## 2 Problem Description
The constraints that should be considered in the mission scheduling problem are as follows:  
\[t_{osi}\geq t_{usi}\wedge t_{oei}\leq t_{wei}, \tag{2}\]  
\[t_{osj}-t_{oei}\geq\Delta t_{Ai,j}\quad g_{ij}=1, \tag{3}\]  
\[t_{dsi}\geq t_{gsk}\wedge t_{dei}\leq t_{gek}, \tag{4}\]  
\[[t_{dsi},t_{dei})\cap\left[t_{dsj},t_{dej}\right)=\varnothing\ \ \ \ \forall 1\leq i\leq n_{t},1\leq j\leq n_{t},y_{i}=1,y_{j}=1,i\
eq j, \tag{5}\]  
\[t_{dsj}-t_{dei}\geq\Delta t_{ds}\lor t_{dsi}-t_{dej}\geq\Delta t_{ds}\ \ \ \ \ \forall 1\leq i\leq n_{t},1\leq j\leq n_{t},y_{i}=1,y_{j}=1,i\
eq j,k_{gi}\
eq k _{gj}, \tag{6}\]  
\[t_{dsi}\geq t_{oei}, \tag{7}\]  
\[0\leq M\leq M_{\max}, \tag{8}\]  
\[0\leq W\leq W_{\max}, \tag{9}\]  
Equation (2) represents the observation time window constraint. Equation (3) represents the attitude maneuver constraint, which means that the interval between two observation missions must be greater than the attitude maneuver time required for the attitude transition of two observation missions. The calculation method of the satellite observation time window and the calculation of \(\Delta t_{Ai,j}\) are introduced in Appendix A. Moreover, the data transmission constraints consist of the data transmission time window constraint, the data transmission mission limit constraint, the data transmission equipment conversion time constraint, the observation data download logic constraint, and the memory capacity constraint, which are expressed as Equations (4)-(8). The data transmission time window constraint requires the data transmission from the satellite to ground stations to be executed within the data transmission time window, and the calculation method of the satellite data transmission time window is introduced in Appendix A. The relationship between \(\Delta t_{d}\) and \(\Delta t_{o}\) is expressed as \(\Delta t_{d}=\frac{R_{cam}}{R_{datatams}}\Delta t_{o}\), where \(R_{cam}\) is the data generation rate of the camera and \(R_{datatams}\) is the data transmission rate of downloading the data to the ground stations. The data transmission mission limit constraint limits the observation data of one target to be downloaded at the same time. The data transmission equipment conversion time constraint requires a device switching time \(\Delta t_{ds}\) between each data transmission in different time windows; in Equation (6), \(k_{gi}\) and \(k_{gj}\) are the serial numbers of the data transmission time windows to download the observation data of target \(i\) and target \(j\). The observation data download logic constraint only allows the satellite to download the observation data after the data are completely stored in the memory. The memory capacity constraint is that the memory capacity occupied by all the observation data cannot exceed the maximum memory capacity. The occupied memory capacity can be calculated as follows:  
Figure 1:0  
where \(R_{in}\) is the data generation rate, \(R_{in}=R_{cam}\), during the observation periods while \(R_{in}=0\) in the spare time. \(M_{era}\), is the erased data volume. After the satellite downloads the target observation data, the occupied memory capacity can be instantly released by erasing the downloaded observation data. Equation (9) represents the electricity constraint, which requires the electrical energy to be greater than 0, while the electrical energy cannot exceed the electrical energy capacity of the battery. The available electrical energy can be calculated as follows:  
Figure 1:1  
where \(W_{initial}\) is the initial electrical energy of the satellite and \(P_{in}\) is the solar arrays' charging electrical power. When the satellite is operating and executing its mission, it consumes electrical energy that can be supplemented by receiving solar energy through solar arrays.