HEQP: A Hypergraph Neural Network-Based Evolutionary Method for Large-Scale QCQPs

Machine learning-based optimization frameworks have attracted increasing attention for accelerating the solution of large-scale quadratically constrained quadratic programs (QCQPs) by exploiting shared problem structure across instances. However, existing machine learning (ML) frameworks often rely on the assumption of parametric models and large-scale solvers. This article introduces HEQP, a hypergraph neural network-based evolutionary optimization framework for large-scale QCQPs. This framework features two main components: 1) hypergraph-based neural prediction, which predicts optimal solutions for QCQPs without assumptions of models; and 2) evolutionary large neighborhood search (Evo-LNS), which employs a McCormick relaxation-based repair strategy to search and apply crossover on neighborhood solutions using a small-scale solver. We further show that our framework is equivalent to the interior-point method (IPM), a polynomial-time algorithm, for quadratic programming. Experiments on two types of benchmark problems and 13 large-scale real-world instances from the QPLIB illustrate that our framework outperforms state-of-the-art solvers (including Gurobi, SCIP, and SHOT) in both solution quality and time efficiency, highlighting the efficiency of ML-based optimization frameworks for QCQPs.