## 5 Experiment Results
### Numerical Analysis  
To evaluate the performance of the proposed task offloading and resource scheduling algorithms, we utilized a set of representative datasets with varying scales. These datasets, denoted as D1, D2, D3, and D4, vary in the number of satellite nodes, tasks, and user terminals, providing a comprehensive evaluation of the algorithm's robustness and scalability. The configuration of these datasets is summarized in Table 2.  
As shown in Figure 3 and Table 3, the proposed D-GTOM algorithm consistently outperforms the five comparative optimization algorithms (TSA, AGA-ES, QPSO, DE, and ABIO) across all four satellite counts (5, 10, 100, and 200 satellites). Specifically, the D-GTOM algorithm achieves a target function value of 6251.00 for five satellites, representing an average reduction of 22.56% compared to the comparative algorithms. For 10 satellites, the value is 12,777.23, a decrease of 18.92%; for 100 satellites, it significantly lowers to 124,328.53, marking a reduction of 56.56%; and for 200 satellites, the value stands at 396,287.42, reflecting a 13.42% decrease relative to the comparative algorithms. These results indicate that the D-GTOM algorithm, through its cooperative optimization framework based on dynamic programming, effectively achieves fairness and efficiency in resource allocation within dynamic network environments. Specifically, the application of dynamic programming and value iteration techniques enables real-time updates of system states and decision variables. By incorporating Gradient Surgery techniques, the D-GTOM algorithm successfully coordinates the relationships between different optimization objectives, avoiding gradient conflicts. This innovative architecture demonstrates exceptional performance in handling high-dimensional and large-scale problems. In contrast, other algorithms struggle to achieve the same level of optimization effectiveness under identical conditions due to limitations in computational complexity and optimization efficiency, further validating the significant advantages and superiority of the proposed method in satellite network resource scheduling. The proposed D-GTOM algorithm consistently achieves significantly higher resource utilization rates across all four satellite datasets compared to the five comparative algorithms, as illustrated in Figure 4. Based on the specific result presented in Table 4, the D-GTOM algorithm attains resource utilization rates of 0.391 for 5 satellites, 0.407 for 10 satellites, 0.486 for 100 satellites, and 0.606 for 200 satellites. These results indicate that the D-GTOM algorithm effectively balances fairness and efficiency in resource allocation through its multi-objective optimization model, while Gradient Surgery techniques ensure the coordination between different optimization objectives, preventing conflicts and imbalances in resource distribution. Additionally, the application of dynamic programming and value iteration techniques allows the D-GTOM algorithm to update system states \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Dataset** & **Satellite Nodes** & **Tasks** & **User Terminals** \\ \hline D1 & 5 & 10 & 4 \\ D2 & 10 & 20 & 4 \\ D3 & 100 & 200 & 4 \\ D4 & 200 & 600 & 4 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Configuration of selected datasets. In Figure 5a and Tables 5 and 6, the proposed D-GTOM algorithm exhibits notably lower running times across all datasets, with values of 0.050 s for 5 satellites, 0.090 s for 10 satellites, 0.027 s for 100 satellites, and 0.266 s for 200 satellites. These running times are significantly reduced compared to the other comparative algorithms, highlighting the computational efficiency advantage of the D-GTOM algorithm. Although in some smaller-scale datasets, the running time of D-GTOM is slightly higher than that of Simulated Annealing and ABIO algorithms, its performance remains highly efficient in large-scale and high-dimensional problems.