## 3 Experimental Results and Discussion
### Comparative Analysis of the Optimization Efficiency of the Parallel EGO Algorithm  
In practical performance optimization problems, the primary source of time consumption is the wall-clock time cost. In a single optimization cycle, the wall-clock time cost primarily consists of three components: experimental model preparation, waiting gap, and experimental evaluation (Figure 10). An effective approach to significantly improving optimization efficiency is to achieve the desired optimization objective with as few optimization cycles as possible. Therefore, the multi-point infill criterion was proposed based on this principle. To investigate the impact of different infill point quantities on the optimization efficiency of the parallel EGO algorithm, Table 3 presents the relevant statistics on the number of optimization cycles required to achieve the predefined convergence criteria for the parallel EGO algorithm based on both OK and GEK models. For the case based on the OK model, the number of optimization cycles continuously decreases with an increasing number of infill points for almost all test functions, except for F3. This result is generally consistent with the findings presented in [24]. However, the reduction in the number of  
Figure 9: Average convergence curves of the GEK-based parallel EGO algorithm on all tested problems. cycles required for the parallel EGO algorithm to reach the convergence criterion does not strictly follow a proportional relationship with the increase in the number of infill points. For example, on F1, taking the parallel EGO algorithm with an infill point count of 2 as the baseline, the parallel EGO algorithm with an infill point count of 4 accelerates the search by approximately \(92.77/49.33\approx 1.88\) times. However, for a strictly linear speedup, the expected factor should be 2. A possible explanation given in previous studies is that as the sequential selection process progresses within a single optimization cycle, an increasing number of IFs are multiplied by the initial EI criterion, making the PEI criterion increasingly unreliable. It is noteworthy that for F5, the parallel EGO algorithm with a point-filling number of 4 achieved an acceleration factor of approximately \(53.13/26.63\approx 2.00\) times. To explain this phenomenon, Figure 11 illustrates the process of the PEI criterion searching for multiple potential improvement points within an optimization cycle. Strictly speaking, the fundamental principle of the PEI criterion remains a sequential process, rather than a true parallel point-filling criterion (its parallel concept is based on the parallelization of external computational resources, rather than the parallelization of the algorithm itself). The initial potential improvement point is identified using the original EI criterion, while subsequent points depend on the approximation accuracy between the current PEI function and the true EI function. When the discrepancy between PEI and true EI remains relatively small, the search process benefits from more reliable information. Conversely, significant deviations may lead to information loss, potentially misleading the EGO algorithm's exploration direction. As the candidate selection process progresses, these approximation errors accumulate, ultimately affecting the overall optimization convergence rate. A truly parallel candidate selection approach would require completely independent selection of multiple points within each optimization cycle. Interestingly, the observed linear relationship between efficiency improvement and increased point-filling quantity in certain special cases may stem from how the influence function-induced differences between PEI and true EI functions provide beneficial algorithmic diversity. This diversity enhances the probability of escaping local optima while promoting faster convergence to higher-quality solutions.