## 3 Results and Discussion
### Optimum Layout of Conformal Cooling Channels for the Cooling Stage  
According to the Moldex3D simulation, the average mold temperature was 89.5 \({}^{\circ}\)C and the average melt temperature was 215.6 \({}^{\circ}\)C at the end of the packing stage. These temperatures were input into COMSOL and served as the initial conditions of the cooling stage. By simulating the cooling process for the planar conformal cooling channels, the variations in the maximum and minimum surface temperature of the melt in the mold cavity were determined (Figure 9a). According to the cooling time suggested by Moldex3D, the lens was ejected at 18.6 s. Figure 9b displays the surface temperature distribution for the lens, with a maximum temperature of 359.713 K, a minimum temperature of 358.601 K, and a temperature difference of 1.112 K.  
The GBA and RGA algorithms of the SmartDO software were employed for evenly reducing the surface temperature of the melt in the mold cavity. The objective function of the two algorithms converged to a minimum value in the optimization procedure (Figure 10). The objective function value of the GBA was 19.78, whereas that of the RGA was 16.54. The optimized design parameters obtained using these two algorithms are displayed in Figure 11. By using these design parameters (Table 2), \begin{table}
\begin{tabular}{c c c c c c} \hline  & **Control factors** & **Level 1** & **Level 2** & **Level 3** & **Level 4** & **Level 5** \\ \hline A & Melt temperature (\({}^{\circ}\)C) & 240 & 255 & 270 & 285 & 300 \\ B & Mold temperature (\({}^{\circ}\)C) & 80.00 & 89.75 & 99.50 & 109.25 & 119.00 \\ C & Filling time (sec) & 0.69 & 0.79 & 0.89 & 0.99 & 1.09 \\ D & Packing time (sec) & 6 & 7 & 8 & 9 & 10 \\ \hline \end{tabular}
\end{table} 
Table 1: Four control factors and five levels used for the design of experiments (DOE) in Moldex3D. Figure 9: (**a**) Surface temperature of the melt during the cooling stage and (**b**) surface temperature of the melt at the default ejection time of 18.6 s when using the planar conformal cooling channels. two conformal cooling channels with different geometric layouts could be created and imported into COMSOL to simulate the cooling process. The cooling efficiency and improvement in the lens temperature distribution were compared between the GBA- and RGA-optimized channels. The conformal cooling channels designed using the GBA were used to simulate the cooling process. The results indicated the variations in the maximum and minimum surface temperature of the melt in the mold cavity, as displayed in Figure 12a. For the planar conformal cooling channel, the default maximum surface temperature for the ejected lens was set as 359.713 K. For a temperature of 359.713 K, the ejection time for the GBA-optimized conformal cooling channels was 16.9 s. However, according to the cooling time suggested by Moldex3D, the lens was ejected at 18.6 s. The temperature distribution for the surface of the lens at 18.6 s is displayed in Figure 12b, with a maximum temperature of 358.906 K, \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Optimized Parameters** & **DV1** & **DV2** & **DV3** & **DV4** & **DV5** & **DV6** & **DV7** & **DV8** \\ \hline Results of GBA & 16.59 & 15.15 & 16.89 & 16.98 & \(-\)7.98 & \(-\)8.00 & \(-\)8.00 & \(-\)6.51 \\ Results of RGA & 13.51 & 14.02 & 14.65 & 17.16 & \(-\)1.99 & \(-\)8.00 & \(-\)6.31 & \(-\)2.47 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The optimized DVs in Figure 11 were obtained from the GBA and RGA. Figure 11: Optimized DVs obtained from: **(a)** the GBA and **(b)** RGA. Figure 10: History of the objective function evolved from: **(a)** the GBA and **(b)** RGA during optimization. a minimum temperature of 358.173 K, and a temperature difference of 0.733 K. Moreover, the ejection time for the RGA-optimized conformal cooling channels was 14.55 s (Figure 13a).