## 3 Results
Finally, the particle updates its own speed \(\mathbf{v}_{j}\) and time source satellite numbers \(\mathbf{x}\mathbf{l}_{j}\) and an iteration of this particle is completed. After all iterations of all particles, the clock transfer trees are generated using the global optimal time source combinations. The main algorithm is shown in Algorithm 1. The minimum sum of weighted time stratum obtained after 10 iterations is 102, as shown in Figure 3. The obtained time source combinations are the same as the second group in Table 1. Six clock transfer trees are constructed with these six time sources as the root nodes. The LEO satellite network topology and clock delivery path are schematically shown in Figure 4. Figure 4 illustrates the network topology for the first time slice and the clock delivery paths established based on the clock delivery trees in Figure 2a. The clock source satellites are marked in yellow, while the other satellites are marked in blue. The numbers represent the other satellites' numbers, and the arrow indicates the clock delivery paths. The curves of the number of iterations of the PSO algorithm and the traversal algorithm with respect to the sum of the minimum weighted clock levels are shown in Figure 3. Using the time monitoring program, the time for 10 iterations of the PSO algorithm is 0.043 s and for \(116\) iterations of the traversal algorithm is 195.63 s, respectively. The PSO algorithm has significantly fewer iterations compared to the traversal algorithm. Analyzed in principle, the traversal algorithm needs to compute all possible clock source combination cases sequentially, i.e., for \(D\) clock sources, each clock source combination case is to add one to only one of the clock source satellite number each time and compute that clock source combination, and the optimal result can only be determined by comparing the size of the sum of the weighted clock hierarchies of all clock source combination cases. These \(116\) calculations are independent of each other, so the results of each calculation do not benefit the results of the next calculation, which leads to an increase in the number of clock source combinations with the increase in the number of \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline Total number of satellites (\(N\)) & 66 \\ \hline Number of time sources (\(D\)) & 6 \\ Satellites in each orbital plane (\(SN\)) & 11 \\ The latitude at which the inter-satellite link is set to be disconnected & 70\({}^{\circ}\) \\ Number of particles (\(NP\)) & 20 \\ Maximum number of iterations (\(T\)) & 100 \\ Learning factors (\(c1\), \(c2\)) & 1.5 \\ Maximum value of time source number for each orbital plane (\(Xmax\)) & 12 \\ Minimum value of time source number for each orbital plane (\(Xmin\)) & 1 \\ Initialization time source (\(\mathbf{x}\)) & [1, 11] \\ Maximum particle velocity (\(Vmax\)) & 2 \\ Minimum particle velocity (\(Vmin\)) & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters table. satellites in the network and a corresponding increase in the amount of calculations in the traversal algorithm. In the PSO algorithm, parameters such as \(D\) clock source satellites for \(NP\) particles are updated simultaneously each time, and the updated results are used to update the parameters for the next iteration, and each update is beneficial to make the computational results closer to the optimal solution. Each particle represents a kind of time source combination, and it can be seen from Equation (3) that for each particle, PSO updates the \(D\) clock source satellite numbers at the same time each time, instead of only one at a time as in the traversal algorithm. Meanwhile, the PSO algorithm utilizes iterative computation, and there is a correlation between the results of the two adjacent computations, as shown in Figure 4.  
Figure 4: Schematic diagram of clock transmission path and topology of the first slice in LEO satellite networks.