# Sketch-Guided Topology Optimization with Enhanced Diversity for Innovative Structural Design
## 4 Experiments
### Analysis of Adaptive-Scale Parallel Computing  
To test the effectiveness of the adaptive parallel scale strategy for the multi-solution TO framework, comparative experiments are conducted with and without this strategy. Hyper-parameters \(N_{0}=10\) and \(N=30\) when they are implemented, and \(N_{0}=N=30\) when they are not implemented, with solution set filtering only after the iteration ends. The initial parallel scale \(M\) is set to 50 with the adaptive parallel scale, and selected from [50; 40; 30] without it. The sketch example of case 2 is utilized as the human input for all cases. The threshold values for the similarity metrics are fixed during the iterations, which ensures that solution pairs are retained as long as their difference is large according to the absolute criteria. Those values are first empirically set to ensure that about 50% of the solutions from the initial solution set are retained, then adjusted to make each similarity metric effective for detecting similar pairs. We set \(t_{SSIM}=0.9\), \(t_{MAE}=0.02\), \(t_{comp}=0.1\), and \(t_{vol}=0.01\). A comparison of the experimental results is shown in Table 4. The number of retained solutions after filtering with the adaptive parallel scale is 16, the same as the number of obtained solutions without this strategy and a smaller initial parallel scale (\(M=30\)). We highlight the results obtained using the two experimental settings in bold in Table 4, as their comparison validates the superiority of adaptive-scale parallel computing. However, this strategy leads to a shorter computing time and improved solution diversity, due to divergent exploration primarily occurring in the early optimization iterations, making a larger initial parallel scale more beneficial. As described in Section 3, due to the conflict between sketch-based constraints and the compliance minimization objective, the generated structures may include some unreasonable features. Figure 15 showcases two examples that include unreasonable features generated under the guidance of the sixth sketch example. In Figure 15a, a very thin protruding branch is generated guided by the stroke-based constraint, but it is not connected to the other side of the structure. From the von Mises stress map, which is useful to visualize the distribution of equivalent stress within the structural field and is computed by the finite element analysis steps as in the TO algorithm, it is clear that this branch is not contributing as a load path, which suggests that it is an unreasonable design. In Figure 15b, \begin{table}
\begin{tabular}{l l l l l l} \hline \hline
**Setting** & \(\mu_{comp}\) & \(\mu_{vol}\) & \(CV_{comp}\) & \(CV_{vol}\) & \(\overline{SSIM}\) & \(\overline{MAE}\) \\ \hline Density perturb (amp = 0) & **3.1164** & 0.3960 & 0.0151 & 0.0033 & 0.9731 & 0.0097 \\ Density perturb (amp = 0.1) & **3.3117** & 0.4019 & 0.0204 & 0.0047 & 0.9084 & 0.0207 \\ Density perturb (amp = 0.4) & **3.8991** & 0.4382 & 0.0192 & 0.0049 & 0.7358 & 0.0663 \\ Load cond perturb & 3.0322 & 0.3955 & 0.0243 & 0.0067 & 0.8700 & 0.0399 \\ Fourier freq perturb & 3.0322 & 0.3955 & 0.0298 & 0.0067 & 0.8641 & 0.0411 \\ Proposed & **3.0322** & **0.3955** & **0.0317** & **0.0075** & **0.8339** & **0.0516** \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparative experiment results for proposed TO framework and alternatives. the protrusion part on the support structure also does not contribute as load-bearing and exists solely to conform to the drawn shape of the sketch. Figure 16 shows examples of recognized regions of conflict using the sensitivity-based method. The regions of conflict are marked in red. The thin protruding branch in the second solution is recognized as unreasonable. It is clear that this feature would be the first to be removed if only compliance minimization and the volume constraint were applied. This solution is removed from the solution set, while the first solution with a smaller region of conflict is retained.