# Large-Scale Multi-Objective Imaging Satellite Task Planning Algorithm for Vast Area Mapping
## 2 Regional coverage results  
Figure 11 shows the coverage display results in Congo (K) using four different algorithms. In Figure 11, the red lines represent the simplified regional boundary of Congo (K), and the lotus root pink strips are the imaging strips obtained using various algorithms. Figure 11a shows the coverage display result of all candidate strips without any algorithm optimization, and Figure 11b-e shows the coverage display result of imaging strips optimized by NSGA-II, LMOCSO, LMEA, and ECL-INS-MOEA, respectively.  
Figure 10: Distribution of planning solution in Congo (K) using different algorithms.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Algorithm** & **Objective** & **Coverage Rate** & **Objective** & **Number of** \\  & **Function 1** & & **Function 2** & **Imaging Strips** \\ \hline LMEA & 0.02902 & 97.10\% & 0.60000 & 81 \\ LMOCSO & 0.00067 & 99.93\% & 0.62963 & 85 \\ NSGA-II & 0.01120 & 98.88\% & 0.68889 & 93 \\ ECL-INS-LMOA & 0.00018 & 99.98\% & 0.47407 & 64 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Optimal coverage solutions in Congo (K) for different algorithms.  
Figure 11: Cont.  
From Figure 11, the following conclusions can be drawn: Firstly, although Congo (K) can be fully covered without any algorithm optimization, the imaging strips are very dense, indicating a severe waste of satellite resources. Secondly, although each algorithm can achieve good coverage for Congo (K) and save satellite resources to varying degrees, the coverage effect varies greatly. On the one hand, there are invalid observations of imaging strips outside the region for three comparative algorithms, because the more decision variables, the more iterations the algorithm requires, and the algorithm has not yet reached the optimal within the maximum evaluation. On the other hand, due to differences in the coverage rate, there are varying degrees of gaps in the imaging schemes of the different algorithms. The imaging schemes of ECL-INS-LMOA and LMOCSO have no apparent gaps, while the imaging schemes of NSGA-II have several small gaps, and the gaps of LMEA are the most obvious. Thirdly, compared to the three comparison algorithms, ECL-INS-LMOA has fewer redundant imaging strips and no obvious gaps in the imaging region, and the distribution of imaging strips is uniform. Therefore, ECL-INS-LMOA outperforms the three comparison algorithms in terms of coverage display. In addition, it should be noted that the comparison algorithms did not obtain a better imaging scheme because the solution obtained within the maximum number of evaluations is still locally optimal. As the number of evaluations increases, all algorithms, including ECL-INS-LMOA, can obtain a better imaging scheme. However, increasing the number of evaluations means increasing the computational consumption. Moreover, the closer it is to the optimal solution, the more disproportionate the 'cost' and 'benefit' of the search solution.  
Figure 11: Coverage displays of task planning results in Congo (K) for different algorithms. (**a**) No optimization; (**b**) NSGA-II; (**c**) LMOCSO; (**d**) LMEA; (**e**) ECL-INS-LMOA.  
Runtime  
Table 6 shows the time consumption of ECL-INS-LMOA and the comparative algorithms for imaging planning in Congo (K). From Table 6, it can be seen that ECL-INS-LMOA has a significantly better runtime than the comparison algorithms. In addition, LMOCSO and LMEA require a longer runtime than NSGA-II. Particularly, the runtime is 10,512 s for LMEA because LMEA requires much time to analyze the decision variables. In summary, compared to the comparison algorithms, ECL-INS-LMOA not only has the best performance, but also the shortest runtime for the imaging task planning problem in Congo (K).