# A Cellular Automata-Based Crossover Operator for Binary Chromosome Population Genetic Algorithms
## 6 Experimental Analysis for _Cgacell_ Crossover Operator in Specific Tasks
#### Train-Test Split Cases
The results, for this case with 200 generations, are in Table 11, and it was found that the _CGACell ECA_ consistently outperformed all traditional crossover methods (single-point, two-point, PMX, OX, etc.) across all data splits (70/30, 60/40, and 50/50). At 200 generations in the 70/30 split case, the _CGACell ECA_ reached 96.10%, exceeding the best classical method (GA-CA Hybrid at 95.02%). Figure 27 shows the classification accuracy for the GA with _CGACell ECA_ crossover and other crossover strategies after 400 generations evaluated under three different data split conditions. The results, for this case with 400 generations, are in Table 12, and it was found that the _CGACell ECA_ once again outperformed all other methods, maintaining the highest average accuracy (96.29%) and slightly improving from the 300-generation run. It should be noted that the GA-CA Hybrid remained a strong second at 94.69%, showing the robustness of CA-integrated strategies; the PMX and Voting Recombination (VR) continued to outperform classical single- and two-point crossovers, and the Heuristic and Masked crossover operators again delivered the lowest accuracies across all three splits. A structured statistical analysis using ANOVA and [PERSON]'s HSD post hoc test for the accuracy comparison table--GA with 400 generations--is presented in the following. This assumes that the precision values per method and division represent the averages of multiple repeated runs in order to have valid ANOVA hypotheses. The ANOVA analysis has the objective to determine whether there are significant differences in mean accuracies between different GA crossover methods. The Null Hypothesis (\(H_{0}\)) is all that crossover methods have equal mean accuracy, and the alternative Hypothesis (\(H_{1}\)) is at least one method differs significantly. _Interpretation for ANOVA test_: Since \(p<0.0001\) (see the Table 13), we reject the null hypothesis. It is attested that there are significant differences among the crossover methods. The Tukey HSD post hoc test results are presented in Table 14. Based on the test results in this table, it is attested that there are significant differences between the crossover methods. Thus, the Tukey HSD confirms distinct performance clusters. **Experiment 2 (CGACell crossover for KNN optimization)**  
In the second experiment, the _CGACell_ crossover operator presented in this paper was used in image classification problems through the KNN algorithm to optimize the parameter \(k\) representing the number of nearest neighbors. The genetic algorithm (_CGACell-GA_) based on _CGACell_ crossover is detailed in Remark 5. The performance outcomes in testing new images for the proposed algorithm are highlighted through an experimental comparative study with standard classification methods such as the Kmeans algorithm, the Principal Component Analysis (PCA) algorithm. (by using the eigenvectors corresponding to the \(kn\) largest eigenvalues, \(kn<=10\%\) of the total number of eigenvalues of the input centering image database covariance matrix. The projections onto the space of eigenvectors corresponding to the \(kn\) largest eigenvalues are used in the stages of new image recognition by determining the minimum Euclidean distance of the projection of the new image onto the space of eigenvectors from the set of eigenvectors \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Source** & **SS (Sum of** & **df** & **MS (Mean** & **Square**) & **F** & \(p\)**-Value** \\ \hline Between Groups & 0.01074 & 11 & 0.000976 & 72.45 & \textless{}0.0001 \\ Within Groups & 0.00162 & 24 & 0.000067 & & \\ Total & 0.01236 & 35 & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 13: ANOVA summary table for accuracy comparison—GA with 400 generations.