## 3 System Model and Problem Formulations
### Advanced Load Balancing Scheme Based on Optimized GA
group select the optimal solution of the load balancing scheme in the former h periods as the crossover object according to the probability and randomly select the crossover starting point and crossover length. After crossover, the two sub-individuals generated are inserted at the end of the population. Finally, the population that has completed all crossover operations is outputted. The specific process of the crossover operation is shown in Algorithm 2:  
```
1. Input:\(Population[N,k];fitness_{ave};fitness(i)\); \(A_{ij}(T_{i-\delta}),P\left(A_{ij}(T_{i-\delta})\right),\delta=1\cdots\) \(h\);
2. Output:\(Population[end,k]\);
3. \(i=1\)
4. while\(i\leq N\)do
5. if\(fitness(i)\geq fitness_{ave}\)then
6. if\(\text{rand}\leq P_{auc}(0)\times\frac{ fitness_{ave}-fitness}{ fitness_{ave}-fitness_{ave}}\)then
7. Randomly choose a crossover starting node
8. Randomly choose the crossover length
9. \(Population[i,k]\) perform a crossover operation with \(Population[i+1,k]\)
10. Sub-individuals are inserted at the end of the population
11. \(i=i+2\)
12. else
13. \(i=i+1\)
14. end if
15. else
16. if\(\text{rand}\leq P_{auc}(1)\)then
17. Select prior high fitness crossover objects by selection probability
18. Randomly choose a crossover starting node
19. Randomly choose the crossover length
20. \(Population[i,k]\) perform a crossover operation with \(A_{ij}(T_{i-\delta})\)
21. Sub-individuals are inserted at the end of the population
22. \(i=i+1\)
23. else
24. \(i=i+1\)
25. end if
26. end while
```  
**Algorithm 2**Crossover  
The mutation module inputs population matrix \(Population[N,k]\), the current evolution generation \(t\), the maximum evolution generation \(t_{max}\), and the probability of single gene selection \(P(B_{i})\). The mutation module judges whether the individual mutates according to the adaptive mutation probability. The mutated individual randomly selects the mutated gene node and selects the mutated gene value according to single-gene selection probability. After mutation, the sub-individual generated is inserted at the end of the population. The population that has completed all mutation operations is outputted. The specific process of the mutation module is shown in Algorithm 3:  
```
1. Input:\(Population[N,k]\); \(t\); \(t_{max}\); \(P(B_{i})\);
2. Output:\(Population[end,k]\);
3. \(i=1\)
4. while\(i\leq N\)do
5. if\(\text{rand}\leq P_{mut}(0)\times\frac{t_{max}-t}{t_{max}}\)then
6. Randomly select gene node for mutation

## 5 Simulation and Analysis

### Simulation and Experimental Design

To verify the performance of the proposed scheme, we constructed a platform to simulate the load balancing of S-IoT-N. This platform consisted of four modules: the satellite simulation module, user simulation module, coverage simulation module, and control and analysis module, as per Figure 7. The satellite simulation module was mainly used to simulate satellite nodes under different satellite configurations, which affected the size of satellite signal coverage on the ground, as well as the SSPs. The user simulation module was mainly used to simulate different DoU, which related to the population distribution and service behavior. The coverage simulation module mainly simulates F-Sat-Beams, F-Ser-Beams, the trajectory of SSPs on the ground, and the constraint boundary corresponding to the population distribution and determined constellation. The control and analysis module was mainly used to complete scenario realization, parameter configuration, and algorithm selection, as well as analysis of the learning ability of the algorithm, the throughput, and the efficiency of the traffic balancing method. Using the simulation platform, we verified the performance of the GA's learning efficiency and load balancing. The parameters of GAs are configured in Table 2.

The parameters of load balancing for S-IoT-N are configured in Table 3. Load balancing simulation scenario considering 9 F-Ser-Beams at the edge of 3 F-Sat-Beams. Similar parameters can be found in the article [20].