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. Our code is available at https://github.com/pnnl/L2O-pMINLP.