## 3 Simulation Results
### Population Diversity  
Table 9 summarizes the population diversity in terms of Hamming distance and its ratio between different PV array configurations. Scenario 2 exhibits the lowest average population diversity (2.414) with a relatively low standard deviation (1.810), indicating a narrow and consistent exploration of the solution space. In contrast, Scenario 3 achieves the highest average diversity (4.478), reflecting a broader exploration but at the expense of increased variability (2.932 standard deviation). The diversity ratio percentages are relatively consistent across configurations; Scenario 3 exhibits the highest average ratio (13.99%) but also shows higher variability (9.16%) compared to Scenario 4, which balances higher diversity with better stability (8.69% standard deviation). These results highlight the trade-off between exploration capacity and stability; Scenario 4 offers a balanced approach, while Scenario 2 prioritizes stability over diversity. Figure 6 provides insight into the efficiency and stability of the algorithm by showing the effect of population diversity and mutation rate on the convergence time. The results show that low mutation rates (0-0.05) and low to medium population diversity (0-2) generally lead to shorter convergence times, as evidenced by the density of data points in the blue regions. This highlights the effectiveness of a controlled mutation rate and a balanced level of diversity in achieving faster convergence. Conversely, higher mutation rates (>0.1) and high population diversity (>5) are associated with longer convergence times, as seen in the scattered yellow dots. These findings indicate that excessive mutation or diversity can hinder the stability of the algorithm and delay convergence by exploring too many suboptimal solutions. Overall, the analysis emphasizes the importance of tuning these parameters to balance exploration and exploitation, ensuring efficient and stable convergence during the optimization process. Figure 7 shows the effects of mutation rate and population diversity on the best fitness values. According to the distribution along the mutation rate and population diversity axes in the figure, it is particularly noticeable that best fitness values are lower (i.e., blue tones) in regions with low mutation rates (around 0.05) and moderate population diversity (2-4). It is shown that low mutation rates (i.e., ~0.05) combined with moderate population diversity (around 2-4) tend to produce the smallest fitness values, as observed in the lower \begin{table}
\begin{tabular}{c c c c c c c} \hline
**PV Array Configuration** & **Number of PV Array** & **Number of Experiments** & **Best Conv. Time (s)** & **Worst Conv. Time (s)** & **Mean Conv. Time (s)** & **Standard Deviation** \\ \hline Scenario 1 & 3 & 63 & **0.002152** & 7.6378595 & 0.858530725 & 1.815959142 \\ Scenario 2 & 3 & 63 & 0.0023528 & 7.05250360 & 0.569619646 & 2.211751740 \\ \hline Scenario 3 & 4 & 63 & 0.6772455 & 19.3184140 & 11.13226950 & 14.72583395 \\ Scenario 4 & 4 & 63 & **0.1102718** & 17.2248415 & 9.764656163 & 23.96659411 \\ \hline \end{tabular}
\end{table} 
Table 8: Best solution quality and stability of algorithm in terms of convergence time. \begin{table}
\begin{tabular}{c c c c c} \hline
**PV Array Configuration** & **Mean of Population Diversity** & **Standard Deviation of Population Diversity** & **Mean of Diversity Rate (\%)** & **Standard Deviation of Diversity Rate** \\ \hline Scenario 1 & 2.414 & 1.810 & 13.413 & 10.058 \\ Scenario 2 & 2.440 & 1.826 & 13.556 & 10.149 \\ \hline Scenario 3 & 4.478 & 2.932 & 13.995 & 9.163 \\ Scenario 4 & 4.452 & 2.783 & 13.915 & 8.699 \\ \hline \end{tabular}
\end{table} 
Table 9: Population diversity. regions of the graph. This suggests that a controlled mutation rate helps prevent excessive degradation of good solutions while maintaining exploration capability. On the other hand, higher mutation rates introduce more variability in fitness values, as seen in the wider distribution of fitness results in regions with higher mutation rates.