Mixed-integer nonlinear programs (MINLPs) arise in diverse domains such as energy systems and transportation but are notoriously difficult to solve, particularly on a large scale. While learning-to-optimize methods have been successful at continuous optimization, extending them to MINLPs is still challenging due to the integer constraints. To overcome this, we propose a novel deep-learning approach with two learnable correction layers to ensure solution integrality and a post-processing step to improve solution feasibility. Our experiments show that this is the first general method capable of efficiently solving large-scale MINLPs with up to tens of thousands of variables in milliseconds, delivering high-quality solutions even when traditional solvers and heuristics fail. This is the first general learning method for MINLP, successfully solving some of the largest instances reported to date. Our code is available at https://github.com/pnnl/L2O-pMINLP.

翻译：混合整数非线性规划（MINLP）广泛出现在能源系统和交通等多个领域，但由于其整数约束，这类问题尤其在大规模情况下求解极为困难。尽管学习优化方法在连续优化问题上已取得成功，但将其扩展至MINLP仍面临挑战。为此，我们提出一种新颖的深度学习框架，该框架包含两个可学习的修正层以确保解的整数性，并采用后处理步骤提升解的可行性。实验表明，这是首个能够高效求解大规模MINLP的通用方法，可在毫秒级时间内处理变量规模高达数万的问题，即使在传统求解器和启发式方法失效时仍能提供高质量解。这是针对MINLP的首个通用学习方法，成功求解了迄今为止报道的部分最大规模算例。代码已发布于 https://github.com/pnnl/L2O-pMINLP。