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arXiv · 2410.03720

NeuralQP: A General Hypergraph-based Optimization Framework for Large-scale QCQPs

Zhixiao Xiong·Fangyu Zong·Huigen Ye·Hua Xu
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Abstract

Machine Learning (ML) optimization frameworks have gained attention for their ability to accelerate the optimization of large-scale Quadratically Constrained Quadratic Programs (QCQPs) by learning shared problem structures. However, existing ML frameworks often rely heavily on strong problem assumptions and large-scale solvers. This paper introduces NeuralQP, a general hypergraph-based framework for large-scale QCQPs. NeuralQP features two main components: Hypergraph-based Neural Prediction, which generates embeddings and predicted solutions for QCQPs without problem assumptions, and Parallel Neighborhood Optimization, which employs a McCormick relaxation-based repair strategy to identify and correct illegal variables, iteratively improving the solution with a small-scale solver. We further prove that our framework UniEGNN with our hypergraph representation is equivalent to the Interior-Point Method (IPM) for quadratic programming. Experiments on two benchmark problems and large-scale real-world instances from QPLIB demonstrate that NeuralQP outperforms state-of-the-art solvers (e.g., Gurobi and SCIP) in both solution quality and time efficiency, further validating the efficiency of ML optimization frameworks for QCQPs.

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Zhixiao Xiong, Fangyu Zong, Huigen Ye, Hua Xu. 2024-09-28. NeuralQP: A General Hypergraph-based Optimization Framework for Large-scale QCQPs. https://arxiv.org/abs/2410.03720

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