## 3 Materials and Methods
### AI-Based Optimization  
The structural optimization section of the methodology redesigns the structural model to decrease the structure's overall mass, volume, or cost, together with its associated risks. This section combines previously explained FEM analysis and reliability analysis with an optimization algorithm as a way of determining the best design. One of the major concerns of structural optimization lies in identifying the corresponding cross-sectional areas of structural members that can lead to the establishment of a lighter structure, while, at the same time, meeting predefined criteria. As previously mentioned, the PyMOO library has been utilized to employ AI-based MAs in this process. Conforming to PyMOO's problem class, the indicated optimization problem is defined as presented in Figure 5. In this class, the design variables, such as cross-sectional dimensions or node coordinates, must be defined along with the lower and upper bounds of these variables. The number of objectives must be specified. Here, reliability constraints can be defined as objectives, and problems can be solved by using MOO algorithms. Reliability can be also defined as a constraint for the problem, and optimization can be solved using Single-Objective Optimization (SOO) algorithms. In the present study, the authors have preferred using the single-objective function to be minimized by applying constraint, which is the reliability index. The optimization process is performed with the help of two different MAs, namely, GAs and DE algorithms, population-based optimization algorithms suitable for solving complex multi-dimensional problems. As a CHT, the Adaptive Epsilon Constraint Handling technique from PyMOO with \"perc_eps_until\" value of 0.25, which represents the percentage of the total optimization run at which the \(\epsilon\) value should become zero (please refer to [17] for more information), has been employed. DE is used with Latin Hypercube Sampling (LHS) as a sampling method to generate the initial population by breaking the range of all the variables into LHS intervals and selecting one random value within the entire intervals. Mutation is also an essential part of DE, which can be described as the production of a new candidate solution by adding a weighted difference of two population vectors to another vector. The DE variant used in this study is DE/rand/1/bin, which means that exactly one difference vector is used, and binomial crossover is used. The crossover rate in the study was set at 0.3, which means the percentage of the total elements taken from the mutant vector is 30%. The GA parameters are integer random sampling with duplicateelimination, simulated binary crossover (SBX) with a probability value set to 1 and eta value set to 3, and polynomial mutation (PM) with a probability value set to 1 and eta value set to 3. Although DE and GA are chosen as the main algorithms, the proposed workflow allows using various algorithms with different settings, facilitated by the PyMoo library depending on designers' preference. The pseudo-code for the optimization part has been depicted in Algorithm 3. ```
Input: Optimization problem with parameters (e.g., population size) Output: Optimized design variables (e.g., cross-sectional areas)
1. Define the optimization problem by using logic in Algorithm 2;
2. Set MA and CHT (e.g., GA with penalty method);
3. Set lower and upper bounds for the design variables;
4. Set constraints for optimization problem;
5. Initialize constraint violation list;
6. whilek \(<\) k\({}_{\max}\), where k\({}_{\max}\) is generation number, do
7. Compute reliability violations by employing FORM
8. Compute objective functions (e.g., mass)
9. Check convergence;
10. if converged: break;
11. k\(\leftarrow\)k + 1;
12. Create new population;
13. end if
13. Return reliability based optimized design variables;
```  
**Algorithm 3**RBDO Problem Definition and Optimization  
Furthermore, to facilitate the use of real-world cross-sections, another function has been integrated into our methodology.