## 3 Results
As the near-polar orbit LEO satellites have a high relative speed of motion at high latitudes, inter-satellite links are difficult to maintain, so the inter-satellite link is set to be disconnected when the satellite's latitude is \(70^{\circ}\). Because there are 11 satellites in each orbital plane, in order to facilitate the program calculation for each orbital plane, the time base number maximum \(Xmax\) is 12 and the minimum \(Xmin\) is 1 so that in the use of Equation (3) calculations the clock source satellite number combination \(x1\) can be assigned to the number of all the numbers of 1-11. Since the time reference number is an integer, it is rounded to obtain the initialized time reference \(x\) (value range 1-11). The particle motion speed is used to control the magnitude of the change in the clock source satellite number for each update, because there are only 11 satellites in each orbital plane, and the satellite number value cannot grow too much in each iteration, otherwise it may exceed the value range of the number 1-11, or skip the optimal value in the middle. So, the maximum value of \(Vmax\) is set to 2, and the minimum value of \(Vmin\) is set to 0, i.e., the satellite number is increased by 1 or 2 in each iteration. The above variables are calculated by the following formulas:  
\[\omega=(0\text{: }1/(T-1)\text{: }1)\times(0.4-0.9)+0.9 \tag{2}\]  
\[x1=rand(NP,D)\times(Xmax-Xmin)+Xmin \tag{3}\]  
\[x=floor(x1) \tag{4}\]  
\[v_{j}=\omega(1)\times v_{j}+c1\times rand\times(\vec{pbest}_{j}-x_{j})+c2\times rand \times(\vec{gbest}-x_{j}) \tag{5}\]  
\[x1_{j}=x_{j}+v_{j} \tag{6}\]  
where the \(rand\) function returns a random number uniformly distributed in the interval (0, 1), the _floor_ function rounds an element to the nearest integer less than or equal to the element, \(j\) denotes the particle number, \(l\) denotes the number of loop iterations, \(v\) is the particle motion velocity, \(\vec{pbest}\) is the historical optimal solution for each particle, and \(\vec{gbest}\) is the historical optimal solution for all particles and the optimal time source combination. The main initial parameters and their corresponding values in the PSO algorithm are shown in Table 2.  
The optimization objective of the PSO is generated through the \(func1\) function, which returns a numerical value of \(sumstr\), as shown in Equation (7). \[sumstr\text{= }func1(x,A,N,D) \tag{7}\]  
The \(func1\) function shown in Algorithm A2 is used to compute one optimization per particle, where \(x\) represents the six time source numbers selected by a particle, \(A\) represents the connection table with the topology of the LEO satellite networks in this time slice, \(N\) is the total number of satellites in the LEO satellite networks, and \(D\) is the number of time source numbers. For particle \(j\), the return value \(sumstr\) of function \(func1\) is calculated by Equation (8) in function \(func1\) and \(a_{i}\) is the time hierarchy of the \(i\)-th satellite. Figure 2:0\[\mathbf{pbest}_{j}=\left\{ \begin{array}{c}sumstr,\ \ \mathbf{pbest}_{j}>sumstr\\ \ \mathbf{pbest}_{j},\ \mathbf{pbest}_{j}<sumstr\end{array} \right. \tag{9}\]  
\[gbest=\left\{ \begin{array}{c}gbest,\ \ \mathbf{pbest}_{j}>gbest\\ \ \mathbf{pbest}_{j},\ \mathbf{pbest}_{j}<gbest\end{array} \right. \tag{10}\]  
Whenever _sumstr_ generates a new value, the particle is compared with its own historical optimal value \(\mathbf{pbest}_{j}\) by Equation (9). If _sumstr_ is smaller, the particle updates and records its own optimal time sources \(\mathbf{x}_{j}\) and the minimum sum of weighted time layers \(\mathbf{pbest}_{j}\). Otherwise, it does not record and update. Then, if \(\mathbf{pbest}_{j}\) is smaller than the global minimum sum of the weighted clock cascades \(gbest\), the global minimum sum of weighted time stratums and global optimal time sources are updated by Equation (10). Otherwise, it does not record and update.