Simultaneous Shape, Size, and Topology Optimization of Truss Structures Using Graph Neural Networks and Metaheuristic Algorithms

This study presents a unified framework for the analysis and optimization of truss structures through the integration of Graph Neural Networks (GNNs) and metaheuristic algorithms. The proposed approach performs simultaneous size, shape, and topology optimization with the objective of minimizing structural weight while satisfying code-based constraints on strength, serviceability, and stability. Conventional optimization methods can become computationally expensive for complex truss systems, particularly when geometric nonlinear behavior is considered. To address this challenge, a physics-informed, dataset-free GNN framework is developed for structural analysis under both linear and geometric nonlinear conditions. The GNN model predicts nodal displacements, from which member forces and stresses are computed, based on structural characteristics such as geometry, connectivity, and loading conditions. The model is validated against finite element analysis results obtained from the commercial finite element software package SAP2000, demonstrating strong agreement and reliable predictive performance. Within the optimization framework, finite element analysis, implemented using a developed Python based direct stiffness method, is used for linear cases due to its efficiency, while the GNN model is directly integrated into the optimization loop for geometric nonlinear analysis, enabling efficient evaluation of candidate designs. Metaheuristic algorithms, including Particle Swarm Optimization, Genetic Algorithm, and Harmony Search, are used to explore the design space. The framework is evaluated through multiple benchmark truss examples, including a pedestrian bridge structure. A comparative evaluation of the optimization algorithms highlights differences in convergence behavior and solution stability. For the pedestrian bridge example, the strength-to-weight ratio is also assessed to provide a more comprehensive measure of structural efficiency. Overall, this research demonstrates the potential of GNN-based approaches as scalable, data-efficient, and code-compliant tools for structural analysis and optimization.