## 4 Experimental Results and Discussion
### First Experimental Scenario: Synthetic Data
The GWO algorithm achieved the best result on two of the six datasets but performed poorly on the rest. Although the SCA did not yield the best result except for one dataset, it achieved an average rank of 2.08, placing first overall. WOA followed closely with an average rank of 2.17, while the PSO algorithm produced the worst results. * **With a missing rate of 15%:** The PSO algorithm performed best on only two of the six datasets, whereas GWO ranked lowest on most datasets. Overall, WOA was the best performer, with an average rank of 1.83, and SCA came second with an average rank of 2. * **With a missing rate of 25%:** WOA achieved the highest performance on the majority of datasets. Although PSO performed best on one dataset, it struggled with the others. In general, WOA was the top performer, followed by SCA and GWO, which shared an average rank of 2.5. Figure 4 shows the convergence curves of the four optimizers, allowing for a comparison of their performance in terms of convergence speed. As illustrated, GWO achieved the best results with a relatively small number of iterations, converging closer to the optimal solution faster than the other algorithms. PSO and SCA produced approximately similar results, while WOA was the slowest. One reason for GWO's superior performance is its reliance on the best three solutions (see Section 2.2), which enhances its ability to escape from local minima compared to the other optimizers that depend solely on a single best solution. In summary, WOA demonstrated superiority over the other optimization algorithms, followed by SCA in second place, GWO in third, and PSO in fourth. While there were differences in performance among the four algorithms, none showed significant outperformance over the others. However, since WOA achieved the best results overall, we will use it in our subsequent experiments. In other words, while the WOA algorithm demonstrated the best performance overall, this does not guarantee it will consistently yield the best results in every scenario. This observation aligns with the findings reported in [39]. In this experiment, another sub-experiment was also conducted to determine the computational time required for each algorithm as a criterion for identifying the best optimization algorithm (PSO, GWO, SCA, and WOA) for our proposed imputation method. We applied the FS method with each of the four optimization algorithms--specifically, FS-PSO, FS-GWO, FS-SCA, and FS-WOA--across three synthetic datasets, each with a different number of features (5, 8, and 12), as shown in Table 4.  
In this simple experiment, we used a 5% missing rate on all datasets, calculated the computation time for each method five times, and then averaged the results. As shown in  
Figure 4: Visualization of the convergence curves of the PSO, GWO, WOA, and SCA algorithms using a synthetic dataset. Table 4, all methods required significantly high computing power. FS-WOA had the longest computation time, followed by FS-GWO in second place and FS-SCA in third. FS-PSO had the shortest computation time among the methods compared. However, in terms of computation power, this experiment shows that there is no significant difference between all optimization algorithms we used.