## 4 Experimental Design and Results Analysis
### Stability Analysis
However, their success rates decline as the number of satellites and ground stations increases. Table 6 suggests these algorithms may struggle with more complex scenarios, potentially falling into local optima or exhibiting slower convergence. In contrast, the success rates of MO-Ring-PSO-SCD, NSGA-II, MOEA/D, and MOGA are  
generally low, particularly in large-scale scenarios. Table 6 implies that these algorithms are more prone to premature convergence or being trapped in local optima when handling complex problems. As shown in Table 7, the MAPSO algorithm achieves relatively short average search times across all scenarios, indicating its ability to identify feasible solutions quickly. This efficiency is primarily attributed to the minimum angle particle selection strategy employed in MAPSO, which significantly enhances search performance. The DRSC-MOAGDE and DSC-MOPSO algorithms also exhibit relatively short average search times in smaller-scale scenarios. However, as the number of satellites and ground stations increases, their average search times slightly exceed those of MAPSO. Table 7 indicates that while these algorithms maintain relatively high search efficiency, they are still less effective than MAPSO. In contrast, the average search times of MO-Ring-PSO-SCD, NSGA-II, MOEA/D, and MOGA are generally longer, particularly in large-scale scenarios. Table 7 suggests that these algorithms have lower search efficiency and require more time to find feasible solutions. As shown in Table 8, the MAPSO algorithm demonstrates relatively low average fitness evaluation counts across all scenarios, indicating its ability to find feasible solutions with fewer iterations. This efficiency is primarily attributed to the minimum angle particle selection strategy and the fitness function employed by MAPSO, which effectively enhance search performance and optimization results. Similarly, the DRSC-MOAGDE and DSC-MOPSO algorithms also exhibit low average fitness evaluation counts, though slightly higher than MAPSO in large-scale scenarios. This suggests that while these algorithms maintain relatively high optimization efficiency, they still fall short compared to MAPSO. In contrast, the MO-Ring-PSO-SCD, NSGA-II, MOEA/D, and MOGA algorithms have significantly  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Experiment** & **MAPSO** & **DRSC-MOAGDE** & **DSC-MOPSO** & **MO-Ring-PSO-SCD** & **NSGA-II** & **MOEA/D** & **MOGA** \\ \hline c1 & 100.00 & 100.00 & 100.00 & 100.00 & 100.00 & 100.00 & 100.00 & 100.00 \\ c2 & 100.00 & 100.00 & 100.00 & 100.00 & 100  
higher average fitness evaluation counts, particularly in large-scale scenarios, indicating lower optimization efficiency and requiring more iterations to locate feasible solutions. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Experiment** & \multirow{2}{*}{**MAPSO**} & **DRSC-MOAGDE** & **DSC-MOPSO** & **MO-Ring-PSO-SCD** & **NSGA-II** & **MOEA/D** & **MOGA** \\ \hline c1 & 2.20 & 2.12 & 2.23 & 2.51 & 3.05 & 3.27 & 3.43 \\ c2 & 2.31 & 2.07 & 2.15 & 2.64 & 3.26 & 3.52 &  
Based on the analysis of these three indicators, the following conclusions can be drawn: The MAPSO algorithm demonstrates superior stability in solving satellite data transmission problems. It consistently identifies feasible solutions, achieves shorter search times, and requires fewer fitness evaluations, highlighting its ability to address complex problems effectively and efficiently. While the DRSC-MOAGDE and DSC-MOPSO algorithms also exhibit high stability, they are slightly less effective than MAPSO. On the other hand, the MO-Ring-PSO-SCD, NSGA-II, MOEA/D, and MOGA algorithms show poor stability, often becoming trapped in local optima or suffering from premature convergence, making them unsuitable for solving large-scale or complex satellite data transmission problems.