This thesis investigates the application of Bayesian Optimization (BO) for the weight minimization of macrostructural systems, focusing on a cantilever beam, a truss, and two gridshells as case studies. Traditional structural optimization methods often struggle with high-dimensional, non-convex design spaces while being constrained by expensive function evaluations due to repeated finite element analyses.
BO addresses these challenges through surrogate modelling with Gaussian Processes (GPs) and probabilistic acquisition functions that balance exploration and exploitation. The study integrates BO with the finite element package RFEM6, enabling automated optimization workflows subject to Eurocode-based strength, stiffness, and stability constraints.

Four case studies of increasing complexity are implemented:
(i) 1D cantilever beam with a varying size variable
(ii) 2D cantilever truss with varying shape and size variables
(iii) 3D 4×4 gridshell with varying size variables
(iv) 3D 9×9 gridshell with varying size variables
The achieved results via the constrained BO algorithm for the 4x4 gridshell show a 1.67× lighter structure than the reference design and 2.54 × lighter structure than the reference design for the 9x9 gridshell confirming that BO can converge towards feasible and lightweight structural designs. The efficiency of the algorithm is further demonstrated by its ability to converge 18 times faster to a design that is only 0.5% heavier than the reference design for the cantilever truss case study.

Furthermore, the 1D case demonstrated robustness and integration feasibility between the Python implementation and the RFEM6 software. The 2D truss highlighted the benefits of embedding structural knowledge in the sampling strategy and showed that using multiple GPs per member improved reliability compared to aggregated models. For high-dimensional 3D gridshells, the optimizer maintained feasibility but faced some scalability issues. Principal Component Analysis (PCA) is introduced to mitigate the “curse of dimensionality” by exploiting the underlying pattern of the cross-sections that depends on the internal forces while reducing computational cost. However, it is found that excessive dimensionality reduction degrade the solution quality, indicating a trade-off between efficiency and accuracy. Therefore, it has to be applied carefully to retain enough structural variance.

Two other key findings can be emphasized. First, increasing the number of surrogate models to approximate the structural constraints for each element in the system improves accuracy but increases the computational cost. Second, informative initialization and structural-domain knowledge can enhance the convergence rate.

The thesis concludes that Bayesian optimization either with or without applying the PCA, is a viable and sample-efficient strategy for structural weight minimization under realistic structural constraints, capable of being integrated with industry-standard FEM software. Future work should explore the scalability of the BO framework in higher dimensional feature space, the implementation of multi-objective BO and apply it to case studies with broader structural typologies such as moment frames composed of different cross- section types.
Finally, a basic version of an interactive tool is developed that integrates the knowledge discussed in this thesis and that can be used by the structural engineers to explore various design options in the early design phase of a project.