## 2 Problem Description  
The satellite Earth observation mission studied in this paper was the observation and data transmission mission of multiple targets by an individual AEOS. The observation target type in this research was the point targets that are fixed on the Earth's surface. A single complete mission involves a satellite using a camera to capture images of a target, generating and storing the observation data, and connecting to the ground stations for data transmission, as shown in Figure 1. We defined the satellite observation mission scheduling problem as a mixed-integer programming problem. The decision variables are as follows:  
* \(x_{i}\in\{0,1\}\)\(i=1,2,\ldots,n_{t}\) represents the decision of whether to observe target \(i\);
* \(g_{ij}\in\{0,1\}\)\(i,j=1,2,\ldots,n_{t}\) represents whether the observation of target \(j\) is after the observation of target \(i\) or not;
* \(y_{i}\in\{0,1\}\)\(i=1,2,\ldots,n_{t}\) represents whether to download the observation data of target \(i\) or not;
* \(h_{ij}\in\{0,1\}\)\(i,j=1,2,\ldots,n_{t}\) represents whether the download mission of target \(j\) is after the observation of target \(i\) or not. The objective function of the problem can be expressed as  
\[\max\quad J=\sum_{i=1}^{n_{t}}v_{i}y_{i}, \tag{1}\] \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Meaning** \\ \hline \(n_{t}\) & The number of targets \\ \(v_{i}\) & The profit of target \(i\) \\ \(t_{s}\), \(t_{e}\) & The start and end time of the scheduling \\ \(\Delta t_{o}\) & The observation time of single target \\ \(t_{osi}\), \(t_{osi}\) & The start time and the end time of the observation of target \(i\), the relationship \\  & between them is \(t_{oei}=t_{osi}+\Delta t_{o}\) \\ \(\Delta t_{d}\) & The data transmission time of single target \\  & The start time and the end time of the data transmission of target \(i\), the \\ \(t_{dsi}\), \(t_{del}\) & relationship between them is \(t_{del}=t_{dsi}+\Delta t_{d}\) \\ \(\Delta t_{ds}\) & The device switching time between each data transmission \\  & in different time windows \\  & The attitude maneuver time required for attitude transition of \\ \(\Delta t_{s,i}\), \(t_{oei}\) & two observation missions \\ \(t_{usi}\), \(t_{oei}\) & The start time and the end time of the observation time window of target \(i\) \\ \(t_{gsk}\), \(t_{ggk}\) & The start time and the end time of the data transmission time window \(k\) \\ \(M\), \(M_{\max}\) & \(M\) is the occupied memory capacity and \(M_{\max}\) is the total memory capacity \\ \(W\), \(W_{\max}\) & \(W\) is the available electrical energy and \(W_{\max}\) is the electrical energy capacity of the battery \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters in the problem description. Figure 1: Schematic diagram of satellite Earth observations. where \(J\) is the objective function value. The objective function attempts to maximize the total profit of targets that complete an observation and data download. The target profit \(v_{i}\) can be described as its value to the users and its importance to the targets. The higher the profit, the more important the target. Meanwhile, profit \(v_{i}\) can also represent the priority of the targets. To obtain a higher objective function value, the targets with a higher profit will be prioritized when conducting observation missions.