Design Optimization of Truss Structures Using a Graph Neural Network-Based Surrogate Model

One of the primary objectives of truss structure design optimization is to minimize the total weight by determining the optimal sizes of the truss members while ensuring structural stability and integrity against external loads. Trusses consist of pin joints connected by straight members, analogous to vertices and edges in a mathematical graph. This characteristic motivates the idea of representing truss joints and members as graph vertices and edges. In this study, a Graph Neural Network (GNN) is employed to exploit the benefits of graph representation and develop a GNN-based surrogate model integrated with a Particle Swarm Optimization (PSO) algorithm to approximate nodal displacements of trusses during the design optimization process. This approach enables the determination of the optimal cross-sectional areas of the truss members with fewer finite element model (FEM) analyses. The validity and effectiveness of the GNN-based optimization technique are assessed by comparing its results with those of a conventional FEM-based design optimization of three truss structures: a 10-bar planar truss, a 72-bar space truss, and a 200-bar planar truss. The results demonstrate the superiority of the GNN-based optimization, which can achieve the optimal solutions without violating constraints and at a faster rate, particularly for complex truss structures like the 200-bar planar truss problem.