## 4 Genetic Algorithm Configuration
### Weighting Factors and Penalty Coefficients  
In the test environment targeting the VLEO (300,km) + LoRa combination, GA-based optimization requires the design of an appropriate fitness function, which depends on the setting of weights for various performance objectives. In this study, we conducted preliminary research to derive the optimal weighting combination to be used in the GA's fitness function. We defined six preliminary weighting sets (sets 1-6) with different weights for various objective metrics, which are detailed in Table 5. Each set was designed to emphasize specific goals. For instance, set 1 assigned the highest total number of satellites (\(w_{1}=6\)), focusing on minimizing the satellite count, while set 2 assigned equal weights to all metrics (\(w_{1}\), \(w_{2}\), \(w_{3}\), and \(w_{4}=1\)) in an attempt to achieve balanced optimization. Set 3 assigned higher weights for the average revisit time and daily data transmission volume (\(w_{2}=3\), \(w_{4}=4\)), set 4 assigned the highest daily transmission volume (\(w_{4}=8\)), set 5 assigned higher average and max revisit times (\(w_{2}=4\), \(w_{3}=2\)), and set 6 is characterized by assigning relatively higher weights to the total number of satellites (\(w_{1}=4\)) and daily data transmission volume (\(w_{4}=5\)). For each weighting set, we performed GA optimization (population = 80, generation = 20) to derive optimized constellations. The performance of each constellation was evaluated using four metrics: the total number of satellites (\(S_{\text{Total}}\)), average revisit time (\(R_{\text{avg}}\)), maximum revisit time (\(R_{\text{max}}\)), and daily data transmission volume (\(D_{\text{avg}}\)). The comprehensive simulation results are presented in Figure 8.  
The performance evaluation showed that some sets did not satisfy the predefined performance thresholds. For example, in the case of set 1, the maximum revisit time (\(R_{\text{max}}\)) exceeded the target threshold of 90 min by approximately 17%, failing to meet the service continuity requirement. While the average revisit time (\(R_{\text{avg}}\)) showed satisfactory results for all sets, for daily data transmission volume (\(D_{\text{avg}}\)), set 1 and set 4 did not meet the target value of 2000 KB. Furthermore, they even fell short of the data transmission target of 1.73 MB defined for the scenario in Section 4, indicating that these sets were not suitable. Based on a comprehensive assessment, we concluded that selecting the set with the smallest total number of satellites (\(S_{\text{Total}}\)) among those satisfying all performance thresholds would represent the most efficient optimization strategy. According to this criterion, set 6 was selected as the final weighting set. Although set 6 showed a result for maximum revisit time (\(R_{\text{max}}\)) exceeding the target threshold by approximately 2 min (refer to Figure 8), this deviation was considered to be within an acceptable range. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Weighting-Factor Set** & \(w_{1}\) & \(w_{2}\) & \(w_{3}\) & \(w_{4}\) & **Characteristic** \\ \hline Set 1 & 6 & 1 & 0.5 & 3 & Highest \(w_{1}\) \\ Set 2 & 1 & 1 & 1 & 1 & Equal weights \\ Set 3 & 2 & 3 & 1.5 & 4 & Higher \(w_{2}\) and \(w_{4}\) \\ Set 4 & 3 & 1 & 0.5 & 8 & Highest \(w_{4}\) \\ Set 5 & 3 & 4 & 2 & 1 & Higher \(w_{2}\) and \(w_{3}\) \\ Set 6 & 4 & 1 & 0.5 & 5 & Higher \(w_{1}\) and \(w_{4}\) \\ \hline \end{tabular}
\end{table} 
Table 5: Comparison of weighting-factor values across preliminary sets (sets 1–6). Meanwhile, penalties were applied during the optimization process for exceeding or falling below thresholds to encourage objective achievement.