## 4 Algorithm Design
### Fast Rerouting Mechanism
Integrated with a multi-objective simulated annealing algorithm, we iteratively derive a node from this set to replace the congested node. As the solutions generated by multi-objective simulated annealing approach global optimality, the selected node facilitates optimal path stability and latency for the new path. Furthermore, we employ the FRR-BP mechanism to address node failures, which can maintain a short backup path rebuilding time in almost all network settings (except for the Ideal networking method with high constellation density). **Author Contributions:** Conceptualization, Y.Z. and H.C.; Methodology, Y.Z. and H.C.; Software, Y.Z. ; Validation, Y.Z. ; Resources, Z.D. ; Writing--original draft, Y.Z. ; Writing--review & editing, H.C. and Z.D. All authors have read and agreed to the published version of the manuscript. **Funding:** This research was funded by the Natural Science Foundation of Zhejiang Province (No. LY24F020001), Ningbo Municipal Commonwealth S&T Project (No. 2022S005), and Major S&T Projects of Ningbo High-tech Zone (No. 2022 BCX05001). **Data Availability Statement:** Data are contained within the article. Figure 4:1 The impact of constellation density on the reconstruction time of backup paths. ## Conflicts of Interest

Author Dr. [PERSON] employed by the company The 54 th Research Institute of China Electronics Technology Group Corporation. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. ## References

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