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.

翻译：混合整数非线性规划（MINLP）问题广泛存在于能源系统和交通等多个领域，但由于整数约束的存在，尤其在大规模情况下求解极为困难。尽管基于学习的优化方法在连续优化问题上取得了成功，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方法，该方法包含两个可学习的校正层以确保解的整数性，并通过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，成功求解了迄今报道的部分最大规模问题实例。