## 5 Numerical Experiments
### Illustrative Cases  
In the subsection, we aim to provide an explanatory illustration of the proposed model and algorithm. Hence, support that the node and link capacities in the network are limited to constant respectively, the priority of all tasks is defined as one, and all tasks have four upload windows and eight downlink windows. Initially, we test our algorithm on the \(20\times 10\) time-space state network shown in Figure 3, including a total of six cases, the specific descriptions of which are shown in Table 7. Table 8 shows partial task-related information for different scenarios. \begin{table}
\begin{tabular}{c c} \hline \hline
**Scenario** & **Specific Instructions** \\ \hline Scenario I & A total of 2 tasks are required, with network node and link capacities capped at 2 and 1. The 2 tasks have the same start and end nodes, the start and end time windows are overlapping, and the inter-satellite network transmission costs are different. \\ Scenario II & A total of 2 tasks are required, with network node and link capacities capped at 2 and 1. The 2 tasks are randomly generated task start and end nodes, with overlapping start and end time windows and identical inter-satellite network transmission costs. \\ Scenario III & A total of 2 tasks are required, with network node and link capacities capped at 2 and 1. The 2 tasks have the same starting and ending nodes, overlapping starting and ending time windows, and identical inter-satellite network transmission costs. \\ Scenario IV & A total of 18 tasks are required, with network node and link capacities capped at 3 and 2. Priority of all tasks is 1, and task repetition is approximately 30\%. \\ Scenario V & Task repetition is the percentage of all tasks in a task set that have the same time window or the same network cost. \\ Scenario V & A total of 18 tasks are required, with network node and link capacities capped at 3 and 2. Priority of all tasks is 1, and task repetition is approximately 60\%. \\ Scenario VI & A total of 18 tasks are required, with network node and link capacities capped at 3 and 2. Priority of all tasks is 1, and task repetition is approximately 100\%. \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Scenario Description. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Scenario**} & \multirow{2}{*}{
\begin{tabular}{c} **Number** \\ **of Tasks** \\ **Window** \\ \end{tabular} } & \multicolumn{6}{c}{**Task 1**} & \multicolumn{6}{c}{**Task 2**} \\ \cline{3-10}  & & **Start Time** & **End Time** & **Start Node** & **Terminate** & **Start Time** & **End Time** & **Start** & **Terminate** \\  & & **Window** & **Window** & **Set** & **Node Set** & **Window** & **Window** & **Node Set** & **Node Set** \\ \hline Scenario I & 2 & [3.5] & [7,15] & [2.5] & [2.3,4,5,6,7,8] & [3.5] & [7,15] & [2,5] & [2,3,4,5,6,7,8] \\ Scenario II & 2 & [4.6] & [8.16] & [2.1] & [2.3,4,5,6,7] & [4.6] & [8.16] & [2.6] & [2.3,4,5,6,7,8] \\ Scenario III & 2 & [4.6] & [8.16] & [2.6] & [2.3,4,5,6,7,8] & [4.6] & [8,16] & [2.6] & [2.3,4,5,6,7,8] \\ Scenario IV & 18 & [3.5] & [7.15] & [2.5] & [2.3,4,5,6,7,8] & [1.3] & [5,13] & [4,9] & [1,2,3,4,5,7,8] \\ Scenario V & 18 & [3.5] & [7.15] & [2.5] & [2.3,4,5,6,7,8] & [5,7] & [9.17] & [4.9] & [1,2,3,4,5,7,8] \\ Scenario VI & 18 & [3.5] & [7.15] & [2.5] & [2.3,4,5,6,7,8] & [8,10] & [12,19] & [4.9] & [1,2,3,4,5,7,8] \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Description of some tasks in the scenarios. As shown in Figure 6, all task transmission routes for the six scenarios are shown. We set up Scenarios I-III to test the algorithm's ability to handle tasks with similar attributes or the same attributes. In Scenarios I and II, we find that the proposed algorithm can handle tasks with the same time attributes or with the same cost attribute very well. Additionally, our algorithm can handle \"mirror tasks\" with the same time and cost attributes in Scenario III because of the proposed dual routes in the reduced search space approach, which can solve the same tasks well.