Large language models enhanced graph neural architecture search for quadratic unconstrained binary optimization - Zhang, Peng; Wu, Junxian; Yang, Hong; Zhou, Chuan; Tian, Zhihong (Knowledge-based systems, 2025)
Quadratic unconstrained binary optimization (QUBO) refers to a subclass of unconstrained combinatorial optimization problems where the objective is to optimize a quadratic polynomial function over a set of binary variables without any explicit constraint. Recently, graph neural networks (GNNs) have been applied to solve QUBO problems by describing a QUBO problem as a graph and then learning the representation of the graph using GNNs. However, the performance of these GNNs is often unsatisfactory due to improper manual settings of the parameters of graph neural architectures. In this paper, we propose a new graph neural architecture search model (GNAS) to solve the QUBO problems (GNAS4QUBO for short). The idea is to develop a graph neural architecture search (GNAS) model based on reinforcement learning to find the best GNNs to learn the representation of the QUBO graph. Moreover, we improve the GNAS model with large language models (LLMs) by designing a new set of GNAS4QUBO prompts to generate the best GNNs under QUBO evaluation feedback and fine-tuning the LLM using LoRA based on new graph neural architectures. The experimental evaluation indicates that the proposed method outperforms existing GNN-based models on multiple QUBO benchmark problems. In particular, the results reveal substantial improvement with respect to cut-size metric and the accuracy score in benchmark tasks, such as maximum cut, set covering, combinatorial auction, and maximum independent set. The codes are available online at https://github.com/Embrasse-moi1/GNAS4QUBO.