## 3 Results  
The independent variables in the design included the display surface thickness, outer layer thickness, and frame material. Both the display surface and outer layer were 0.2-0.4 mm thick, where the thickness of each was changed in 0.05 mm steps. The frames were made of acrylonitrile butadiene styrene (ABS) and polystyrene (PS). ABS provides favorable mechanical properties such as impact resistance, toughness, and rigidity. PS is clear, hard, brittle, and inexpensive. In total, there were 50 different combinations of these three design variables. The environmental impacts of these 50 combinations could be obtained using the LCA software, and they were assessed using Eco-Indicator 996. More specifically, the use of fossil fuels was used as an evaluation indicator because fossil fuels produce the most significant pollution. The detailed data are listed in Supplementary Table S1. The  
Figure 4: Multi-disciplinary and multi-objective optimization flowchart. RSM parameters were defined as listed in Table 1. The display surface thickness, outer layer thickness, and frame material were defined as the independent variables, whereas the environmental impacts were considered to be the dependent variables. In order to reduce the error rates of the regression models, the three types of models were obtained and compared to select the one with the smallest error rates for multi-disciplinary and MOO. First, the 50 sets of data in Supplementary Table S1 were divided into validation and training sets. The former consisted of the 7 th, 14 th, 21 st, 28 th, 32 nd, 39 th, and 46 th sets, while the remaining 43 sets were taken as the training sets. All the data of the training sets were used for the calculations to attain the required regression coefficients (Supplementary Tables S2-S4) and the regression equations shown as Equations (5)-(7). The error rates of the training and validation sets were compared, as illustrated in Supplementary Tables S5-S7. \[V_{1}(X)=-0.155+2.981X_{1}+1.665X_{2}+0.236X_{3} \tag{5}\]  
\[V_{1}(X)=0.188+2.25X_{1}+1.217X_{2}+0.01396X_{3}+0.113X_{1}X_{2} \tag{6}\]  
\[+0.464X_{1}X_{3}+0.276X_{2}X_{3}\]  
\[V_{1}(X)=0.193+2.293X_{1}+1.205X_{2}+0.122X_{1}X_{2}+0.464X_{1}X_{3}+0.276X_{2}X _{3}\]  
\[-0.07762X_{1}X_{1}+0.0164X_{2}X_{2}+0.004652X_{3}X_{3} \tag{7}\]  
Similar to the environmental impact evaluation, the mechanical strength assessment took the material, display surface thickness, and outer layer thickness as the adjustable independent parameters. In the meantime, the locations and numbers of the internal locking holes of the frames were kept constant. It was assumed that a user would apply a force of 4 N under normal operation conditions. The 50 sets of von Mises stress data for the components are listed in Supplementary Table S8. The RSM parameters were defined as listed in Table 2. The display surface thickness, outer layer thickness, and frame material were the independent variables, whereas the mechanical strength was the dependent variable. Next, similar to the procedures in the environmental impact evaluation, three types of regression models were computed, and the one with the smallest error rate was chosen for the multi-disciplinary and MOO. The training and validation sets were defined in the same way as those adopted for the environmental impact evaluation. The calculated regression coefficients are given in Supplementary Tables S9-S11, and the regression equations are listed as Equations (8)-(10). The error rates of the training and validation sets are compared \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 \(Y_{1}\) & use of fossil fuels & 1.05 mpt-2.21 mpt \\ \hline \end{tabular}
\end{table} 
Table 1: Definition of RSM parameters for the environmental impact model.