###### Abstract  
A comparative analysis between Bidirectional Evolutionary Structural Optimization (BESO) and Smoothing-ESO (SESO), simultaneously considering Reliability-Based Topology Optimization (RBTO) and the structure's self-weight in the case of three-dimensional elasticity, is presented in this study. Due to the important role of the existence of uncertainties in making the structural design more realistic, geometry, volumetric fraction, modulus of elasticity, compliance, and loading are considered random variables with normal probability distribution. When adopting the First Order Reliability Method (FORM), the failure probability is calculated based on the reliability index. Furthermore, considering the influence of self-weight in problems involving large structures in civil engineering, especially in the case of bridges, this makes the optimal configuration more reliable for design. A series of examples are covered to validate the methods presented, showing their efficiency and robustness. 3D-topology optimization; BESO; SESO; RBTO; self-weight Article  
BESO and SESO: Comparative Analysis of Spatial Considering Self-Weight and Structural Reliability  
[PERSON], [PERSON], [PERSON], M.  
wide variety of OT problems for two-dimensional structures, including compliance minimization by [16; 17], frequency maximization, and displacement constraint by [18]. BESO for compliance minimization was applied to three-dimensional structures by [19], who presented a code in Python; [16] applied it to strut-and-tie models and [20] in continuous structures with self-supporting geometric constraints. Ref. [21] extend the BESO method to the RBTO of three-dimensional structures, considering an elastic-plastic topology optimization. Ref. [22] used BESO for RBTO for 3D structures in conjunction with the standard response surface method and (b) SESO, which is also a bidirectional TO procedure and is efficient and robust in several problems with restriction of displacement, voltage, compliance, and frequency. Recently, it was extended to spatial structures in the work of [23; 24], which uses as a restriction the minimization of compliance coupled with the reliability analysis procedure via the FORM method, considering geometry, elastic modulus, compliance, force, and von Mises stress as random variables with normal probability distribution. For comparative analysis, RBTO-BESO (Reliability-Based Topology Optimization BESO) and RBTO-SESO (Reliability-Based Topology Optimization SESO) were implemented, inserting the structure's self-weight, making the optimal configurations more realistic in structural design. Furthermore, the proposed algorithm can determine the tensile (blue) and compression (red) regions in the optimized structure using a modal filter and the partial derivative of the von Mises stress field. After identifying the sign of the derivatives, a radius is defined for the filter, which aims to search neighboring elements in relation to their state (traction or compression). This approach allows, in regions with many tensioned/compressed elements, that the presence of a single tensioned/compressed element is considered insignificant and, therefore, neglected by the algorithm, since it is in a region with tensioned/compressed neighbors. This technique provides smoothing of the regions, making them clearer and cleaner in terms of traction and compression, which significantly contributes to the robustness and effectiveness of the optimization process. As BESO is a more stable method compared to ESO and its variants, a comparative analysis between BESO and SESO is necessary. SESO, a variant of ESO employing a bidirectional heuristic similar to BESO, warrants such scrutiny. This article expands on previous efforts to enhance the SESO-3D method, proposing a computational algorithm that integrates RBTO while considering the structure's self-weight. Considering self-weight in TO impacts mass distribution, internal forces, and dynamic performance, thereby enhancing safety, reliability, and material efficiency in design.