Vertex-based graph neural network classification model considering structural topological features for structural optimization

Traditional surrogate models always face the challenge of low accuracy when dealing with high-dimensional problems in structural optimization, this study aims to overcome this problem and proposes a vertex-based graph neural network (GNN) classification model. In contrast to conventional machine learning models that treat design variables as independent inputs, the proposed model develops a vertex-based graph representation to transform structural topological features and critical physical information into the graph data. According to a message passing mechanism based on the graph convolutional, it can extract the correlations among design variables and enhance its capability in handling high-dimensional structural optimization problems. Three truss examples, including a 10-bar with 10 variables, a 600-bar with 25 variables, and a 942-bar with 59 variables, are utilized to investigate the performance of the proposed surrogate model. The results demonstrate that the GNNbased surrogate model outperforms traditional machine learning approaches, particularly in the two high- dimensional problems, showcasing its superior ability to capture complex variable correlations and handle high-dimensional structural optimization tasks. Moreover, the proposed method significantly reduces the computational expenses by over 60% compared to conventional metaheuristic algorithms, while yielding optimal designs with comparable quality. These results demonstrate the efficiency and effectiveness of the GNN-based surrogate model in tackling complex, high-dimensional structural optimization problems.