## 1 Introduction
[PERSON] and [PERSON] [23] proposed a modified ordered SIMP method and applied a filter radius of 8.4 and an initial design variable of 0.2 to the minimum compliance optimization problem of a two-dimensional four-phase bridge; simultaneously, in the design of steel and aluminum cantilever beams, the filter radius was set equal to 1/100 of the structure length. A too-small filter radius leads to thin bars in the structural configuration. [PERSON] [24], using HyperWorks and a three-dimensional node model, analyzed the effects of the volume fraction, penalty factor, dimensional constraints, symmetry constraints, and checkerboard pattern control on the TO configurations. The performed study revealed that the reasonable range for the volume fraction is 30% to 40%, and when the penalty factor was set as 6, the TO model could meet the structural performance, manufacturability, and ease of the processing requirements. The reasonable range for the minimum member size constraint is 3 to 4 times the average unit size, whereas the maximum member size constraint is 2 times the minimum member size constraint. Moreover, symmetry constraints could make the distribution of structural units more reasonable, and checkerboard pattern control could make the surface of the structural configuration smoother. However, existing investigations on the factors affecting TO essentially focus on two-dimensional and three-dimensional geometric models and analyze only a subset of the influencing factors, while the study of complex three-dimensional models is insufficient in practical engineering applications. In addition, the current proposed parameter standards are mostly absolute values, lacking generality and applicability. Furthermore, due to the typically complex geometric configurations generated by TO, traditional manufacturing processes often find them difficult or impossible to fabricate. The AM enables the fabrication of complex geometric structures via layer-by-layer stacking of materials to form solid parts [25; 26]. However, current AM technologies are still constrained by geometric limitations, and fully unrestricted fabrication is not yet achievable [27; 28]. Therefore, it is necessary to perform geometric reconstruction on the structural configurations generated by TO [29; 30] to meet the limitations of AM fabrication (e.g., sharp corners, closed internal holes, and overhang angles) [31; 32; 33; 34]. [PERSON] et al. [35] conducted TO on antenna brackets based on the forming constraints and design rules of selective laser melting (SLM) and optimized the redesigned structure through shape optimization, ultimately achieving a weight reduction of 30.43% and a 50.18% increase in fundamental frequency. [PERSON] et al. [36] proposed a part design process that combines SLM and TO. In their investigation, with minimum compliance as the objective function and volume as the constraint, they utilized HyperWorks to design and verify an aircraft bracket, which ultimately achieved a 28% reduction in weight and a twofold increase in the safety factor. [PERSON] et al. [37] performed geometric reconstruction on a heavy-load aerospace bracket after TO and optimized the reconstructed model through size optimization. They also performed loading tests on an aerospace bracket manufactured using the SLM. The obtained results revealed that the bracket achieved an 18% reduction in weight while meeting the mechanical performance requirements. Such investigations effectively combine the advantages of TO and AM, especially by fully considering the AM constraints during geometric reconstruction. However, these studies have not fully addressed the feature handling issues in TO structural configurations that may affect the performance of the structure, nor have they deeply explored the effects of TO numerical instability on the optimization results.