# Sketch-Guided Topology Optimization with Enhanced Diversity for Innovative Structural Design
## 4 Experiments
### Impacts of Human Control on Design Quality and Diversity  
The qualitative analysis of the experimental results as above has verified the effectiveness of the proposed TO framework to generate conceptual structural designs while providing flexible human controllability. The results also indicate that human control may conflict with the compliance minimization objective of the TO algorithm, leading to an increase in the compliance minimization. In the following, an ablation study is presented that quantitatively analyzes the impact of the three human control approaches on both the solution quality and diversity. The design quality metrics include the total structural compliance and volume. Although multiple aspects in mechanics, fatigue life, heat transfer, manufacturability, etc., are necessary to verify the engineering applicability of design, it is too costly and time-consuming to carry out a detailed analysis for all design in the conceptual stage. Thus, using compliance and volume criteria can effectively find the initial designs that meet the basic requirements. Diversity metrics include the image-based average SSIM index and MAE index between pairs of solutions, denoted as \(\overline{SSIM}\) and \(\overline{MAE}\), respectively, and the coefficients  
Figure 10: Experimental results of human controllability by integrating \(l_{min}\) and \(\lambda\). of variance for the compliance and volume ratio, denoted as \(CV_{comp}\) and \(CV_{vol}\). Their computation formulas are given in Equations (16)-(18). \[\overline{SSIM} =\frac{\sum_{i\
eq j}SSIM(i,j)}{M} \tag{17}\] \[\overline{MAE} =\frac{\sum_{i\
eq j}MAE(i,j)}{M}\] (18) \[CV_{*} =\frac{\sigma(*)}{\mu(*)}\times 100\% \tag{19}\]  
where \(\sigma(*)\) is the standard deviation of the metrics' values, and \(\mu(*)\) is the mean of the metrics' values. In the ablation experiment of the stroke-based constraint, parameter \(\beta_{Inc}\) is selected from [0, 5 \(\times\) 10\({}^{-5}\), 2 \(\times\) 10\({}^{-4}\), 5 \(\times\) 10\({}^{-4}\), 8 \(\times\) 10\({}^{-4}\)]; a closed-shape-based constraint is not applied (\(\lambda\) = 0). In the ablation experiment of the closed-shape-based constraint, as contour lines are essential to make the drawn shape visually prominent, \(\beta_{Inc}\) is set to 5 \(\times\) 10\({}^{-4}\), and \(\lambda\) is selected from [8 \(\times\) 10\({}^{-5}\), 4 \(\times\) 10\({}^{-4}\), 2 \(\times\) 10\({}^{-3}\), 1 \(\times\) 10\({}^{-2}\), 5 \(\times\) 10\({}^{-2}\)]. In the ablation experiment of the minimal allowed feature size, \(l_{min}\) is selected from [3; 6; 9; 12], \(\beta_{Inc}\) is set to 5 \(\times\) 10\({}^{-4}\), and \(\lambda\) is set 0.05. The other hyper-parameters are the same as in Table 1. The sketch images of Figures 5 and 6 are utilized as case 1 and case 2. The experimental results of the ablation study are shown in Figures 11-14. Quantitative results of several TO algorithm runs are given in Table 2. An increase in \(\beta_{Inc}\) leads to obviously larger compliance. The average compliance value is 2.62 when this constraint is not applied, but increases to 3.15 and 2.87 for case 1 and case 2, respectively, given \(\beta_{Inc}\) = 5 \(\times\) 10\({}^{-4}\). Importantly, an increase in \(\beta_{Inc}\) does not reduce the solution diversity but slightly improves it. A possible reason is that this constraint makes it easier to escape local optima through interfering with the compliance minimization objective while avoiding limiting the material distribution in the regions surrounding the strokes, thereby exploring the design space more divergently. Therefore, the undirected structural boundary constraint is very beneficial to preserve freedom of design exploration under sketch-based human control. In contrast, the experimental results reveal that the closed-shape-based constraint reduces the solution diversity but has no obvious impact on the compliance or volume ratio.