## 3 Results
### Hyperparameter Tuning Results  
This section highlights the results of the HPT process. Figure 7 shows the progress of the tuning process. The initial design phase is represented by the 50 black data points on the left side of the graph. Each point represents the result of the evaluation at different stages of our initial design phase. The more data points that are evaluated for the initial design, the more accurate our surrogate model will be at the start of the optimization process. The continuous red line that follows the initial points traces the trajectory of the best hyperparameter setup found so far within the tuning progresses. It can be seen that the value of the objective function could be reduced after initialization through optimization. Figure 8 illustrates the comparison of results over the entire evaluation horizon, in terms of MAE, computation time, and memory consumption between the tuned model and the model with default parameters. It is evident that the tuned model consistently outperformed the default algorithm, in terms of MAE, throughout the evaluation period. However, it is noteworthy that the tuned model consumed more computation time and memory resources than the default model. This can be explained by the fact that, as explained in Section 2.3.1, the weighting of the MAE in this particular tuning run was significantly higher than the weighting of the time and memory consumption. To statistically prove the improvement in performance, with respect to the metric, a one-sided \(t\)-test, as explained in Section 3.1.4, was performed again, with the following hypothesis:  
\[H_{0}:\mu_{HTR_{tuned}}-\mu_{HTR_{default}}\geq 0\] \[H_{1}:\mu_{HTR_{tuned}}-\mu_{HTR_{default}}<0.\]  
The result of the \(t\)-test stated that the zero hypothesis had been rejected. This meant that the average deviations of the predictions of the tuned model were significantly lower than those of the default model. The increase in computation time and memory consumption can be attributed to the values of the tuned parameters. Table 3 presents a comparison between the tuned and the default values for each hyperparameter, along with their respective importance, as determined during the SPOT optimization. It is evident that the leaf model and the prediction function of the leaves exerted the most significant influence on the evaluation outcomes. Upon contrasting the tuned and default values, the reasons behind the higher memory consumption and computation time in the tuned model became apparent. Specifically, the grace period, set at a value of 12, notably deviated from the default model's value of 200. Consequently, a considerably greater number of splits occurred in the tuned model. Figure 7: Visualization of the hyperparameter tuning progress. The Y-axis represents the values of the objective function, whereas the X-axis relates to the tuning steps. The solutions from the initial design are black, and the subsequent solutions from the optimization process are red. Hyperparameter Tuning for Improving Time and Memory Consumption  
In production processes, certain conditions may necessitate the optimization of algorithms, with respect to time and memory consumption. These conditions may include a requirement for near-real-time capability, limited RAM capacities, or the need to conserve energy. Consequently, we conducted an overhead experiment, to demonstrate that the HTR can be optimized for these two criteria, using SPOT. We adjusted the weightings as described in Section 2.3.1 to prioritize optimization (MAE: 1, memory consumption: 10, calculation time: 10). Figure 9 illustrates that, over the entire evaluation horizon, the computation time and memory consumption of the tuned model were significantly lower than those of the default model. However, it is also evident that the tuned model exhibited a higher deviation in the predictions of vibration development due to the altered optimization priority.