# An Enhanced Multi-Constraint Optimization Algorithm for Efficient Network Topology Generation
## 5 Results
### Algorithm Performance  
In terms of the average inter-satellite link connection duration, which reflects the stability of the satellite network topology, we observe different performances among the LCT, SLI, and our proposed MCOTG methods. From the statistical summary in Table 3, we note that the mean link duration for the LCT method is highest, at 7382.50 min, followed by the MCOTG at 6345.00 min, and the SLI strategy at 6257.50 min.  
The lower standard deviation of 327.229 for MCOTG indicates that it has a more consistent performance compared to LCT and SLI. This suggests that the MCOTG method is capable of maintaining a more stable link connection duration across different satellite network topologies.  
Although the MCOTG's mean link length is lower than that of the LCT, it is important to note that this method provides a higher communication efficiency as indicated by its shorter average link length. Furthermore, the upper limit of the 95% confidence interval for the MCOTG method indicates a potential to achieve higher link durations, with a value close to the mean of the LCT method.  
Overall, while the LCT strategy can achieve a longer average link duration, our proposed MCOTG algorithm provides a balance between communication efficiency and network stability. This balance is crucial for satellite networks, where both aspects play an important role in achieving an optimal performance. Figures 6 and 7 show that the average link length of the LCT scheme is higher than the other two topology generation methods, indicating that the communication efficiency of the network topology generated by the MCOTG algorithm and SLI strategy is higher than the LCT strategy. In terms of communication efficiency, the MCOTG algorithm is 14.3397% higher than the LCT strategy and 0.8876% lower than the SLI strategy.  
Figure 5: Visualization of the constellation network topology.  
demonstrates a higher level of stability than does the LCT strategy, with a stability increase of 13.0753% and a reduction of 6.4387% compared to the LCT strategy.  
As is shown in Table 4, although the LCT strategy yields the highest mean value, indicating a longer average link lifetime, its standard deviation and standard error are also higher, suggesting less consistency in its performance. On the other hand, the SLI strategy, while demonstrating lower mean values and thus shorter average link lifetimes, does provide a more consistent performance, as indicated by its smaller standard deviation and standard error.  
Figure 8: Comparison of average link lifetime in network topology.  
Figure 9: Analysis of average link lifetime in network topology.  
In contrast, the proposed algorithm offers a notable improvement in both aspects. Despite its mean value being lower than LCT, it is significantly higher than SLI, indicating longer average link lifetimes than the latter. More importantly, its standard deviation and standard error values are the lowest among the three methods, which means it provides the most consistent performance.  
Further, the 95% confidence intervals, defined by the lower and upper limits in Table 4, substantiate our results. Briefly, a 95% confidence interval is a probable range for the true mean lifetime, with a narrower interval indicating more precise estimation. For the MCOTG method, its tighter interval underscores its superior stability and efficiency.  
In conclusion, while the LCT and SLI strategies have their own strengths, the MCOTG algorithm, proposed in this study, outshines them by offering a more reliable and efficient solution for satellite link lifetime management in complex communication environments.