## 4 Experimental Design and Results Analysis
### Experimental Results and Performance Analysis
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Experiment** & \multirow{2}{*}{**MAPSO**} & **DRSC-** & **DSC-** & **MO-Ring-** & \multirow{2}{*}{**NSGA-II**} & **MOEA/D** & **MOGA** \\
**ID** & & **MOAGDE** & & & & & & \\ \hline c1 & 33,266 & 33,266 & 33,266 & 33,266 & 33,266 & 33,266 & 33,266 \\ c2 & 55,126 & 55,126 & 55,126 & 55,126 & 55,126 & 55,126 & 55,126 \\ c3 & 60,425 & 60,425 & 60,425 & 60,425 & 60,425 & 60,425 & 60,425 \\ c4 & 65,052 & 65,052 & 65,052 & 65,052 & 65,052 & 65,052 & 65,052 \\ c5 & 19,420 & 19,385 & 19,433 & 19,473 & 19,468 & 19,344 & 19,268 \\ c6 & 29,722 & 29,706 & 29,750 & 29,757 & 29,795 & 34,810 & 35,090 \\ c7 & 44,272 & 44,267 & 44,306 & 44,349 & 44,402 & 46,476 & 52,374 \\ c8 & 55,345 & 55,354 & 55,393 & 55,482 & 55,619 & 57,923 & 63,666 \\ c9 & 61,746 & 61,763 & 61,808 & 61,995 & 62,671 & 62,897 & 62,647 \\ c10 & 17,299 & 17,287 & 17,325 & 17,372 & 17,457 & 17,532 & 17,740 \\ c11 & 21,268 & 21,264 & 21,297 & 21,404 & 21,422 & 26,604 & 26,763 \\ c12 & 28,012 & 28,034 & 28,069 & 28,250 & 28,562 & 29,382 & 34,825 \\ c13 & 44,455 & 44,619 & 44,770 & 45,216 & 46,153 & 48,141 & 51,127 \\ c14 & 46,449 & 46,460 & 46,518 & 46,571 & 46,720 & 47,884 & 55,554 \\ c15 & 48,428 & 48,491 & 48,604 & 48,742 & 49,619 & 53,497 & 53,570 \\ c16 & 12,597 & 12,469 & 12,505 & 12,519 & 12,536 & 12,561 & 12,630 \\ c17 & 21,262 & 21,183 & 21,208 & 21,234 & 21,267 & 21,794 & 22,374 \\ c18 & 23,899 & 23,925 & 23,958 & 24,016 & 24,087 & 25,035 & 25,224 \\ c19 & 30,815 & 30,953 & 31,056 & 31,257 & 31,368 & 33,324 & 35,193 \\ c20 & 40,033 & 40,189 & 40,246 & 40,448 & 40,504 & 43,510 & 45,514 \\ c21 & 43,309 & 43,852 & 44,127 & 45,036 & 46,362 & 47,955 & 50,385 \\ c22 & 44,965 & 45,431 & 45,751 & 46,460 & 47,707 & 50,446 & 51,806 \\ c23 & 45,630 & 46,062 & 46,359 & 47,198 & 48,247 & 50,707 & 52,055 \\ c24 & 47,409 & 47,736 & 48,094 & 48,731 & 49,974 & 51,080 & 52,337 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Algorithm planning time for data transmission tasks in different scenarios (s). Figure 7: _Cont._  
Figure 8 illustrates the final scheduling results for satellite data transmission tasks under different scenarios. The \(x\)-axis represents the scheduling time window, and the \(y\)-axis represents the ground stations. Satellites are recorded in the figure by sequence number. If a satellite is within the range of 1 on the \(y\)-axis, it indicates that the satellite is transmitting data to the first ground station, and so on. In Figure 8, we present a selected Pareto optimal scheduling result for different configurations of ground stations and satellites. Each subplot illustrates a scheduling outcome under varying conditions. The displayed scheduling result was chosen because it effectively demonstrates the balance between minimizing transmission time and maximizing resource utilization. While multiple Pareto optimal solutions exist, this result provides a representative and clear visualization of our algorithm's performance. It highlights how our approach handles the complexities of large-scale multi-objective optimization in satellite data transmission scheduling. The results in Figure 8 show that the MAPSO algorithm provides a better scheduling plan for satellite data transmission tasks. The MAPSO algorithm enhances the efficiency of solving multi-objective SDTSPs, making it more suitable for handling satellite data transmission tasks across various scenarios. MAPSO enhances the system's service capability, meeting diverse user needs. The scheduling results indicate an improved Pareto front, increasing the efficiency and accuracy of satellite data transmission tasks. The MAPSO algorithm employs a minimum angle particle selection strategy in dynamic scheduling, effectively selecting _gbest_ and _pbest_ particles. Combined with objective functions tailored to satellite data transmission characteristics,  
Figure 7: (**a**) Description of Two stations, 50 satellites Pareto; (**b**) Description of Three stations, 60 satellites Pareto; (**c**) Description of Four stations, 90 satellites Pareto.