Learning to Optimize for Mixed-Integer Non-linear Programming with Feasibility Guarantees

Bo Tang, Elias Boutros Khalil, Jan Drgona

Keywords: Learning to Optimize, Differentiable Optimization, Mixed-Integer Nonlinear Programming

Abstract: Mixed-integer nonlinear programs (MINLPs) arise in domains as diverse as energy systems and transportation, but are notoriously difficult to solve, particularly at scale. While learning-to-optimize (L2O) methods have been successful at continuous optimization, extending them to MINLPs is challenging due to integer constraints. To overcome this, we propose the first general L2O method for parametric MINLPs with two integer correction layers to ensure the integrality of the solution and a projection step to ensure the feasibility of the solution. We prove that the projection step converges, providing a theoretical guarantee for our method. Our experiments show that our methods efficiently solve MINLPs with up to tens of thousands of variables, providing high-quality solutions within milliseconds, even for problems where traditional solvers and heuristics fail.

Submission Number: 5