非线性约束的耦合，大规模求解极为困难。许多实际问题以参数化形式出现，需对相关实例快速可靠求解。尽管学习优化（L2O）在连续优化中表现优异，但将其扩展至MINLP需在数据驱动框架中同时保证可行性与整数性。本文提出一种针对参数化MINLP的L2O方法，通过整数修正层强制整数约束，并采用基于梯度的投影确保不等式约束的可行性。理论上，我们给出了投影步骤的渐近与非渐近收敛保证。实验表明，该框架可处理含数万变量的MINLP，在毫秒级内生成可行且高质量的解，显著优于传统求解器和启发式基线，在重复求解场景中表现突出。
原文摘要 · Abstract (English)
Mixed-integer nonlinear programs (MINLPs) arise in domains such as energy systems, process engineering, and transportation, and are notoriously difficult to solve at scale due to the interplay of discrete decisions and nonlinear constraints. In many practical settings, these problems appear in parametric form, where objectives and constraints depend on instance-specific parameters, creating the need for fast and reliable solutions across related instances. While learning-to-optimize (L2O) methods have shown strong performance in continuous optimization, extending them to MINLPs requires enforcing both feasibility and integrality within a data-driven framework. We propose an L2O approach tailored to parametric MINLPs that generates instance-specific solutions using integer correction layers to enforce integrality and a gradient-based projection to ensure feasibility of the inequality constraints. Theoretically, we provide asymptotic and non-asymptotic convergence guarantees of the projection step. Empirically, the framework scales to MINLPs with tens of thousands of variables and produces feasible high-quality solutions within milliseconds, often outperforming traditional solvers and heuristic baselines in repeated-solve settings.
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