## 3 Materials and Methods
### AI-Based Optimization
Moreover, the proposed methodology achieved a minimum probability of failure equal to 0.102%, which meets typical structural reliability requirements and is considered a safe structure, whereas structural optimization without a reliability constraint led to an extremely high probability of failure (48.4%), indicating that the structure is practically unsafe and that nearly half of all cases would face failure. Figure 8: Convergence history for 10-bar truss. RBDO required approximately 400 min to perform 5000 FORM analyses, along with FEM evaluations in 100 generations. As can be seen, this value is more than four times higher compared to the previous example. Since FORM is an iterative method that searches for the most probable point (MPP) of failure, different structures can exhibit different convergence characteristics based on the nonlinearity of the limit state function. Additionally, there are three limit states defined for this example, which significantly increases the FEM calls within the FORM function. Nevertheless, it is an important example of RBDO that highlights the main bottleneck of current applications. Figure 9 provides insights into graphics about the convergence history and optimization process. To show the adaptability of the proposed method to 3D structures, a 36-bar space truss example is optimized on the cross-sectional areas and bottom node's z coordinates using RBDO. Sectional areas, as mentioned above, consists of discrete and real-world cross-sectional areas. Table 3 presents the results. The results in Table 4 found by GA provide important insights about the RBDO applicability in real-world examples and systems, illustrating how the mass gap increases when the computational cost is higher, which is a current problem of the proposed methodology. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{2}{c}{**Structural**} & \multicolumn{2}{c}{**RBDO**} \\  & **Optimization** & & \\ \hline  & **This Study** & [57] & **This Study** \\ \hline Objective (m\({}^{3}\)) & 2.38 & 3.06 & 3.014 \\ \(\beta_{1}^{MCS}\), \(\beta_{2}^{MCS}\), \(\beta_{3}^{MCS}\) & 1.75, 0.17, 0.04 & 4.65, 3.04, 3.12 & 4.11, 3.084, 3.12 \\ Employed MA & GA & GA & DE \\ Population Size & 50 & 100 & 50 \\ Generation Number & 100 & 120 & 100 \\ Separate Runs & 2 \(\times\) DE, 2 \(\times\) GA & 50 & 2 \(\times\) DE, 2 \(\times\) GA \\ A1 (cm\({}^{2}\)) & 206.45 & 334.19 & 250.32 \\ A2 (cm\({}^{2}\)) & 170.97 & 187.74 & 227.74 \\ A3 (cm\({}^{2}\)) & 441.93 & 487.74 & 487.74 \\ A4 (cm\({}^{2}\)) & 250.32 & 366.45 & 334.19 \\ A5 (cm\({}^{2}\)) & 278.71 & 345.81 & 382.58 \\ A6 (cm\({}^{2}\)) & 118.06 & 176.13 & 157.42 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of frame structure results. Figure 9: Convergence history for frame structure. ## 5 Discussion

The manuscript provides a clear understanding of the application of MAs, reliability analysis, and structural optimization in the context of the BIM environment for reliability-constrained structural design optimization. The proposed methodology for design creation and optimization incorporates VP, and AI-based metaheuristic approaches that allow the process to go from design creation to the assessment of reliability in consideration of the design variable uncertainties, such as material properties and loading conditions. The direct integration of the RBDO into BIM tools allows for interdisciplinary work and makes the proposed workflow suitable for implementing real-world engineering projects. All in all, this integration between the optimization and BIM environments ensures that the data are well-shared and boosts the decision-making processes that occur in the design stage. The results section showed that the proposed framework efficiently optimizes the benchmark problems obtained from the literature for this study. At the same time, the study revealed certain opportunities to improve the work, one of which is the time required to obtain FE and reliability analysis solutions when working on complex structures.