## 4 Rule-Based Large Neighborhood Search Algorithm (RLNS)
### Heuristic Rules and Various Operators
#### 4.2.5. Onboard Data First-Come-First-Served Transmission Operator
This is especially so when the satellite is executing imaging and digital transmission tasks at the same time; if the satellite's fixed memory capacity at this time cannot satisfy the current observation task, then according to the rules in this paper, this task will not be successfully executed in the current task sequence. However, if the current mission can be moved backward for a certain period of time within the range allowed by the time window, after the satellite completes the current digital transmission mission, there will be possible memory space to realize the current observation mission, as shown in Figure 16. Therefore, in order to achieve better search results and avoid the optimal solution being unreachable, the execution start time of tasks in the task scheme can be designed to be locally adjusted based on the execution time of the tasks, instead of the current simple sequence-based neighborhood operator. ## 8 Conclusions

In this paper, the integrated scheduling problem for parallel imaging and data transmission of agile Earth observation satellites is explored, considering sliding time window and ground station resource constraints, as well as satellite energy and memory capacity constraints. To solve the problem, the RLNS algorithm is first proposed and a genetic algorithm is designed on the basis of its operator design, and the solution performance of these two algorithms is compared with that of the cplex and cp solvers through simulation experiments to verify the effectiveness of the algorithms. By analyzing the neighborhood space of the algorithm, we found that some parts of the neighborhood space that could potentially lead to better solution results were discarded due to the use of certain heuristic rules. This leads to the limited effectiveness of the heuristics proposed in this paper. Cplex performs well and is fast when dealing with small-scale problems. However, its performance is limited when dealing with larger scale problems, whereas the heuristics are faster in searching and can produce better solution results for larger scale problems. For this problem, possible future algorithmic improvements are to relax the heuristic rules for data transfer scheduling and the neighborhood search for imaging and digitizing task start times, or to use advanced heuristic information such as the degree of temporal slack in the time window in which the task is located, and the degree of satellite on-board fixed memory capacity slack to guide the neighborhood search. Conceptualization, G.Y. and K.Z. ; Data curation, G.Y. ; Formal analysis, G.Y. ; Funding acquisition, K.Z. ; Investigation, G.Y. and K.Z. ; Methodology, G.Y. ; Project administration, G.Y. ; Resources, G.Y. ; Software, G.Y. ; Supervision, K.Z. ; Validation, G.Y. and K.Z. ; Visualization, G.Y. ; Writing--original draft, G.Y. ; Writing--review and editing, K.Z. All authors have read and agreed to the published version of the manuscript. This research was funded by the Science and Technology Innovation Program of Hunan Province (Grant No. 2022 RC1241). Not applicable. All data used in this study were presented in this paper. Figure 16: Schematic diagram showing the start time of the task moving within the time window. **Conflicts of Interest:** The authors declare no conflicts of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results. ## Abbreviations

The following abbreviations are used in this manuscript:

MILP Three mixed-integer linear programming

RLNS Rule-based Large Neighborhood Search Algorithm

GA Genetic Algorithm

## References

* (1) [PERSON] Research on the Scheduling Problem of Imaging Reconnaissance Satellites. Ph.D. Thesis, National University of Defense Technology: Changsha, China, 2004. (In Chinese)
* (2) [PERSON] Research on the Scheduling Problem of Optical Earth Observation Satellites under Uncertain Cloud Conditions.