## 6 Result Analysis
### Spatial Positions and Impulse Conditions  
Figure 7 shows the operational trajectories of two detection satellites (A1-A2) and two intelligent satellites (D1-D2) in three-dimensional orbital space. Solid and dashed lines of different colors represent the orbital paths of different numbered detection and intelligent satellites. The figure clearly demonstrates that each intelligent satellite achieves a relatively favorable deployment position through strategic maneuvers, effectively avoiding potential collisions with detection satellites. Meanwhile, the corresponding detection satellites attempt to obtain optimal observation conditions through complex maneuver trajectories to accomplish their missions. This dynamic process reflects the game characteristics between the two parties in orbital space and reveals the importance of orbital maneuvers and coordinated deployment in achieving detection missions.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Model** & **Name** & **Parameter Settings** \\ \hline \multirow{2}{*}{Zebra Optimization Algorithm (ZOA)} & Population size & 50 \\  & Maximum number of iterations & 1000 \\  & Perturbation amplitude & 0.01 \\ \hline Co-evolution & Number of evolutionary rounds & 20 \\ \hline \multirow{4}{*}{Comprehensive effectiveness evaluation} & Detection success rate & 0.25 \\  & Fuel consumption & 0.25 \\ \cline{1-1}  & Mission time cost & 0.25 \\ \cline{1-1}  & Target coverage degree & 0.25 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Optimization parameter settings.  
Figure 6: The change of the efficiency function.  
Table 5 presents the impulse statistics of detection and intelligent satellites during the entire mission period, including mission duration, total impulse, and number of impulses. The data show that the mission completion times for the two intelligent satellites (D1-D2) are 125,580 s and 116,500 s, respectively, with both reaching or approaching 30 impulses. The two detection satellites (A1-A2) performed 23 and 27 impulses, respectively, with impulse amounts smaller than their corresponding intelligent satellites. The statistical results indicate that both sides adopted high-frequency impulse strategies during the mission, demonstrating highly intense dynamic game characteristics.  
Through precise impulse strategies, the intelligent satellites effectively optimized orbit adjustments and maneuver strategies, achieving superior spatial deployment and maintaining safe distances, while the detection satellites attempted to achieve optimal detection through flexible maneuver trajectories. These results reflect the importance and complexity of strategy selection in multi-to-multi scenarios. Overall, all intelligent satellites demonstrated excellent maneuverability and tactical execution capabilities, achieving superior comprehensive scheduling effects through reasonable impulse strategies during the game process. This indicates that satellite clusters can achieve effective resource coordination and strategy optimization in multi-objective mission environments.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{
\begin{tabular}{c} **Mission** \\ **Duration** \\ \end{tabular} } & \multicolumn{2}{c}{**Intelligent Satellites**} & \multicolumn{2}{c}{**Detection Satellites**} \\ \cline{2-6}  & \multirow{2}{*}{**ID**} & **Impulse** & **Number of** & **Impulse** & **Number of** \\  & & **Magnitude (m/s)** & **Impulses** & **Magnitude (m/s)** & **Impulses** \\ \hline
125,580 & 1 & 25.08307 & 28 & 1 & 12.61028 & 23 \\
116,500 & 2 & 20.99062 & 30 & 2 & 6.08755 & 27 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Impulse statistics for detection and intelligent satellites.  
Figure 7: Three-dimensional spatial paths of satellite constellations.