## 4 Algorithm Design
### Fast Rerouting Mechanism
``` Input:\(G\), \(Source\), \(Target\), \(path1\), \(length1\), \(path2\), \(length2\), \(fault\_node\) Output:\(path1\), \(path2\)
1 Find the shortest path from \(Source1\) to \(Target1\) by traditional Dijkstra algorithm taking the geographical distance as the weight -> \((path1,length1)\) ;
2 Find the shortest path from \(Source2\) to \(Target2\) by traditional Dijkstra algorithm taking the geographical distance as the weight -> \((path2,length2)\) ;
3 if\(fault\_node\) in \(path2\)then
4 //A node failure occurred

## 5 Simulation Experiment Evaluation

### Simulation Environment

We utilized the SILLEO-SCNS simulator proposed by [PERSON] [16], which is a simulation tool designed for studying routing in large-scale satellite networks. This tool enables the simulation of various satellite network architectures and routing schemes, allowing for performance evaluation. The architecture of this simulator primarily consists of a graphical user control interface, constellation class, and simulation class, as shown in Figure 4. The constellation class serves as the core component responsible for generating satellites, ground stations, and network structures. The simulation class handles the visualization of the satellite network and all associated animations. The GUI provides a user control interface that allows users to configure constellation parameters, set the source and destination for path planning, and specify satellite connectivity options. Communication between the GUI and simulation is facilitated through interprocess communication for information exchange. The simulation adopts a Walker constellation configuration of 100/10/1, with an orbit altitude of 1200 km and an orbital inclination of 60\({}^{\circ}\). To facilitate analysis and calculations, the sampling period for the constellation data is set to 10 s. The setting of simulation parameters is shown in Table 2. In the temperature cooling schedule for multi-objective simulated annealing, the initial temperature is set to 1000 \({}^{\circ}\)C. Following [PERSON] et al. 's analysis, the Boltzmann constant during temperature cooling is set to 0.95. The iteration limit is set to 2500, and the iteration stops when the temperature cools to the minimum temperature or the iteration count reaches the upper limit. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Value** & **Meaning** \\ \hline T & 1000 \({}^{\circ}\)C & The temperature at the current moment, \\  & & with an initial value of 1000 \({}^{\circ}\)C. \\ \hline cooling\_rate & 0.95 & T * cooling ratio for each cooling process. \\ \hline min\_T & 0.01 \({}^{\circ}\)C & Stop iteration when the temperature \\  & & reaches the minimum temperature. \\ \hline n & 1 & Current number of iterations. \\ \hline max\_n & 2500 & Stop iteration when the maximum number \\  & & of iterations is reached. \\ \hline step & 10 s & The time interval for \\  & & obtaining constellation data and routing. \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of the simulation. Figure 4: Simulator class diagram. ### Benchmarking Algorithms and Complexity Analysis

Our proposed MOLM algorithm aims to address network congestion issues, and we analyze its complexity in this part. The core idea of the MOLM algorithm is to establish a continuous neighbor set during network congestion and then utilize a multi-objective simulated annealing framework to select the best node from this set to replace congested nodes, achieving the goals of avoiding congestion while maintaining path stability and low latency. _Optimum_ is based on a greedy algorithm for node replacement. It employs a greedy strategy to select nodes from the continuous neighbor set, optimizing path stability and latency of the entire path. The strategy of _Shortest Path_ generates the shortest path for congested traffic in the network, aiming to minimize latency. The difference between the two is that _Optimum_ selects one node from a limited number of nodes, namely those in the continuous neighbor set, to minimize latency.