## 4 Experimental Results and Analysis
### Analysis of Algorithm Performance
#### 4.3.3 Comparison of PBIL and GA  
According to the optimization goal in Section 2, we carry out the comparison experiments of the real-coding PBIL algorithm and real-coding Genetic Algorithm for solving multi-satellite scheduling under the same conditions.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Number**} & \multicolumn{2}{c}{**Optimal Fitness Value**} & \multicolumn{2}{c}{**Running Time (s)**} & \multicolumn{2}{c}{**Encoding Length**} \\ \cline{2-7}  & **Real-Coding** & **Binary-Coding** & **Real-Coding** & **Binary-Coding** & **Real-Coding** & **Binary-Coding** \\  & **PBIL** & **PBIL** & **PBIL** & **PBIL** & **PBIL** & **PBIL** \\ \hline
1 & 3731 & 3251 & 850.5 & 1236.46 & 50 & 729 \\
2 & 3754 & 3058 & 856.7 & 1207.07 & 50 & 729 \\
3 & 3712 & 3159 & 866.2 & 1221.49 & 50 & 729 \\  
The Evolutionary curves of 10 simulation experiments for 50 targets are shown in Figure 12, and the statistical results of different target quantities are shown in Table 5 and Figure 13. All the data as follows are the average of the results of 10 simulation experiments.  
As can be seen from the figure above, to solve the multi-satellite scheduling problem under the same conditions, the PBIL algorithm converges rapidly around iteration 80, while the GA algorithm converges after iteration 100, indicating that the PBIL algorithm has faster computational performance than the GA algorithm.  
In addition, the evolution curve of 10 simulation experiments shows that the evolution curves obtained by the PBIL algorithm have small fluctuation, while that obtained by the GA algorithm have significant fluctuation and difference, indicating that the PBIL algorithm is also better than the GA algorithm in terms of computational stability.  
For different target quantity scales, the ability of PBIL and GA for solving multi-satellite scheduling is further compared and analyzed.  
As shown in the table and the figure above, the running time of the PBIL algorithm is obviously much shorter than that of the genetic algorithm, where the computational  
Figure 12: The evolutionary curves of the comparison experiments.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Quantities of Targets**} & \multicolumn{2}{c}{**Optimal Fitness Value**} & \multicolumn{2}{c}{**Running Time (s)**} \\ \cline{2-5}  & **Real-Coding** & **Real-Coding** & **Real-Coding** & **Real-Coding** \\  & **PBIL** & **GA** & **PBIL** & **GA** \\ \hline
25 & 550.2 & 1340.6 & 2015 & 1993 \\
50 & 857.2 & 2113.5 & 3779 & 3635 \\
75 & 1135.3 & 3197.2 & 5623 & 5446 \\
100 & 1563.2 & 3718.7 & 7436 & 7046 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Statistical results of comparison experiments between PBIL and GA.with different target quantity scales.  
Figure 13: The statistical results of the comparison experiments.  
efficiency is almost doubled, and most of the optimal fitness values are slightly higher than that of GA.  
Therefore, considering algorithm stability, computational efficiency and optimization quality, etc., the PBIL algorithm is superior to the genetic algorithm in solving satellite mission planning problems to some extent.