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

TL;DR

NeuralQP introduces a hypergraph-based ML framework for large-scale QCQPs that predicts solutions and iteratively refines them, outperforming traditional solvers in quality and speed.

Contribution

It presents a novel hypergraph neural network approach that does not rely on strong problem assumptions and proves equivalence to the Interior-Point Method for quadratic programming.

Findings

NeuralQP outperforms Gurobi and SCIP in solution quality.

NeuralQP is more time-efficient on benchmark and real-world QCQPs.

The framework is theoretically equivalent to the Interior-Point Method.

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.