# Large-Scale Multi-Objective Imaging Satellite Task Planning Algorithm for Vast Area Mapping
## 2 Regional coverage results
#### 4.2.3 Results of ECL-INS-LMOA for Larger Regions  
To verify the effectiveness of ECL-INS-LMOA in large-scale multi-objective optimization problems, four regions larger than Congo (K), including India, Australia, the United States, and Antarctica, are used as imaging regions. Figure 12 shows the distribution of non-dominated solutions obtained by each algorithm in different regions. Table 7 lists the optimal coverage solutions of ECL-INS-LMOA and the comparison algorithms in each region, as well as the corresponding regional coverage rate and the number of participating imaging strips. Figure 13 shows the coverage display of ECL-INS-LMOA in different regions. The meanings of each element in Figures 12 and 13 and in Table 7 are the same as in Section 4.2.2.  
From this experiment, the following conclusions can be drawn: Firstly, ECL-INS-LMOA can obtain reliable results in task planning for regions with different decision variable scales. The coverage rate always remains above 98.5%, and the percentage of participating imaging strips remains within 0.5. There is no significant decrease in performance as the number of decision variables increases. Although the coverage rate of LMOCSO in the United States is 0.15% higher than the ECL-INS-LMOA, the number of imaging strips required for LMOCSO is 140 more than that of ECL-INS-LMOA, which is too costly. ECL-INS-LMOA always achieves the best results except for this factor. Importantly, the coverage display of ECL-INS-LMOA in various regions shows an overall uniform arrangement of imaging strips, without obvious redundant observations, and only with  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Region** & **Algorithm** & \begin{tabular}{c} **Objective** \\ **Function 1** \\ \end{tabular} & **Coverage Rate** & \
\begin{tabular}{c} **Objective** \\ **Function 2** \\ \end{tabular} &
\begin{tabular}{c} **Number of** \\ **Imaging Strips** \\ \end{tabular} \\ \hline \multirow{4}{*}{India} & LMEA & 0.01037 & 98.96\% & 0.38636 & 102 \\  & LMOCSO & 0.00389 & 99.61\% & 0.62121 & 164 \\  & NSGA-II & 0.01418 & 98.58\% & 0.65530 & 173 \\  & ECSO-NSGA-II & 0.00113 & 99.89\% & 0.36364 & 96 \\ \hline \multirow{4}{*}{Australia} & LMEA & 0.03913 & 96.09\% & 0.54745 & 225 \\  & LMOCSO & 0.01430 & 98.57\% & 0.67153 & 276 \\  & NSGA-II & 0.03689 & 96.31\% & 0.55961 & 230 \\  & ECSO-NSGA-II & 0.00736 & 99.26\% & 0.43552 & 179 \\ \hline \multirow{4}{*}{The United States} & LMEA & 0.02598 & 97.40\% & 0.42974 & 211 \\  & LMOCSO & 0.00542 & 99.46\% & 0.65173 & 320 \\  & NSGA-II & 0.02597 & 97.40\% & 0.57434 & 282 \\  & ECSO-NSGA-II & 0.00688 & 99.31\% & 0.36660 & 180 \\ \hline \multirow{4}{*}{Antarctica} & LMEA & 0.04870 & 95.13\% & 0.51504 & 411 \\  & LMOCSO & 0.01726 & 98.27\% & 0.68797 & 549 \\ \cline{1-1}  & NSGA-II & 0.07696 & 92.30\% & 0.58647 & 468 \\ \cline{1-1}  & ECSO-NSGA-II & 0.01158 & 98.84\% & 0.36591 & 292 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Optimal coverage solutions of each algorithm in different regions.  
Figure 13: Coverage displays of ECL-INS-LMOA in different regions. (**a**) India; (**b**) Australia; (**c**) the United States; (**d**) Antarctica.  
small and limited gaps. Secondly, for NSGA-II in different regions, the proportions of participating imaging strips are around 0.6, but the coverage rates decrease, which is most evident in Antarctica with a coverage rate of only 92.30%. Thirdly, the performance of the comparison algorithm LMOCSO is relatively stable. For regions with different decision variable sizes, the coverage rate can always reach over 98%, but the percentage of participating imaging strips remains between 0.6 and 0.7. Satellite resources are wasted compared with ECL-INS-LMOA. Fourthly, for LMEA, although a higher number of evaluations is assigned based on its principles, its performance is not fully reflected.  
In summary, the effectiveness of ECL-INS-LMOA in regional task planning problems with large-scale decision variables is further verified.