## 5 Experiment Results
### Numerical Analysis
This high efficiency is primarily due to the D-GTOM algorithm's construction of latency optimization and resource efficiency models, which effectively balance fairness and efficiency in resource allocation. Additionally, the use of dynamic programming and value iteration techniques allows the D-GTOM algorithm to update system states and decision variables in real time, swiftly responding to the high temporal variability and complex constraints of the network. These characteristics not only enhance the convergence speed of the algorithm but also optimize the utilization of computational resources, ensuring scalability and robustness in large-scale satellite networks. This outstanding performance is primarily attributed to the collaborative optimization framework based on dynamic programming employed by the MSGT algorithm. By constructing latency optimization and resource efficiency models, and integrating multi-objective optimization with Gradient Surgery techniques, the MSGT algorithm ensures high resource utilization and low system latency in dynamic network environments. Furthermore, the application of dynamic programming and value iteration techniques enables the MSGT algorithm to swiftly respond to the high temporal variability and complex constraints of the network, thereby enhancing the algorithm's convergence speed and optimization accuracy. In contrast, other benchmark algorithms struggle to achieve comparable \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{4-6}  & **D1** & & **D2** & & **D3** & **D4** \\ \hline TSA [42] & \(0.331/-15.10\%\) & \(0.342/-15.50\%\) & \(0.374/-23.88\%\) & \(0.556/-8.26\%\) & \(0.401/-15.69\%\) \\ AGA-ES [41] & \(0.298/-23.29\%\) & \(0.337/-17.64\%\) & \(0.366/-24.69\%\) & \(0.572/-5.89\%\) & \(0.393/-17.88\%\) \\ OPSO [39] & \(0.373/-4.59\%\) & \(0.358/-12.32\%\) & \(0.409/-15.99\%\) & \(0.583/-3.91\%\) & \(0.431/-9.20\%\) \\ DE [40] & \(0.344/-12.50\%\) & \(0.388/-4.40\%\) & \(0.382/-21.43\%\) & \(0.573/-5.31\%\) & \(0.422/-10.91\%\) \\ ABIO [38] & \(0.370/-5.21\%\) & \(0.353/-13.23\%\) & \(0.394/-18.36\%\) & \(0.561/-7.43\%\) & \(0.420/-11.06\%\) \\
**D-GTOM** & **0.391** & **0.407** & **0.486** & **0.606** & **0.4725** \\ \hline \hline \end{tabular}  
* **Note:** This table presents the resource utilization rates and their corresponding reduction ratios (negative percentages) for various algorithms across four datasets (D1–D4). The results for D-GTOM are highlighted in bold because it is the proposed method in this study. Higher resource utilization rates generally indicate more effective use of system resources, but trade-offs with computational efficiency should also be considered.  
\end{table} 
Table 4: Resource utilization rate and reduction ratios across 4 datasets. Figure 5: Running time and improvement rates of algorithms across 4 datasets. running efficiency and optimization effectiveness when confronted with large-scale and highly complex problems, due to their higher computational complexities and limitations in optimization strategies. As shown in Figure 6, the proposed D-GTOM algorithm demonstrates competitive performance in terms of average task delay across four satellite datasets with varying scales. Specifically, while D-GTOM achieves a task delay of 0.185 s for 5 satellites and 0.176 s for 10 satellites, it is slightly outperformed by the Simulated Annealing algorithm, which records delays of 0.180 s and 0.169 s, respectively. In larger-scale scenarios, D-GTOM maintains commendable performance with delays of 0.191 s for 100 satellites and 0.192 s for 200 satellites, although Particle Swarm Optimization achieves marginally lower delays of 0.186 s and 0.189 s in these cases. These observations indicate that while D-GTOM does not consistently yield the lowest task delays across all datasets, it balances delay with other critical performance metrics effectively.