## 4 Results  
### Experimental Setting  
All the algorithms were run on a laptop with an Intel (R) Core (TM) i7-7600U CPU at 2.80 GHz 10 with 8 GB of RAM. The orbit parameters of the EOSs in the experiment were determined by referring to the orbit parameters in the studies [1; 19; 41], and the EOS orbit parameters are shown in Table 1. The scheduling horizon was 86,400 s. The duration of each observation mission followed a uniform distribution with the range of [1; 10]. The profit of the static and dynamic missions were random values within [1; 10] and [5; 15]. Static missions were submitted before the start time of the scheduling horizon, and static missions were allowed to be observed during all the scheduling horizon, while the dynamic missions arrived randomly during the scheduling horizon and the length of ETW is generated in the uniform distribution with the range [15,000 s, 35,000 s]. The observation missions were randomly generated in the area of latitude 3\({}^{\circ}\) N-S\({}^{\circ}\) N and longitude 74\({}^{\circ}\) E-133\({}^{\circ}\) E. Scheduling scenarios with low, medium, and heavy loads were investigated, where the  
Figure 4: Backtracking insertion.  
numbers of static missions were 400, 600, and 800, respectively. For each load situation, four test cases with different numbers of dynamic missions were studied where the ratios of the number of dynamic missions to the number of static missions were 25%, 50%, 75%, and 100%, respectively. Therefore, there were 12 test cases in the experiments and the test scenarios are denoted by \"Cases\(\_\psi\)\" where \(\varsigma\) and \(\psi\) are the numbers of the static missions and dynamic missions.  
The multi-objective optimization algorithms for comparison in this paper were as follows: SPEA2 [40], NSGA-II [42], MOEA/D [43], I-MOMA, and D-MOMA [44]. SPEA2 [40], NSGA-II [42], and MOEA/D [43] are the classical indicator-based MOEA, domination-based MOEA, and decomposition-based MOEA, respectively. I-MOMA and D-MOMA [44] are state-of-the-art multi-objective scheduling algorithms for the EOS-mission-scheduling problem, which combine a multi-objective evolutionary optimization algorithm and a local search algorithm. I-MOMA and D-MOMA are designed based on the indicator-based multi-objective optimization algorithm and the domination-based multi-objective optimization algorithm, respectively.  
After testing the performance of different parameters related to the MODMSA, we chose the parameters with the best performance as the parameters for the MODMSA. The parameters related to the MODMSA are listed in Table 1. The population size for all multi-objective scheduling algorithms was 100, and the number of the archive size in the SPEA2 was 50. The maximum number of iterations was 200, and the number of iterations in the local search algorithm was 10. The other parameters remained the same as the default ones in the SPEA2, NSGA-II, MOEA/D, I-MOMA, and D-MOMA.  
\begin{table}
\begin{tabular}{l l} \hline
**Satellite Parameters** & **Value** \\ \hline Semimajor axis (km) & 6678 \\ \hline Inclination (\({}^{\circ}\)) & 96.576 \\ \hline Right ascension of the ascending node (\({}^{\circ}\)) & 0, 18, 36 \\  & 54, 72, 90 \\  & 108, 126 \\  & 144, 162 \\ \hline Eccentricity (\({}^{\circ}\)) & 0.000627 \\ \hline Argument of perigee (\({}^{\circ}\)) & 0 \\ \hline Mean anomaly (\({}^{\circ}\)) & 20, 38, 56 \\  & 74, 92, 110 \\  & 128, 146 \\  & 164, 2 \\ \hline \(a_{1},a_{2},a_{3},a_{4}\) & 5, 10, 16, 22 \\ \hline \(v_{1},v_{2},v_{3},v_{4}\) (\({}^{\circ}/s\)) & 1.5, 2, 2.5, 3 \\ \hline Parameters related to the MODMSA & Value \\ \hline Pop size & 100 \\ \hline \(ite_{max}\) & 200 \\ \hline \(\epsilon_{C},\epsilon_{M},\epsilon_{RD}\) & 2, 2, 1.5 \\ \hline \(\epsilon_{ID},\epsilon_{R}\) & 1.5, 1.5 \\ \hline \(P_{Mu}\) & 0.8 \\ \hline \(P_{II},P_{12},P_{13},P_{14}\) & 0, 0.25 \\  & 0.50, 0.75 \\ \hline \(P_{C}^{m},P_{M}^{m}\) & 0.6, 0.4 \\ \hline \(P_{D}^{m},P_{D}^{m}\) & 0.2, 0.2 \\ \hline \end{tabular}
\end{table}
Table 1: Parameter setting.