## 4 Design of the POM-PSASIDEA Algorithm
### Progressive Optimization Mechanism
#### 4.1.1 Allocation Optimization Phase  
The allocation optimization phase (AOP) is designed to maximize the mission benefit as the optimization goal. Based on the satellite resource set, target mission set, and mission benefit value, several satellite and target mission allocation sequences are matched to form an initial mission planning scheme, which provides a reference sequence for the time window optimization phase. Figure 4 explains the allocation optimization phase's process in the form of an example. Among them, the red circle represents the selected satellite. Firstly, for the large-scale target mission scenario where the number of satellites is significantly less than the number of target missions, this section constructs a task benefit repository, which is used to record the task benefit value of each satellite when it performs each target mission, and the task benefit value can be directly called from the task benefit repository to perform the evolution operation during the optimization search process, so as to improve the efficiency of the task assignment and reduce the resource consumption of real-time computation. The mathematical expression of the constructed mission benefit repository is shown in Equation (14):  
\[Efficiency(x_{ji})=\left[ \begin{array}{ccc}Efficiency(x_{11})&\ldots&Efficiency (x_{(1,T)})\\ \vdots&\ddots&\vdots\\ Efficiency(x_{s_{n}1})&\ldots&Efficiency(x_{s_{n}N_{T}})\\ 0&\cdots&Efficiency(x_{(1,N_{T})})\\ \vdots&\ddots&\vdots\\ Efficiency(x_{(s_{n},N_{T})})&\cdots&0\\ \end{array} \right], \tag{14}\]  
Figure 4: Allocation optimization phase process. where \(Efficiency(x_{i\parallel})\) denotes the mission benefit of \(sat_{j}\) performing \(Target_{i}\), and \(Efficiency(x_{(i,u)})\) denotes the mission benefit of the imaging satellite completing \(Target_{i}\) and then performs \(Target_{i}\), starting from \(Target_{u}\). Secondly, \(N_{T}\) target tasks are randomly assigned to satellite \(S_{n}\). Theoretically, there is \((N_{T})^{S_{n}}\) variety of allocation possibilities, and there is a limitation on the observation demand of the target tasks and the observation capability of the satellites, meaning not every target task can be observed by an arbitrary satellite. Therefore, based on the given target mission set and satellite resource set information, the MSIMPLTS-MLOO model superstructure constraints are invoked to restrict the observation satellites of the target mission, and the potential satellite resource set is filtered to obtain the potential satellite resource set \(Sat_{potential}\), so as to achieve an effective reduction in the solution space of the mission planning scheme. Thereafter, each target task is paired with a randomly selected satellite from its potential satellite resource set; traverses the task benefit repository to obtain the corresponding target task benefit; and takes the execution satellite number, target task number, and its corresponding task benefit as a sequence of satellite and target task assignments and cyclically matches them until all satellites have been assigned to the target task, which constitutes a population separate to several satellites and the sequence of target task assignments. The POM-PSAISIDEA algorithm performs an optimization search to generate a sequence allocation scheme that maximizes the mission benefits. The algorithm framework is shown in Algorithm 2.