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

TL;DR

This paper introduces a learning-based optimization method for large-scale parametric mixed-integer nonlinear programs, ensuring feasibility and integrality with theoretical guarantees and fast, high-quality solutions.

Contribution

It develops a novel L2O framework for MINLPs that enforces feasibility and integrality, with proven convergence and scalability to large problems.

Findings

Scales to MINLPs with tens of thousands of variables

Produces feasible solutions within milliseconds

Often outperforms traditional solvers and heuristics

Abstract

Mixed-integer nonlinear programs (MINLPs) arise in domains such as energy systems, process engineering, and transportation, and are notoriously difficult to solve at scale due to the interplay of discrete decisions and nonlinear constraints. In many practical settings, these problems appear in parametric form, where objectives and constraints depend on instance-specific parameters, creating the need for fast and reliable solutions across related instances. While learning-to-optimize (L2O) methods have shown strong performance in continuous optimization, extending them to MINLPs requires enforcing both feasibility and integrality within a data-driven framework. We propose an L2O approach tailored to parametric MINLPs that generates instance-specific solutions using integer correction layers to enforce integrality and a gradient-based projection to ensure feasibility of the inequality constraints. Theoretically, we provide asymptotic and non-asymptotic convergence guarantees of the projection step. Empirically, the framework scales to MINLPs with tens of thousands of variables and produces feasible high-quality solutions within milliseconds, often outperforming traditional solvers and heuristic baselines in repeated-solve settings.