## 2 State of the Art
### Reliability Analysis  
As mentioned previously, the design codes create a path to follow to achieve one of the many missions of civil engineers: to create safe buildings. However, in real-world scenarios, the design parameters are quite uncertain since there are profound levels of ambiguity in environmental excitations and the system parameters and models [44]. The referenced article states [45], \"A truly optimum design should consider the behaviour of the structure for various types of loading conditions as well as possible strength deteriorations\", where the concept of the reliability analysis of structures emerged, which considers uncertainties in real-world problems. Through a stochastic reliability analysis, a structure's performance or reliability is meant to be maximized, while, at the same time, guaranteeing structures to perform as was intended despite the presence of variability. It follows the processes that aim to calculate the Limit State Function (LSF), which separates the safe region from the failure region [46] with the aim of modelling uncertainties and the violation of engineering practices [47]. There are some difficulties in adapting the method in structural optimization as nonlinear mathematical problems characterized by restrictions on the probability that design requirements will be met within a specific period need to be solved. An iterative procedure that includes sub-optimization problems and reliability databases is used to obtain efficient solutions to that type of problem [48; 49]; however, computational power was the main obstacle ahead of this method for decades. To employ RBDO, the reliability index or probability of failure must be calculated. There are different methods, such as the FORM, Second-Order Reliability Method (SORM), and MCS, available in the literature to calculate the probability of failure (for more information, please refer to [50; 51; 52]). With the advent of computers, the computational power obstacle has been diminished and, as the pioneering research referenced in the article [53], employed GAs to perform RBDO for space trusses. Another approach has been proposed for the RBDO of steel plate girders with corrugated webs [54]. The research combines the FEM with tools such as the Stochastic Perturbation Technique (SPT), Semi-Analytical Approach (AM), and MCS for uncertainties because of manufacturing imperfections or corrosion effects. Based on the limit states such as Ultimate Limit State (ULS) and Serviceability Limit State (SLS) and taking the reliability investigation with time dependency into account, it illustrates how to identify the optimum girder cross-sectional areas to achieve reliability over a fifty-year service duration. In [55], the RBDO method for industrial robots based on simulation and principles of probability has been described. The method combines Latin Hypercube Sampling, computer simulation, the response surface method, and the Sequential Optimization and Reliability Assessment (SORA) algorithm to increase the reliability of the design. It shows that it can make robot arms lighter by substantial margins while possessing equal dependability. A different focus on the computational aspect of the reliability-based topology optimization (RBTO) problem and the use of stochastic-gradient-based approaches studied by [56]. The authors approximated failure probabilities and improved layouts at lesser computational costs with a minimum of random samples per iteration. Many researchers preferred using OpenSees for their methodology since it facilitates the integration of reliability analysis with structural optimization processes and works with Tool Command Language (Tcl) scripting for the integration without requiring the code compilation of the source code, interface, and GAs. The referenced study [52] describes approaches developed to provide a reliability-based methodology for the optimum design of three-dimensional trusses, namely, the transmission towers.