## 1 Introduction
The RBTO analysis for 3D structures proposed by [24] is performed using BESO and the stochastic response surface method (SRSM) to determine the limit state functions' approximations. In their research, [PERSON]. [25] focused on developing RBTO on a structure that is used to design joints and connections for building applications under uncertainty considerations. The procedure is performed by integrating the TO algorithm, reliability analysis, random vibration analysis, additive manufacturing, computer simulations, and parametric design. In addition, they proposed an investigation of the potential of topologically optimized 3D-printed hybrid materials. [PERSON] et al. [26] proposed a decoupled reliability-based design optimization method that is implemented in an internal computational code combined with external optimization to assess the RBTO problem. The goal is to obtain a new structural scheme with at least the same stiffness as the optimal setting provided by the DTO approach. Both structures undergo the same reliability-based parametric optimization process, considering the target reliability index from the previous RBTO with the same probabilistic information. In more recent applications, several works can be cited on structural analysis, using the RBTO method, such as in [27; 28; 29] wherein plane stress analysis is performed by different approaches. Even construction process [30], dynamic or seismic aspects and effects with structural analysis on wind farm, brick and reinforced concrete structures are evaluated in the works [31; 32; 33; 34] by optimization methods. In the present study, we applied the RBTO analysis using evolutionary methods, such as ESO, SESO, SERA and SIMP, using the approach of [16], where the design variables are the structure's geometry, load, elasticity module and the volume, since the latter is an explicit function of geometry. The limit state functions are the structure's performance index, maximum displacement and maximum compliance. The displacement is obtained using the Kolmogorov-Smirnov test, and it is imposed as a constraint in the optimization procedure. In addition, we used the Jacobi preconditioned conjugate gradient (PCG)method to solve the linear system generated in the equilibrium equation at each iteration. As the mechanical behavior, the stress constraints, or better, the tractions, are assumed on the part of the boundary, and they are called Neumann-type constraints (free or prescribed tractions). In the RBTO formulation, the sensibility analysis is evaluated by the performance index (PI), for which it is taken into account the minimization, the compliance or the strains, so stress constraints are not prescribed in this sense. As known, evolutionary optimization methods present mathematical deficiencies in guaranteeing the global optimum, but the designs achieved by the present applied methods are viable for manufacturing, as already proved by several works. In addition, these intrinsic deficiencies are potentialized when integrated with reliability procedures. However, the insertion of the PI as a limit state function aims to monitor the stable mechanical behavior of the structure, represents a sufficient criterion for the RBTO analysis, and, associated with displacement and volume constraints, provides good configurations that are more reliable than deterministic topologies for the same weight. The most important novelties of this article are the expansion of the SERA and SESO methods for the RBTO analysis of 3D elastic structures considering the PI as the limit state function. Furthermore, an expansion of the algorithm proposed by [16] for 3D analysis with the inclusion of seven random variables is evaluated. The remaining of the article is organized as follows: Section 2 presents the proposed evolutionary methods and their formulation for the compliance minimization problem, the hexahedral finite element filtering scheme, the sensitivity calculation, and the convergence criterion.