## 3 Model Construction
### Problem Description  
This section constructs MSIMPLTS based on Multi-layer Objective Optimization (MSIMPLTS-MLOO) for large-scale objective scenarios. By setting up a three-layer structure to hierarchically process the optimization objectives and their constraints, the objective functions are constructed with the aims of maximizing the task benefit objective function, maximizing the task allocation rate objective function, and minimizing the response time objective function. Subsequently, according to the progressive optimization mechanism, maximizing the task benefit objective function is considered in the allocation optimization stage to generate the allocation sequences of satellites and target tasks; in the time window  
Figure 2: Observation time window conflict diagram. optimization stage, maximizing the task allocation rate objective function is considered according to the decision-making scheme in the allocation optimization stage to allocate a feasible observation time window to each target task; and finally, minimizing the response time objective function is further considered in the global optimization stage to combine the decision-making results of the previous two stages and thus output an MSIMPLTS scheme adapted to the current environment. The MSIMPLTS-MLOO model involves mathematical definitions and decision variables as specified below:  
1. Satellite resource \(Sat=\{sat_{1},\ldots,sat_{S_{n}}\},sat_{j}=<\theta^{j}_{ssa},\theta^{j}_{Fov}, Time^{j}_{begin},Time^{j}_{end},orbit_{j}\), \(R^{j}_{obs}>\) in which \(S_{n}\) denotes the number of satellites, \(sat_{j}\) denotes satellite \(j\), \(\theta^{j}_{ssa}\) denotes the maximum side-swing angle of the load carried by satellite \(j\), \(\theta^{j}_{Fov}\) denotes the observation field-of-view angle of satellite \(j\), \(Time^{j}_{begin}\) denotes the longest start-up time of satellite \(j\), \(Time^{j}_{end}\) denotes the shortest start-up time of satellite \(j\), the satellite resource set executable orbits are \(Orb=\{Orbti_{1},\ldots,Orbit_{N_{0}}\}\), \(orbit_{o}\) denotes the orbital parameters where satellite \(j\) is located, \(N_{o}\) denotes the number of executable orbits, and \(R^{j}_{obs}\) denotes the observation resolution of the payload carried by satellite \(j\). 2. Target task \(Task=\{Target_{1},\ldots,Target_{N_{T}}\},Target_{i}=<p^{i}_{lat},p^{i}_{lon}, pri_{i},Time^{i}_{during}\), \(R^{i}_{obs}>\), where \(N_{T}\) denotes the number of target tasks, \(Target_{i}\) denotes the \(i\)-th target task, \(p^{i}_{lat}\) and \(p^{i}_{lon}\) denote the latitude and longitude of the target task, \(pri_{i}\) denotes the task priority of the target task \(i\), \(Time^{i}_{during}\) denotes the duration of the target task \(i\), and \(R^{i}_{obs}\) denotes the resolution requirement of the target task \(i\). 3. The set of visible time windows of the target mission \(W_{Target}=\{w_{Target1},w_{Target2},\ldots,\)\(w_{TargetNi}\},\forall w_{Targeti}\in W_{Target},w_{Targeti}=<st^{\delta},et^{\delta}>\), where \(w_{Targeti}\) denotes the visible time window of the target \(i\), and \(st^{\delta}\) and \(et^{\delta}\) denote the start and end times of the visible time window of the target mission, respectively. 4. The set of visible time windows of the satellite \(W_{sat}=\{w_{sat1},w_{sat2},\ldots,w_{s_{n}}\},\forall w_{satj}\in W_{sat}, w_{satj}=\left\{w^{1}_{satj},\ldots,w^{n}_{satj}\right\},w^{g}_{satj}=<st^{ \delta}_{satj},et^{\delta}_{satj}>\), where \(st^{\delta}_{satj}\) and \(et^{\delta}_{satj}\) denote the start and end times of the visible time window \(g\) of satellite \(j\), respectively. 5.