## 4 Experimental Evaluation of the GAGAN Model
### Assessment of GAGAN Stages  
Diversity metrics are crucial for evaluating and monitoring the variation within a population of individuals (each representing a potential solution or set of weights) at different stages of the genetic algorithm process. In this study, we measured two key diversity metrics throughout various phases of the genetic algorithm cycle. The Initial Population Diversity quantifies the variety among individuals in the starting population, helping ensure a broad base of solutions to increase the likelihood of optimization. The Final Population Diversity measures how diverse the population is at the end of a generation cycle, after genetic operations. It helps assess whether the population is prematurely converging on similar solutions or continuing to explore diverse options effectively. Table 1 provides the numerical values of these metrics across different training runs.  
More specifically, Population Diversity is quantified using the Euclidean distance as the primary metric, which calculates the average pairwise distances between weight vectors in the population. This approach effectively captures the variation among individual solutions. The Initial Population Diversity measures the extent of variation at the start of the algorithm, ensuring a diverse range of potential solutions before genetic operations like crossover and mutation. The Final Population Diversity evaluates the variation remaining after these operations, indicating whether the algorithm maintains diversity or prematurely converges.  
To illustrate the crossover operation during a specific training phase, Figure 6 presents the two-point crossover process, where two parent weight vectors (Parent #1 and Parent #2) exchange segments at randomly selected points. This exchange produces two offspring solutions, Offspring #1 and Offspring #2, which inherit segments from the respective opposite parent. Offspring #1 retains a section from Parent #2, while Offspring #2 inherits a portion from Parent #1, as highlighted in the subplots.  
The upward and downward fluctuations in the lines represent variations in weight values across the vectors, with overlapping sections indicating the regions preserved from each parent. This process facilitates genetic exploration by introducing new combinations of features, promoting diversity within the population and ensuring broader exploration of the solution space.  
Diversity metrics play a critical role in preventing premature convergence by maintaining sufficient variation in the population. The graphs appear immediately after evaluating diversity, indicating that the crossover operation occurs right after the initial population assessment. By actively enhancing the search space with varied offspring solutions, the two-point crossover process strengthens the model's robustness, helping GAGAN avoid local optima and achieve more effective training outcomes.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Training Run No.** & **Initial Population Diversity** & **Final Population Diversity** &
\begin{tabular}{c} **Diversity of the Population with** \\ **the Best Individual** \\ \end{tabular} \\ \hline
1 & 0.69109 & 0.5348 & 0.5359 \\
2 & 0.67069 & 0.6109 & 0.5904 \\
3 & 0.65262 & 1.3420 & 1.2684 \\
4 & 0.67069 & 0.6109 & 0.5904 \\
5 & 0.67539 & 0.8560 & 0.7979 \\
6 & 0.68734 & 0.9153 & 0.8700 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Diversity assessment through different trainings.  
Figure 6: Two-Point crossover in GAGAN.