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 GNN-based 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.