## 4 Rule-Based Large Neighborhood Search Algorithm (RLNS)
### Heuristic Rules and Various Operators
#### 4.2.5. Onboard Data First-Come-First-Served Transmission Operator
When scheduling the times, the observation tasks are arranged in the order of execution, and for each task, the start time of the observation is scheduled according to the arrival order of the time windows, while ensuring that the observation tasks do not overlap, as shown in Figure 3.

#### 4.2.7 Repair Algorithms Based on Onboard Capacity Constraints and Satellite Energy Constraints

The Repair Operator is based on onboard capacity constraints and satellite energy constraints: after completing the task scheduling scheme for the satellite and ground station, it is also necessary to calculate the fixed capacity limitations of the satellite while performing observation tasks. If there are task schedules that do not meet the capacity constraints, adjustments to the scheduling scheme are required. To reduce the computational complexity of the repair operator, a method of eliminating conflicting tasks is employed to repair the original scheduling scheme. In addition to verifying the satellite's fixed capacity, it is also necessary to examine the satellite's energy consumption. If the satellite's energy consumption exceeds its maximum energy limit, adjustments to the scheduling plan are required. To minimize the impact of these adjustments on the original plan, a simple method of canceling the last executed observation tasks is employed until the satellite's energy constraints are satisfied, as shown in Figure 4.

Figure 3: Flowchart of sequence-based observation tasks scheduling Algorithm. ### Process of the RLNS

The process of the large neighborhood search algorithm based on constraint information is shown in Figure 5.

Figure 4: Flowchart of repair algorithm. Figure 5: Flowchart of the large neighborhood search algorithm based on constraint information. In the iterative framework of the algorithm, a reference is made to the Metropolis criterion of the simulated annealing algorithm to enhance the search efficiency of the algorithm. ## 5 Genetic Algorithms (GA)

Through the analysis we found that due to the high coupling of the scheduling schemes of the imaging and digital transmission tasks in this integrated scheduling problem, the destruction and repair operators of the designed RLNS are relatively simple and the solution effect is relatively limited; therefore, the population-based genetic algorithm is designed on the basis of the multiple rule operators of the RLNS. ### Algorithm Description

In the RLNS, task start scheduling is performed by a simple first-come-first-scheduled rule. This single heuristic rule could potentially lead to optimal solutions that cannot be found by neighborhood search. As shown in Figure 6, if only the first-come-first-served rule is followed, goal 2 will not be scheduled; however, it may be possible to adjust the execution time of goal 1 backward so that goal 2 can also be executed. As shown in Figure 7, if only the first-come-first-served rule is followed, Satellite 2 will not be able to perform the observation as planned due to insufficient on-board fixed memory capacity during the observation mission. Figure 6: Graph of the adjustments to the sequence of tasks. Figure 7: Graph of the adjustments to the sequence of time windows for stations. ### Algorithm Design

In order to realize the perturbation of the first-come-first-schedule rule based on the time window sequence and achieve better search results, the operators of the genetic algorithm are designed as the perturbation of the task sequence on the satellite and the perturbation of the time window timing sequence between the satellite and the ground station.