Learning to Optimize for Mixed-Integer Non-linear Programming

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.