## 4 Simulation and Analysis
### DGDOP Analysis  
The reliability of the algorithms in the experiment was quantified by the ratio defined as the DGDOP value of a given algorithm divided by the DGDOP value obtained using the exhaustive search method. A lower ratio indicates that the DGDOP value of the selection result generated by an algorithm is closer to the optimal DGDOP value obtained through an exhaustive search; in particular, the associated results demonstrate the superior performance of the MSFGWO method. Figures 9-11 illustrate the DGDOP values of the satellite selection results per second for different algorithms selecting four, five, or six satellites, respectively. Figure 12 presents a comparison of the average DGDOP values, while Figure 13 compares the ratios of these average DGDOP values.  
Figure 10: Comparison of DGDOP values when selecting five satellites.  
Figure 9: Comparison of DGDOP values when selecting four satellites.  
Based on analysis of the data presented in Figures 9-13 and Table 1, it is evident that as the number of selected satellites increases, the DGDOP values calculated by each algorithm are significantly higher than the number of satellites.  
Figure 11: Comparison of DGDOP values when selecting six satellites.  
Figure 12: Comparison of average DGDOP values under different numbers of selected satellites.  
Figure 13: Comparison of average DGDOP ratio under different numbers of selected satellites.  
exhibit a consistent downward trend. Specifically, among the four algorithms, the DGDOP value obtained with the SFGWO-A was closest to that of the traversal method, with a ratio of 1.02 when selecting six satellites. This indicates that integrating the perturbation mechanism of the VNS algorithm and the mutation strategy of the GA into the GWO algorithm significantly enhances its global search capability for optimal solutions. In contrast, SFGWO-B aims to optimize the satellite continuous observation time through incorporating the EWM algorithm into the GWO algorithm. However, this approach resulted in a slight increase in DGDOP values in exchange for extended continuous observation times. Due to the tendency of the GWO algorithm to fall into local optima, the DGDOP value of SFGWO-B was higher than that of the standard GWO algorithm, representing the highest DGDOP value among the four algorithms. Conversely, the MSFGWO algorithm proposed in this study achieved a balance between optimizing the DGDOP value and ensuring continuous satellite observations. Consequently, its DGDOP value was lower than that of the traditional GWO algorithm and SFGWO-B but slightly higher than that of SFGWO-A and the traversal method. Additionally, the MSFGWO algorithm demonstrated relatively stable optimization performance, with a ratio of 1.03 when selecting six satellites, indicating that it effectively balances practical continuous observation requirements with higher accuracy.  
The aforementioned experimental results substantiate that incorporating the perturbation mechanism of the VNS algorithm and the mutation strategy of the GA into the GWO algorithm significantly enhances the population diversity and effectively mitigates the risk of converging to local optima. This integration boosts the overall optimization capability of the GWO algorithm, thereby reducing the DGDOP value. However, the introduction of the EWM algorithm to optimize the continuous satellite observation time resulted in a marginal increase in the DGDOP value.