## 5 Experiment Results
### Results of HCNN as the Initial Solution  
To validate the generalization capabilities of the HCNN as the initial solution of the iterative meta-heuristic algorithm, we conducted comparative experiments with TS and SA algorithms with task scales of 50, 100, 150, and 200. These scales of samples are representative and sufficient for comparing two algorithms. Since these algorithms possess randomness, we ran them ten times and calculated their average results. For the tabu search (TS), when the historical optimal solution is not updated for 100 iterations, this algorithm stops and outputs the historical optimal solution. Each iteration of the TS algorithm searches multiple domain solutions, but only one single algorithm is performed in the simulated annealing (SA) algorithm. Thus, we set the iteration to have no improvement for 1000 times for SA. In addition, due to the randomness of these meta-heuristic algorithms, we ran these algorithms 30 times and calculated the standard deviation (std.) to compare their stability. The parameters of the greedy randomized iterated search (GRILS) are almost identical with the study [25]. However, since this paper focuses on the AEOSSP for the single orbit, and the maximum number of completed tasks is much less than that of [25], we therefore set NumoFIterNolmp\", which is the number of interactions without the updated optimal solution, as 10. The average task total profits, the standard deviation, and the total running time of HCNN and its competitors are shown in Table 10. From this table, it can be seen that the profit of the HCNN is obviously higher than those of the other competitors; for example, G-HCNN achieves more profits than G-W and G-P. Besides, the std. of the HCNN is mostly smaller than its competitors, indicating that the HCNN can maintain a stable and high-quality initial solution for different task scales and corresponding meta-heuristic algorithms. Figure 11 displays the average profits for all algorithms as an initial solution, showing that the performance of the algorithms with GRILS is better than that of other competitors, and the G-HCNN completes the most average profits. For example, in size-25, because G-W achieves more 17.65% average profits than TS-W and G-P achieves more 20.67% average profits than SA-P, the GRILS algorithm reveals its superior performance to the other two algorithms. Furthermore, in size-200, TS-HCNN achieves 23.33% and 10.21% improved performance compared to TS-W and TS-P, respectively, suggesting that the HCNN model as the initial solution can better ameliorate the performance of the iterative meta-heuristic algorithm than other two algorithms. Although the results of three different GRILS algorithms are similar, the advantages of G-HCNN can still be discovered. To further explore the differences among these three algorithms, we count the average number of iterations of ten solution processes, shown in Figure 12. From this figure, it can be obtained that G-HCNN maintains the advantage of quality during the algorithm operations, because the profit quality at the early iterations of GRILS achieves the same level of the profit quality at the later iterations of other competi  
Figure 10: Performance of HCNN at different sizes. (**a**) Average profits for the single-orbit scenarios with 50 tasks; (**b**) Average profits for the single-orbit scenarios with 100 tasks. tors, and the total number of iterations are relatively smaller. This finding demonstrates that HCNN can output the effective task priority sequence, select high-quality tasks, and provide high priority for observation, which accelerates the iterations of GRILS. Furthermore, during the initialization of the algorithms, the quality of the initial solutions by the three algorithms has been improved, which benefits from the INSERT operator of GRILS algorithm. The INSERT operator is able to arrange tasks for observation as much as possible but causes the algorithm to iterate slowly.