## 3 Results
### Dynamic Satellite Number Selection Experiment  
Based on the experimental conditions, we conducted simulation experiments comparing dynamic satellite selection in the environment shown in Figure 2. Figure 3 presents a comparison of the average dynamic satellite selection outcomes and their corresponding DGDOP values over the UAV's full flight trajectory, alongside the Pareto optimal frontier. The results demonstrate how closely the selection algorithms approach the theoretical performance limits. The DGDOP values optimized by the GWO algorithm are slightly higher than those of the other algorithms when the number of selected satellites is 6 or 7. The PSO algorithm generally performs worse than the NSWOA and NSGAII algorithms, with both NSWOA and NSGAII algorithms being closer to the theoretical frontier. When the number of selected satellites is less than 8, the DGDOP value of the NSWOA is lower than that of NSGAII, with an average reduction of 1.9136. However, when the number \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Meaning** & **Value** \\ \hline \(N\) & Satellite Combination Index Subset Size & 200 \\ \(T\) & Maximum Iteration Count & 100 \\ \(n_{max}\) & Satellite Selection Threshold & 10 \\ \(\beta\) & Leadership Selection Pressure Parameter & 4 \\ \(\alpha\) & Grid Expansion Coefficient & 0.1 \\ \(nGrid\) & Number of Grids per Dimension & 7 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: NSWOA parameters. Figure 2: Unmanned aerial vehicle simulation scenario. (**a**) Flight trajectory: A UAV, cruising at approximately 50 m/s, flew over a coastal region in Asia for 65,550 s, covering 327.5 km. The trajectory included a straight climb to 1500 m, followed by an “8”-shaped cruising maneuver, and a descent back to 1000 m. (**b**) The trajectories of satellites: The visible Starlink and Orboomm satellites are shown by green and yellow solid lines, respectively, while the red line represents the trajectory of the satellite as it moves out of the observable range. of selected satellites is between 8 and 10, the proposed NSWOA outperforms NSGA-II, with an average reduction of 0.5881. Moreover, NSWOA also outperforms the GWO and PSO algorithms, with the average DGDOP value decreasing by 2.0521. Table 5 summarizes the execution times of the compared algorithms. The proposed NSWOA achieves computation time reductions of 27.06%, 27.05%, and 68.57% compared to GWO, PSO, and NSGA-II, respectively. These results indicate that NSWOA not only yields solutions closer to the theoretical optimum but also demonstrates significantly improved computational efficiency. This advantage makes it particularly well-suited for real-time satellite selection in UAV-based applications. To evaluate the performance of multi-objective satellite selection algorithms, the Inverted Generational Distance (IGD) metric is used. IGD measures both the convergence and diversity of the solution set. It calculates the average distance from each point in a reference Pareto-optimal front to the nearest solution produced by the algorithm. A lower IGD value means that the solutions are close to the true Pareto front (good convergence) and well distributed along it (good diversity). In this way, IGD penalizes both inaccuracy and poor coverage. The IGD is calculated as follows:  
\[\text{IGD}=\frac{1}{n_{p}}\cdot\sqrt{\sum_{i=1}^{n_{p}}u_{i}^{2}} \tag{12}\]  
In Equation (12), \(n_{p}\) denotes the number of theoretical Pareto optimal solutions in the satellite combination reference set, and \(u_{i}\) represents the Euclidean distance between the theoretical Pareto optimal solution of the \(i\)-th satellite combination in the reference set and the nearest Pareto optimal solution obtained by the optimization algorithm. In the IGD metric, the Euclidean distance quantifies how close the theoretical satellite combination solution is to the nearest Pareto optimal solution in the algorithm's objective space.