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

• URL: http://arxiv.org/abs/2410.03720v1
• Date: Sat, 28 Sep 2024 10:42:47 GMT
• Title: NeuralQP: A General Hypergraph-based Optimization Framework for Large-scale QCQPs
• Authors: Zhixiao Xiong, Fangyu Zong, Huigen Ye, Hua Xu,
• Abstract summary: This paper introduces NeuralQP, a general hypergraph-based framework for large-scale Quadratically Constrained Quadratic Programs (QCQPs) We 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.
• Score: 8.503330120957052
• License: http://creativecommons.org/licenses/by/4.0/
• 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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