## 3 Results and Discussion
### Optimum Layout of Conformal Cooling Channels for the Cooling Stage
The temperature distribution on the lens surface at 18.6 s for the RGA-optimized channels is displayed in Figure 13b, with a maximum temperature of 357.861 K, a minimum temperature of 357.255 K, and a temperature difference of 0.606 K. Thus, after the planar conformal cooling channels were modified, the GBA- and RGA-optimized three-dimensional conformal cooling channels enhanced the cooling efficiency and improved the temperature distribution of the melt in the mold cavity. Comparison of the Conformal Cooling Channels Designed by Using Different Algorithms for the Entire Injection Molding Process  
The conformal cooling channels designed using the GBA and RGA optimization algorithms were imported into Rhinoceros 3D software, which was used to construct the solid mesh models. The models were then used to execute the entire injection molding simulation with the Moldex3D software. The computation time was approximately 45 min when using two 2.4-GHz Intel Xeon E5-2620 CPUs with 64 GB of RAM. The results indicated that the optimized conformal cooling channels  
Figure 12: (**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 GBA-optimized cooling channels. Figure 13: (**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 RGA-optimized cooling channels. exhibited a lower average surface temperature for the melt compared with that exhibited by the planar conformal cooling channels (Figure 14). At the end of cooling, the surface temperatures simulated using Moldex3D were consistent with those simulated using COMSOL (Figure 9b, Figure 12b, and Figure 13b). If the temperature on the lens surface could be evenly distributed, the thermal-displacement-induced warpage could be improved. Therefore, to evaluate the thermally induced warpage, 18 measured nodes were selected on the lens surface. The locations and numbering of these measured nodes are displayed in Figure 15a. Measured nodes 1-16 were located on the top and bottom edges of the lens and used to calculate the total thermal warpage. The results were used to evaluate the variation in the circularity (roundness) due to the warpage. The average thermal warpage values for the planar conformal cooling channels, GBA-optimized conformal cooling channels, and RGA-optimized conformal cooling channels were 98.296, 98.214, and 98.121 \(\upmu\)m, respectively (Figure 15b,c). Thus, the optimized conformal cooling channels exhibited a lower thermal warpage than the planar conformal cooling channels. Moreover, measured nodes 17 and 18 were located at the centers of the top and bottom surfaces of the lens, respectively. These two measured nodes were used to observe the relative thermal warpage in the vertical direction (z-direction). The vertical thermal warpage values for the GBA- and RGA-optimized conformal cooling channels were 21.617 and 21.565 \(\upmu\)m, respectively. Both these values were lower than the vertical thermal warpage of the planar conformal cooling channels (21.638 \(\upmu\)m). Figure 14: Average surface temperature of the melt in cavity during the complete injection molding cycle with different conformal cooling channels. When designing cooling channels, the rules for their geometric layout should be considered and the temperature difference between the inlet and outlet should be minimized to prevent the warpage of the lens due to uneven temperature distribution in the mold. Generally, if the product requires high accuracy, the temperature difference between the inlet and outlet should be lower than 2.5 \({}^{\circ}\)C [28]. The simulation results of the GBA- and RGA-optimized cooling channels indicated that the temperature difference between the inlet and outlet of the optimized cooling channels was lower than that of the planar conformal cooling channels regardless of the upper and bottom channels (Figure 16).