## 5 Experiment Results
### Numerical Analysis
The underlying collaborative optimization framework based on dynamic programming enables D-GTOM to achieve high resource utilization and robust performance under dynamic network conditions. Additionally, the integration of multi-objective optimization and Gradient Surgery techniques facilitates efficient resource allocation and minimizes latency where possible. Consequently, D-GTOM offers a well-rounded solution that prioritizes both efficiency and fairness in resource distribution, making it a reliable choice for complex and large-scale satellite network environments despite not always being the top perform \begin{table}
\begin{tabular}{l c c c c} \hline \hline \multirow{2}{*}{**Algorithm**} & \multicolumn{4}{c}{**Datasets**} & \multirow{2}{*}{**Average**} \\ \cline{2-2} \cline{4-5}  & **D1** & **D2** & **D3** & **D4** \\ \hline TSA [42] & / & 60.00\% & 93.50\% & 448.00\% & 200.50\% \\ AGA-ES [41] & / & 2.01\% & 121.72\% & 707.11\% & 276.95\% \\ QPSO [39] & / & 4.25\% & 51.67\% & 299.69\% & 118.54\% \\ DE [40] & / & 1.73\% & 60.72\% & 345.04\% & 135.83\% \\ ABIO [38] & / & 2.59\% & 67.23\% & 386.05\% & 151.95\% \\
**D-GTOM** & / & **1.80\%** & **0.54\%** & **5.32\%** & **2.55\%** \\ \hline \hline \end{tabular}  
* **Note:** This table presents the algorithm running time improvement rates across three datasets (D2-D4) relative to D1. The improvement rate is computed as the percentage increase in speed compared to the execution time on D1, where higher values indicate greater reductions in computational time. The results for D-GTOM are highlighted in bold because it is the proposed method in this study.  
\end{table} 
Table 6: Algorithm running time improvement rates compared to D1 across 3 datasets. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline \multirow{2}{*}{**Algorithm**} & \multicolumn{4}{c}{**Datasets**} & \multirow{2}{*}{**Average**} \\ \cline{2-2} \cline{4-5}  & **D1** & **D2** & **D3** & **D4** \\ \hline TSA [42] & 0.002/96.00\% & 0.120/\(-\)33.33\% & 0.187/\(-\)592.59\% & 0.896/\(-\)237.31\% & 0.301/\(-\)191.81\% \\ AGA-ES [41] & 0.389/\(-\)678.00\% & 0.782/\(-\)768.99\% & 47.350/\(-\)1750.88\% & 275.066/\(-\)1032.33\% & 80.899/\(-\)1057.53\% \\ QPSO [39] & 0.301/\(-\)502.00\% & 1.280/\(-\)1322.22\% & 15.552/\(-\)574.07\% & 90.206/\(-\)338.20\% & 26.835/\(-\)684.12\% \\ DE [40] & 0.238/\(-\)376.00\% & 0.411/\(-\)356.67\% & 1.452/\(-\)534.26\% & 82.119/\(-\)307.30\% & 24.055/\(-\)393.56\% \\ ABIO [38] & 0.022/56.00\% & 0.057/36.67\% & 1.479/\(-\)537.78\% & 8.493/\(-\)3095.49\% & 2.263/\(-\)885.15\% \\
**D-GTOM** & **0.050** & **0.090** & **0.027** & **0.266** & **0.108** \\ \hline \hline \end{tabular}  
* **Note:** This table presents the running time (in seconds) of various algorithms and their corresponding reduction ratios (negative percentages) across four datasets (D1–D4). The reduction ratio represents the percentage decrease relative to the baseline performance. The results for D-GTOM are highlighted in bold because it is the proposed method in this study.  
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Table 5: Algorithm running time (in seconds) and reduction ratios across 4 datasets. Additionally, the experiments were conducted on a large-scale dataset comprising 300 satellites, with task numbers corresponding to 600, 900, 1500, 2400, and 3600. The numerical results from large-scale satellite network experiments highlight the performance of different algorithms under increasing task sizes, as shown in Figure 7 and Table 7. Figure 7a demonstrates that D-GTOM achieves superior resource utilization across varying task scales. Specifically, for 600 tasks, D-GTOM attains a utilization rate of approximately 0.48, surpassing TSA and AGA-ES, which fall in the 0.35-0.45 range. For larger-scale scenarios, such as 3600 tasks, D-GTOM achieves a utilization rate nearing 0.9, outperforming other algorithms capped at around 0.85.