## 3 Results  
The traditional traversal approach is shown in Algorithm A1. All combinations of time sources are selected with the increasing number of orbital planes and satellites, and for each combination, the sum of the weighted clock layers is computed. All 1,771,561 time source combinations are calculated according to the above steps, and a minimum sum of the weighted clock hierarchy of 102 is obtained. The optimal time combination serial numbers indicate the positions in the above 1,771,561 combinations. A total of eight combinations can achieve this goal, and the corresponding satellite numbers for each combination are shown in Table 1. The program is set up to monitor the time and it took a total of 195.63 s to calculate all 1,771,561 clock source combinations. The time transfer trees corresponding to the group 2 and group 5 time source combinations of Table 1 are shown in Figure 2a,b, respectively, in which the time sources are used as the root nodes of the clock transfer trees. The numbers in the time transfer trees denote the numbers of the satellites, and the column of serial numbers 0-3 on the left side of the clock transfer trees denotes the time cascade corresponding to the satellites in this row. The time synchronization information is transferred from the time source satellites to the other satellites along the clock hierarchy with the connections between the satellites. The minimum sum of the weighted cascades of the time slice is \(min\{s_{1}s_{2},\cdots,s_{1,771,561}\}\), and its corresponding optimal time source combination can be found with the _find_ function in Algorithm A1, whose searching condition is \(s_{k}==\min\{s_{1},s_{2},\cdots,s_{1771561}\}\). The minimum sum of weighted clock level calculated by the means of the traversal is 102. In the particle swarm algorithm of this thesis, the size of the number of population particles \(NP\) is generally between a few and in the tens. When the \(NP\) is small, the iteration can easily fall into the local optimal solution. When the \(NP\) is large, the results of the calculation of many particles in each iteration are not facilitated, which wastes the computational resources and reduces the efficiency, so the \(NP\) can be set to 20. \(N\) is the total \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Group**} & \multicolumn{2}{c}{**Optimal Clock Source Combination**} & \multicolumn{5}{c}{**Satellite Numbers**} \\  & **Serial Numbers** & & & & \\ \hline
1 & 993,418 & 7 & 13 & 32 & 38 & 45 & 63 \\
2 & 993,429 & 7 & 13 & 32 & 38 & 46 & 63 \\
3 & 1,133,788 & 8 & 12 & 27 & 43 & 46 & 62 \\
4 & 1,148,429 & 8 & 13 & 27 & 43 & 46 & 62 \\
5 & 1,510,256 & 10 & 16 & 24 & 41 & 49 & 66 \\
6 & 1,524,897 & 10 & 17 & 24 & 41 & 49 & 66 \\
7 & 1,678,566 & 11 & 16 & 30 & 35 & 49 & 65 \\
8 & 1,678,577 & 11 & 16 & 30 & 35 & 50 & 65 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Optimal clock source combination table of the first slice obtained by traversal algorithm. Figure 2: Time transfer trees: (**a**) the second group, (**b**) the fifth group in Table 1.  
number of satellites of the Iridium constellation, which is set to 66. The particle dimension \(D\) is the time base number, which is set to six. \(SN\) is the number of satellites in each orbital plane, which is set to 11. The maximum number of iterations is set based on the iteration results. If a small number of iterations can produce optimal iteration results, the maximum number of iterations can be set to a very small number of iterations, so as to avoid useless calculations. According to the results of the PSO calculations in this example, usually dozens of iterations can produce the optimal results, thus \(T\) is set to 100. The maximum number of iterations affects the inertia weight \(\omega\) of the particles as shown in Equation (2). As shown in Equation (5), the learning factors affect the motion speed of the particles, which cannot be too large compared to the weight \(\omega\). The two learning factors \(c1\) and \(c2\) are usually set to 1.5 in the PSO algorithm.