## 3 Experimental Results and Discussion
### Comparative Analysis of the Optimizing Diversity of the Parallel EGO Algorithm
#### 3.3.2 Exploitation and Exploration  
Almost all global optimization algorithms aim to achieve a reasonable balance between local exploitation and global exploration, and the EGO algorithm is no exception. To evaluate the impact of different point-filling numbers on the balance between local exploitation and global exploration in the parallel EGO algorithm, the percentage change trends of exploitation-exploration throughout the optimization process were calculated using the following formula:  
\[\textit{exploration}(l)=\left(\frac{\textit{Pop}_{\textit{div}}(l)}{max(Pop_ {\textit{div}}(l))}\right)\times 100\% \tag{25}\]  
\[\textit{exploration}(l)=\left(\frac{\left\|Pop_{\textit{div}}(l)-max(Pop_{ \textit{div}}(l))\right\|}{max(Pop_{\textit{div}}(l))}\right)\times 100\% \tag{26}\]  
Here, \(Pop_{\textit{div}}\) is defined in Equation (24) and represents the diversity of the entire population.  
Figures 14 and 15 show the trends of the exploration-exploitation ratio over the process of optimization for the parallel EGO algorithm based on the OK and GEK models, respectively, under different point-filling quantities. Overall, it can be observed that the parallel EGO algorithm with different point-filling quantities maintains a high level of exploration during the early stages of optimization, allowing the algorithm to explore a broader design space for global optima. As the optimization progresses, the exploration  
Figure 13: Population diversity curves of the GEK-based parallel EGO algorithm on all tested problems.  
rate gradually decreases while the exploitation rate increases, enabling the algorithm to continue improving the solution quality in the vicinity of local optima. For the case based on the OK model, as shown in Figure 8, the point-filling quantity of 2 consistently achieves the best convergence speed on F1, F4, F6, F8, and F9. Therefore, with a point-filling quantity of 2, the parallel EGO algorithm better maintains a reasonable balance between local exploitation and global exploration. This conclusion can be drawn from the trend of the exploration-exploitation curves in Figure 14, as the exploration-exploitation curves for the case with two points remain smaller and larger than those for the other point configurations throughout almost the entire optimization process.  
For the case based on the GEK model, as shown in Figure 9, except for F1, F3, and F8, where there is a significant difference in convergence speed between different point-filling quantities, the convergence speed for the other test functions only shows slight differences in the early stages of optimization. As the optimization iterations progress, the convergence speed remains nearly consistent. Therefore, as shown in Figure 15, the differences in the impact of different point-filling quantities on the balance between local exploitation and global exploration of the parallel EGO algorithm are negligible for these test functions. This indicates that the GEK model provides greater reliability and stability to the parallel EGO algorithm.  
Figure 14: Exploration and exploitation curves of the OK-based parallel EGO algorithm on all tested problems.