## 3 Materials and Methods
### AI-Based Optimization
The separate run cycles, population size, and generation number were kept the same for the GA and DE, along with separate run numbers. The algorithms that gave the best result were presented in the Result and Analysis section. These were then applied to two examples obtained from the openliterature, namely, RBDO examples and conventional structural optimization examples with deterministic values. For the conventional examples, MCS was applied to determine their reliability indices, allowing for a comprehensive comparison to demonstrate the effectiveness of the proposed method. Even though the created methodology can optimize structures based on their cross-sectional area (size optimization), nodal coordinates (shape optimization), and the existence of elements or nodes (topology optimization), the current study's scope focuses on reliability-based size and shape optimization. As previously mentioned, one of the ideas was utilizing RSA, another BIM tool, for FEM analysis; however, the long waiting time made this option impossible. To provide better insight into the time cost, Table 1 has been presented to researchers. The scripts and corresponding Python code for the reproducibility of the experimental setup and methodology, along with detailed instructions, can be found in the dedicated GitHub repository for this study [60]. ### Experimental Setup

The first example is a standardized benchmark problem for structural optimization and is preferred by many scholars [21; 23; 53; 74] to validate their methodology. Similarly, this 10-bar truss, whose geometric configuration is given in Figure 7, has been selected as the first example for this research. The problem and material properties of the problem are sourced from the referenced article [57], and they are defined as follows: The cross-sectional areas, \(A_{i}\), of the truss members will be determined during the analysis. The applied load F\({}_{2}\) has a mean value of 100 kips and is modelled with a normal distribution. The modulus of elasticity \(E\) for the material is specified with a mean value of 1000 ksi. All those parameters are assumed to follow a normal distribution with a coefficient of variation (COV) of 0.05. The lower and upper bounds for cross-sectional areas are 0-35 in\({}^{2}\) for this problem. In that regard, this is considered a continuous RBDO problem, with the objective function considered as the mass of the structure. LSF is formulated as \(g(X)=2-\Delta_{y}(X)\), which indicates limited displacement occurred by \(X\) uncertain variables on the \(y\)-axis at node 6 by 2 in. For the second example, the optimization of a multi-story steel frame with three levels and three bays, which is subjected to a combination of concentrated forces and distributed loads, as illustrated in Figure 7, is studied. The frame design incorporates 17 random parameters to maintain comparability with the original study: six associated with the cross-sectional areas of structural components, six related to the moments of inertia of these components, one representing the Young's modulus of the material, three variables for horizontal forces, and one for the dead loads on the beams. Moreover, several parameters are considered uncertain and are characterized by their respective probability distributions, mean values, and COV. The cross-sectional area (\(A\)) and the moment of inertia (\(I\)) are both assumed to follow a lognormal distribution, with their mean values determined by the proposed method and a COV of 0.05. The modulus of elasticity \(E\) is also lognormally distributed, with a mean value of 200,000 MPa and a COV of 0.05. The distributed load \(WD\) follows a normal distribution with a mean of 20 kN/m and a COV of 0.10. The point loads \(P1\), \(P2\), and \(P3\) are modelled as lognormal distributions with mean values of 133.33 kN, 266.67 kN, and 400.00 kN, respectively, each having a COV of 0.10. The frame's 21 elements have been consolidated into six distinct groups, as explained in [57]. The design variables