Learning to Optimize for Mixed-Integer Non-linear Programming

2024-10-14

arXiv.org

AI Summary

To address the computational intractability and low efficiency of solving large-scale mixed-integer nonlinear programming (MINLP) problems, this paper proposes the first general-purpose learning-based optimization framework. Methodologically, it introduces a differentiable bilevel integer correction mechanism that enables end-to-end learnable optimization within the continuous relaxation space, integrated with projection-based integer constraint enforcement and heuristic feasibility-enhancing post-processing. The key contribution is the first fully end-to-end learnable solver for MINLP, overcoming dual bottlenecks—scalability and speed—that limit conventional solvers. Experiments demonstrate that the framework achieves millisecond-level solution times on MINLP instances with ten-thousand variables, consistently delivering higher-quality solutions than state-of-the-art commercial solvers (e.g., Gurobi, BARON) and classical heuristics. Notably, it successfully solves the largest publicly available MINLP benchmark instance to date.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Intelligent Robots: Learning & Optimization for ROB

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

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.

Problem

• Mixed-Integer Nonlinear Programming
• MINLP
• Large-Scale Problems

Innovation

• Deep Learning Method
• Mixed-Integer Nonlinear Programming (MINLP)
• Large-Scale Optimization