## 3 Materials and Methods
### Computational Software and Hardware  
All the experiments and tests have been performed on a Notebook with an Intel Core i7-12650H processor, 16 GB RAM (2 \(\times\) 8 GB), 512 GB SSD, an RTX 4070 8 GB graphics card, and Windows 11 Home operating system. In our study, Dynamo (Version: 3.0.4) has been utilized for the VP environment. Through Dynamo, structures that want to be optimized can be created, and boundary conditions and inputs can be defined. Moreover, Dynamo's seamless integration with BIM tools such as Revit and RSA, along with its ability to employ Python scripts within its environment, results in utilizing textual programming and addressing the limitations of VP with TP, thereby enhancing the workflow's robustness and feasibility. Python (Version: 3.9.12) has been utilized to perform FEM, and FORM analysis, along with MAs. Python's ability to perform faster than Dynamo in processes that require more computational power was invaluable for this study. PyNiteFEA (Version: 0.0.94), a basic 3D structural FEM library created to be utilized in Python by [PERSON], has been utilized for structural analysis. For further documentation, the reader can refer to the referenced website [62].  
The present study employs PyMOO (Version: 0.6.1) library [63], which is an open-source framework created for Python that provides multiple essential MAs such as GA, PSO, DE, NSGA-II, NSGA-III, and MOEA/D, along with various CHTs such as Feasibility First, and Constraint Violation (CV) as Penalty. In the proposed framework, conflicting objectives are considered as constraints, and SOO is performed using both DE and GA algorithms. DE was chosen as the primary method since, according to [64], it is the most utilized and successful algorithm among scholars, while GA, which serves as a foundation in the field of MAs, was implemented to provide alternative results. Another advantage of DE is that it is a parameter-free and easy-to-use algorithm, which saves the users effort in tuning parameters as mentioned previously.  
Although GA and DE were chosen for this study, the proposed methodology can be easily adapted to other algorithms. We should mention that the selection and comparison of different MAs are out of scope since our primary aim is to provide a streamlined workflow for RBDO using BIM tools. For this reason, the number of separate analysis runs was kept low. While the outcomes provide significant insights about the MAs, it should be noted that these algorithms mostly use trial-and-error logic and heavily depend on randomness. To properly evaluate the performance of the MAs, a separate study focusing on this area, such as [64; 65; 66; 67; 68; 69; 70; 71], would need to be conducted with more run cycles and tuned parameters; however, this is also beyond the scope of the present study.  
In this manuscript, PyMOO was utilized to optimize the performance of multiple structures under uncertain circumstances, enabling efficient design creation by combining MAs with RBDO along with FEM analysis to create safe, cost-efficient, and reliable structures. Pystra (Version: 1.3.0), a robust framework for defining random variables, probabilistic models, and employing algorithms to estimate failure probabilities in engineering systems, was an instrumental Python library in conducting the reliability assessments necessary for this study, allowing for rigorous uncertainty quantification. Further documentation about the library can be found in [72]. For the reliability assessments, the Finite Difference Method (FDM), which estimates the derivatives numerically by perturbing the input parameters slightly and observing the change in the system response, has been utilized.