## 2 Methods
### Procedure of the NSWOA-Based Satellite Selection Algorithm
Here, \(\mathbb{R}_{n_{i}}=\left\{y_{1},y_{2},\ldots,y_{L}\right\}\), where \(L\) represents the length of the selectable satellite strategy decision space \(\mathbb{R}_{n_{i}}\), which varies with the number of selected satellites \(n_{i}\). The selected satellite combination agent is denoted as \(x_{j}^{(t)}\), referring to the \(j\)-th satellite combination agent within the set \(\overset{\rightarrow}{x}^{(t)}.If\left(x_{j}^{(t)}<1\right);x_{j}^{(t)}=y_{1}\); \(elseif\left(1\leq x_{j}^{(t)}\leq L\right);x_{j}^{(t)}=\left[x_{j}^{(t)}\right] ;elseif\left(x_{j}^{(t)}>L\right);x_{j}^{(t)}=y_{L};End\). **Step 6. ** Boundary Adjustment  
Considering the stochastic nature of the search process, after updating the satellite combination subset \(\overset{\rightarrow}{x}^{(t)}\), it is possible for the satellite combination agent to exceed the boundaries of the satellite selection strategy decision space \(\mathbb{R}\), leading to cases where \(x_{j}^{(t)}\
otin\mathbb{R}\). Therefore, it is necessary to adjust and filter the satellite combination agents to ensure they remain within the defined boundaries. The selection module begins by initializing the satellite search agents \(\overset{\rightarrow}{x}^{(1)}\) and the associated parameters based on the input data, the specified agent population size \(N\), and the number of iterations \(T\). The objective fitness values of the satellite search agents \(\overset{\rightarrow}{x}^{(1)}\) are then calculated. Non-dominated satellite combinations are updated in the archive, and  
\begin{table}
\begin{tabular}{l} \hline
**NSWOA Process** \\ \hline
**Step 1. ** Initialization \\  Initialize the satellite combination subset and parameters. Randomly initialize parameters \(a\), \(A\), and \(C\), and generate \(N\) initial satellite combination agent subsets \(\left\{\overset{\rightarrow}{x}_{1}^{(1)},\overset{\rightarrow}{x}_{2}^{(1)}, \ldots,\overset{\rightarrow}{x}_{N}^{(1)}\right\}\in\overset{\rightarrow}{x} ^{(1)}\), where \(\overset{\rightarrow}{x}^{(t)}\) represents the subset of satellite combination agents in the \(t\)-th iteration, with \(\overset{\rightarrow}{x}^{(t)}\in\mathbb{R}\), \(\left|\overset{\rightarrow}{x}^{(t)}\right|=N\) \\
**Step 2. ** Calculate Fitness Function Values  
Compute the objective vector fitness function values \(J(x)=[f_{1}(x),f_{2}(x)]\), where \(f_{1}(x)=DGDOP\) represents the DGDOP of the observed non-cooperative LEO satellite combinations, reflecting positioning accuracy, and \(f_{2}(x)=n\) represents the number of selected satellites, reflecting the computational burden. Update and determine the fitness values \(f_{1}(x)\) for the \(t\)-th satellite combination. **Step 3. ** Archiving Control  
Based on Step 2, calculate the objective vector fitness function values \(J(x)\) for each satellite combination in the subset \(\overset{\rightarrow}{x}^{(t)}\). Determine the dominance of each satellite combination and assess the non-dominated satellite combinations in \(\overset{\rightarrow}{x}^{(t)}\) for archiving. If the archiving criteria are met, store the qualifying non-dominated combinations in the archive and make necessary adjustments. **Step 4. ** Select Guiding Combination agent and Update Satellite Combination Subset  
After obtaining the current archive, divide the archive space into grids and calculate crowd density. Based on the crowd density results, assign different selection probabilities to each grid. Use the guiding selection mechanism to choose a guiding satellite combination agent \(\overset{\rightarrow}{x}_{n}^{(t)}\) from the non-dominated satellite combination archive. Update the satellite combination subset \(\overset{\rightarrow}{x}^{(t)}\) based on the guiding satellite combination agent using Equations (7) and (8). The iterative process continues until the specified number of iterations \(T\) is reached. Finally, the archive is output, and the non-dominated Pareto satellite combinations \(x^{*}\) contained in the archive are identified as the selected optimal satellite combinations.