# An On-Orbit Task-Offloading Strategy Based on Satellite Edge Computing
## 4 Algorithm Introduction and Simulation Analysis
### Simulation Analysis
\begin{table}
\begin{tabular}{c c} \hline \hline
**Algorithm Parameter** & **Value** \\ \hline Maximum number of iterations, \(I\) & 4000 \\ Number of particles, \(U\) & 100 \\ Learning factor, \(C1,C2\) & 2, 2 \\ Inertia weights, \(W\) & 0.8 \\ Crossover probability, \(P_{c}\) & 0.6 \\ Mutation probability, \(P_{m}\) & 0.1 \\ \hline
**Scene Parameter** & **Value** \\ \hline Time slot, \(\Delta t\) & 10 s \\ Subtask original data size, \(D\) & [200, 250] Mb \\ Subtask result data size, \(RD\) & [2, 5] Mb \\ Computational complexity, \(\zeta\) & \(\frac{1900}{8}\) \\ ISL bandwidth, \(B\) & 10 Mb/s \\ ISL transmission power, \(P_{trans}\) & 100 J/s \\ Satellite computational power, \(P_{com}\) & [5, 10] J/s \\ Satellite computational performance, \(C_{k}\) & [5, 10] Ghz \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameter setting. robust search capacity, enabling speedy convergence to a better solution, as illustrated in Figure 5a. As the number of feasible solutions in the search domain decreased sharply, the convergence speed and optimal solution deteriorated. However, the GABPSO algorithm still outperform the other three algorithms, which is shown in Figure 5b. Firstly, we explored the relationship between system cost and the number of high-load satellites. The system cost of each algorithm gradually increased as the proportion of high-load satellites rose, as indicated in Figure 6. This is because there were more satellite nodes available that were closer to the source satellite node when there were fewer high-load satellites. This resulted in a smaller number of hops required for offloading through the ISL, which led to a subsequent decrease in transmission delay and energy consumption. In contrast, when the percentage of high-load satellites was large, there were fewer available satellite nodes closer to the source satellite node, causing inter-satellite offloading to be longer delayed and more energy-intensive. The GA algorithm was able to obtain lower system cost than the MPSO and BPSO algorithms. This was the same as the analysis of the convergence curve. The GABPSO algorithm, on the other hand, was able to maintain the best performance over time because it combined the advantages of both. Figure 4: System cost vs. the value of \(\beta\). Figure 5: (a) Convergence curve for 6 high-load satellites; (b) Convergence curve for 18 high-load satellites. Next, we set the number of high-load satellites to 3 (30 \(\times\) 10% = 3). On the basis of this, we studied the effect of other system parameters on the system cost. At first, we investigated how the quantity of original data in the subtasks would affect the system cost. As seen from Figure 7, the system cost grew gradually and with a more pronounced trend. The increased quantity of original data for subtasks led directly not only to an increase in computational delay and energy consumption but also to an increase in inter-satellite transmission delay and energy consumption. It led to a relatively fast curve change. Similarly, the GABPSO algorithm consistently outperformed the other baseline algorithms. The MPSO algorithm used the inverse of the particle velocity to achieve the particle variation. It was difficult to make essential changes to the particle population, and the entire search domain could not be fully explored. As a result, the MPSO method did not significantly outperform the BPSO algorithm. Further, we explored the changes brought about by computational complexity. The increase in computational complexity indicated that the task took longer to compute on the satellite nodes. This, in turn, caused an increase in the overall system cost. As depicted in Figure 8, all four algorithm times increased as the computational complexity grew. The MPSO algorithm and BPSO algorithm lacked powerful global search capability for a better solution, leading to the worst performance, while the GABPSO algorithm performed the best.