## 3 Results and Discussions
### Optimizing Printing Parameters with MOPSO
#### 3.4.2 Optimized Printing Parameters for an Angled Strut  
To extend our study, we apply the same approach to a 60\({}^{\circ}\) angled strut. The objective functions and the considering printing parameters (including the upper and lower bounds) are the same as the vertical strut, but the difference is that surface roughness is different in upper and lower sides. When the angle of the strut is 60\({}^{\circ}\) as shown in Figure 11, the result from the upper side of the strut is expected to have no major difference from the vertical strut. However, on the lower side, there exists an additional effect on surface roughness since the light penetration from the upper layer may polymerize resin deeper to the layer below. To visualize this difference, we performed two MOPSO considering surface roughness of the lower and the upper side of a strut and compared the result in Figure 10. The Pareto optimal sets in the figure clearly display the trade-off between surface roughness and printing time; minimizing total printing time increases RMSE, and vice versa. Point C and D are two extremes of optimizing lower side of the 60\({}^{\circ}\) angled strut. The optimized parameters of point C and D are (PI = 53.89 mol/m\({}^{3}\), PA = 6.10 mol/m\({}^{3}\), LT = 20.00 \(\upmu\)m, CT = 1.00 s, RMSE = 2.13 \(\upmu\)m, printing time = 300.00 s) and (PI = 72.4 mol/m\({}^{3}\), PA = 2.03 mol/m\({}^{3}\), LT = 120.00 \(\upmu\)m, CT = 4.00 s, RMSE = 19.25 \(\upmu\)m, printing time = 48.33 s), respectively. It is interesting to see that when the printing time is maximized and RMSE is minimized, PA is the maximum value at the upper bound and LT is minimum value at the lower bound. On the contrary, when the printing time is minimized, LT is maximized and PA is minimized. When the upper side of surface profile is considered, the two extremes E and F are (PI = 60.56 mol/m\({}^{3}\), PA = 6.10 mol/m\({}^{3}\), LT = 20.00 \(\upmu\)m, CT = 1.00 s, RMSE = 5.48 \(\upmu\)m, Printing time = 300.00 s) and (PI = 64.30 mol/m\({}^{3}\), PA = 3.91 mol/m\({}^{3}\), LT = 120.00 \(\upmu\)m, CT = 1.00 s, RMSE = 18.28 \(\upmu\)m, Printing time = 48.33 s), respectively. The details of all four extremes are displayed in Table 9. This result also supports the high correlation between the RMSE and (PA) and LT as discussed in Section 3.2. Figure 11: 60\({}^{\circ}\) angled strut and its mean profiles for upper (red) and lower (blue) surface profile. \begin{table}
\begin{tabular}{c c c c c c} \hline \multirow{2}{*}{**Objectives**} & \multicolumn{2}{c}{**Optimized Parameters of Group A**} & \multicolumn{2}{c}{**Optimized Parameters of Group B**} & \multicolumn{2}{c}{**Non-Optimized Parameters 1**} & \multicolumn{2}{c}{**Non-Optimized Parameters 2**} \\  & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} \\ Total printing time (s) & **54.79** & **48.33** & 108.85 & 72.49 & 48.33 \\ Surface roughness (\(\upmu\)m) & **1.45** & **1.5** & 1.45 & 1.94 & 2.39 \\ \hline \end{tabular}
\end{table} 
Table 8: Objectives comparison between optimized and non-optimized printing conditions. The Pareto optimal set clearly visualizes the difference produced by the light penetration. Since the printing time is dominated by LT, the extreme in the printing times between both cases remain the same. However, the surface profile RMSE in Figure 10 shows a clear difference because it is very likely that the light penetrated from the upper layer changes the surface profile.