## 4 Simulation and Analysis
### Analysis of Time Consumption  
The computational time directly reflects the efficiency of a satellite selection algorithm, where a shorter computation time indicates a higher efficiency in satellite selection. Figure 14 illustrates the computational time per second for the different algorithms when selecting four, five, or six satellites. Figure 15 provides a comparison of the average computational time across different algorithms. Figure 16 presents the comparative analysis of the average difference in computational time between various algorithms and the exhaustive search method. Table 2 summarizes the computational time for different algorithms and the time difference relative to the exhaustive search method, thereby offering a comprehensive evaluation of the performance of these algorithms in terms of their satellite selection efficiency. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**4 Satellites**} & \multicolumn{2}{c}{**5 Satellites**} & \multicolumn{2}{c}{**6 Satellites**} \\ \hline Traversal & Average & Ratio & Average & Ratio & Average & Ratio \\ GWO & 262.71 & & 234.06 & & 216.28 & \\ SFGWO & 301.39 & 1.15 & 251.11 & 1.07 & 229.27 & 1.06 \\ SFGWO-A & 273.14 & 1.04 & 240.16 & 1.03 & 220.88 & 1.02 \\ SFGWO-B & 324.21 & 1.24 & 263.29 & 1.13 & 231.79 & 1.07 \\ MSFGWO & 283.12 & 1.08 & 243.14 & 1.04 & 222.08 & 1.03 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: DGDOP values under different numbers of selected satellites. Figure 14: The differences in time consumption under different numbers of selected satellites. Figure 15: Comparison of average time consumption under different numbers of selected satellites. Based on analysis of the data presented in Figures 14-16 and Table 2, it is evident that as the number of selected satellites increases, the computational time required for each algorithm exhibits an upward trend. Specifically, the traversal method demonstrated significant fluctuations in computational time per second, whereas the intelligent optimization algorithms showed relatively minor variations. Moreover, the increase in computational time for the traversal method was markedly higher, when compared to the intelligent optimization algorithms, as the number of selected satellites increased. Notably, the GWO and SFGWO-B algorithms exhibited slightly lower computational times than the SFGWO-A and MSFGWO algorithms. This suggests that the incorporation of the VNS perturbation mechanism and the GA mutation strategy into the GWO algorithm increases its computational complexity, thereby leading to a longer computational time. The minimal difference in computational time between the GWO and SFGWO-B algorithms, as well as between the SFGWO-A and MSFGWO algorithms, indicates that the introduction of the EWM algorithm has a limited impact on computational time. Although the MSFGWO algorithm proposed in this study had the highest computational time among the four optimization algorithms, it remained significantly lower than that of the traversal method. For instance, when selecting six satellites, the MSFGWO algorithm consumed 0.0174 s, and the calculation efficiency is increased by 93.43% when compared to the traversal method. In summary, the experimental results indicate that incorporating the perturbation mechanism of the VNS algorithm and the mutation strategy of the GA into the GWO \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**4 Satellites**} & \multicolumn{2}{c}{**5 Satellites**} & \multicolumn{2}{c}{**6 Satellites**} \\ \hline  & Average & Efficiency & Average & Efficiency & Average & Efficiency \\  & (s) & Improvement (\%) & (s) & Improvement (\%) & (s) & Improvement (\%) \\ Traversal & 0.0442 & & 0.1110 & & 0.2650 & \\ GWO & 0.0088 & 80.09 & 0.0092 & 91.71 & 0.0106 & 96.00 \\ SFGWO-A & 0.0151 & 65.84 & 0.0164 & 85.23 & 0.0173 & 93.47 \\ SFGWO-B & 0.0089 & 79.86 & 0.0099 & 91.08 & 0.0108 & 95.92 \\ MSFGWO & 0.0162 & 63.35 & 0.0166 & 85.05 & 0.0174 & 93.43 \\ \hline \hline \end{tabular}
\end{table}