## 3 Results
\begin{table}
\begin{tabular}{c c c} \hline
**ID** & **Parameter** & **Value** \\ \hline \(X_{1}\) & display surface thickness & 0.2 mm, 0.25 mm, 0.3 mm, 0.35 mm, 0.4 mm \\ \hline \(X_{2}\) & outer layer thickness of the frame & 0.2 mm, 0.25 mm, 0.3 mm, 0.35 mm, 0.4 mm \\ \hline \(X_{3}\) & material & 1 (ABS), 2 (PS) \\ \hline \(Y_{2}\) & von Mises stress & \(151,248\) (N/m\({}^{2}\)) \(\sim\) 432, 188 (N/m\({}^{2}\)) \\ \hline \end{tabular}
\end{table} 
Table 2: Definitions of RSM parameters for the mechanical strength model. in Supplementary Tables S12-S14. According to the errors of the six equations, for both the environmental impacts and mechanical strength, the first-order models generated the greatest errors, so they were discarded. In contrast, the interactive first-order model for the environmental impacts outperformed its second-order counterpart, while the performance of the interactive first-order model for the mechanical strength fell considerably behind that of the second-order model. Therefore, the second-order models, i.e., Equations (7) and (10), were chosen. \[V_{2}(X)=683,365.192-199,420.3X_{1}-196,287.756X_{2}-133.136X_{3} \tag{8}\]  
\[V_{2}(X)=81,415.101-1,648,210.1X_{1}-618,513.711X_{2}-554.836X_{3} \tag{9}\]  
\[+1,444,079.254X_{1}X_{2}-5.31X_{1}X_{3}+1389.877X_{2}X_{3}\] \[V_{2}(X)=1,095,087.928-3,586,671.207X_{1}-685,783.288X_{2}+915,672. 330X_{1}X_{2}\] \[-5.310X_{1}X_{3}+1389.877X_{2}X_{3}+3,542,698.597X_{1}X_{1} \tag{10}\]  
Since \(V_{1}(x)\) and \(V_{2}(x)\) in the multi-objective function are parameters from two completely different fields, normalization is necessary before the function can be treated as a single-objective function for optimization. In this study, two normalization methods were applied, and \(V_{1}(x)\) and \(V_{2}(x)\) were assigned different weights, w, for optimization. The first normalization (Method 1) divided the objective function by its maximum value (Equation (11)), whereas the second method (Method 2) first computed the difference between the function and its minimum value and then divided the absolute difference by the difference between the maximum and the minimum (Equation (12)). The weighted normalized objective functions are given as Equations (13) and (14). \[\left(\frac{V_{i}(X)}{V_{i(max)}},\ \ i=1,\ 2,\ \ V_{1(max)}=2.21,\ \ V_{2(max)}=432,188\right) \tag{11}\]  
\[\left(\frac{V_{i}(X)-V_{i(min)}}{V_{i(max)}-V_{i(min)}},\ \ i=1,\ 2,V_{1(max)}=2.21,\ \ V_{1( min)}=1.05,\right. \tag{12}\]  
\[\left.V_{2(max)}=432,188,\ \ V_{2(min)}=151,248\right)\]  
\[V(X)=w1\times\frac{V_{1}(X)-V_{1(max)}}{V_{1(max)}-V_{1(min)}}+w2\times\frac{ V_{2}(X)}{V_{2(max)}},\ \ w1+w2=1 \tag{13}\]  
\[V_{2}(X)=683,365.192-199,420.3X_{1}-196,287.756X_{2}-133.136X_{3} \tag{8}\]0  
The multi-objective function equation is denoted as \(V(X)\). For the GA, the length of the gene code of a single individual was set as 12, and the total number of populations equaled 20. \(X_{1}\) to \(X_{3}\) were defined as the gene codes of individuals in the GA. The ultimate goal was to obtain the minimum value of \(V(X)\). Thus, the fitness function was defined as \(1.0/V(X)\), given that \(1.0/V(X)>0\). The ranges of \(X_{1}\) to \(X_{3}\) are listed in \[V_{2}(X)=683,365.192-199,420.3X_{1}-196,287.756X_{2}-133.136X_{3} \tag{8}\]1 The crossover rate, \(P_{c}\), was set as 0.8, while the mutation rate, \(P_{m}\), was \(1/12\). The calculation ended when the number of evolutionary iterations reached 1000. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Gene Code ID** & **Gene Code Length** & **Actual Range** \\ \hline \(X_{1}\) & 5 & 0.2 mm\(\sim\)0.4 mm \\ \hline \(X_{2}\) & 5 & 0.2 mm\(\sim\)0.4 mm \\ \hline \(X_{3}\) & 2 & 1, 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Ranges of optimization parameters.