## 5 Simulation Results
### Comparison with State-of-the-Art Distribute Algorithms  
We compare the proposed PIDSM with the existing distribution algorithms CBBA [30], CNP [36], and ECNP [32] based on the performance metrics in Section 5.1. The statistics results of comparison for small-type, medium-type, and large-type instances are shown in Tables 5-7, respectively. \begin{table}
\begin{tabular}{l c c c c c c c c c c c c c c c c} \hline  & \multicolumn{4}{c}{**CBBA**} & \  
The performance of all algorithms varies markedly in terms of \(\delta\), \(\varphi\), \(bRPV\), and \(aRPV\); the optimal values are given in bold. From Tables 5-7, we can conclude the following:  
(1) The PIDSM enables the AEOS constellation to successfully observe almost all targets with \(\delta\geq 95\%\) for each instance. It demonstrates that the proposed PIDSM has outstanding performances in the time-dependent observing schedule problem. Moreover, except in some isolated cases, the ECNP has a similar \(\delta\) to the PIDSM. The CNP can observe fewer targets than the ECNP and the PIDSM and CBBA obtain the worst \(\delta\). (2) The PIDSM terminates after the least communication times in small-sized and medium-sized instances. In particular, although the ECNP requires marginally more communication times than the CNP for the same instance, the ECNP always obtains a better solution because it uses adaptive bidding with swarm intelligence to improve the solution quality, but the CNP does not. In a small-type (respectively, medium-type) instance, the communication times of the CNP is three (respectively, six) times than of the PIDSM. Moreover, in the large-type instance, the value of \(\varphi\) for the PIDSM increases with the growth of the satellite number. For example, in the F-constellation, the PIDSM's \(\varphi\) is greater than that of the CNP. (3) The PIDSM obtains the best \(aRPV\) and \(bRPV\) in almost all kinds of instances. With significantly higher communication times, the ECNP has a slightly inferior performance. The CNP is worse than both the PIDSM and the ECNP, and exhibits the largest fluctuations. The CBBA performed the worst among all methods. In summary, compared with other competitors, the PIDSM can observe more targets with the least communication burden in most instances. In addition, the fitness value of the PIDSM is always better than that of the CBBA, CNP, and ECNP. The variations for each algorithm on different instances are further illustrated in Figure 6. Compared with the CBBA, CNP, and ECNP, the proposed PIDSM exhibits more stability and better performance in solving the time-dependent AEOS constellation observing schedule problem with different scales. The impact of target number: We consider six instance combinations whose target number belongs to {10, 20, 50, 100, 200, 500}, but all have a C-constellation, low-density distribution, and long-term observation duration. For each combination, test instances are generated randomly, and the CNP, ECNP, and PIDSM are implemented 10 times independently for each instance to eliminate data randomness. As shown in Table 8, the PIDSM outperforms the CNP and ECNP in almost all instances, and only for the instance with a target number of 10, the ECNP achieves a marginal lead. As shown in Figure 7, when the target number does not exceed 20, all three algorithms achieve the best RPV. As the target number grows gradually, the \(RPV\) of the CNP drops more sharply than the ECNP and PIDSM. Compared with the CNP and ECNP, the variation of the target number has the least impact on the performance of the PIDSM. This demonstrates that the PIDSM is more suitable for solving satellite observation schedule problems with a large number of targets. The impact of target distribution density: We consider eight combinations with 100 targets, a C-constellation, and a long-term observation duration. The target distribution density is represented by the average shortest distances between targets, and the values for these eight combinations are 1 km, 5 km, 10 km, 50 km, 100 km, 200 km, 500 km, and 1000 km, respectively.