## 3 Results and Discussions
### Optimizing Printing Parameters with MOPSO
#### 3.4.1 Optimized Printing Parameters for a Vertical Strut  
In this section, we apply MOPSO to determine optimal printing parameters that minimizes two objective functions: surface roughness of a printed strut and printing time when the angle of the strut is 90\({}^{\circ}\) from the horizontal plane (vertical strut). Table 7 shows the upper and lower bounds of the parameters considered.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Level** & **PI** & **PA** & **O** & **LT** & **CT** \\ \hline
1 & \(-\)1.2319 & 4.7418 & \(-\)0.4110 & 4.3692 & \(-\)1.9269 \\
2 & \(-\)0.6055 & \(-\)1.2770 & \(-\)0.9787 & \(-\)1.8804 & \(-\)0.3418 \\
3 & \(-\)0.2605 & \(-\)5.5626 & \(-\)0.7081 & \(-\)4.5867 & 0.1708 \\ Delta & 0.9714 & 10.3044 & 0.5677 & 8.9559 & 2.0977 \\ Rank & 4 & 1 & 5 & 3 & 2 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Response table for signal-to-noise ratio: smaller the better.  
Figure 9: SN ratio analysis based on RMSE response. The level corresponding to the maximum value of mean of SN ratios is selected for each factor.  
After performing MOPSO, the graphical representation of Pareto set shown in Figure 10 was generated. \(x\)- and \(y\)-axis are surface roughness and printing time, respectively. All the agents produce Pareto front, but the shape of Pareto front consists of two major groups, as listed in Table 7. The corresponding objective values are (RMSE = 1.45 \(\upmu\)m, printing time = 54.79 s), (RMSE = 1.5 \(\upmu\)m, printing time = 48.33 s) for group A and B, respectively. For a vertical strut, higher PI and lower PA improve surface roughness, so that it reduces the surface profile RMSE while giving the small effect on the printing time. In addition, since CT does not change the roughness significantly, it stays at the lower bound to minimize the total printing time, as expected. Table 8 shows the comparison between the several printing times and surface roughness of non-optimized printing examples and optimized examples of Group A and B, shown in the bold in Table 8. The parameter sets for non-optimized printing conditions 1, 2, and 3 are [PI = 65.44 mol/m\({}^{3}\), PA = 4.74 mol/m\({}^{3}\), LT = 53 \(\upmu\)m, CT = 1.00 s, PI = 64.12 mol/m\({}^{3}\), PA = 3.04 mol/m\({}^{3}\), LT = 80 \(\upmu\)m, CT = 2.00 s, PI = 54.09 mol/m\({}^{3}\), PA = 2.66 mol/m\({}^{3}\), LT = 120 \(\upmu\)m, CT = 4.00 s], respectively. When the Group A and the result from non-optimized parameter 1 are compared to each other, it is realized that the proposed optimization framework can reduce the printing time 50% while keeping the surface quality. In addition, the comparison between the Group B and the result from non-optimized parameter 3 shows that the proposed optimization framework reduces 38% of surface roughness when the printing process is at the minimum printing time. Lastly, the result from non-optimized parameters 2 shows the higher printing time and the surface roughness, which often happens when the printing parameters are not optimized. Based on this result, it is clearly seen that the optimized parameters provide better or at least similar surface roughness while significantly reducing printing time.