# 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  
Next, we will analyze the data recognition performance for the GA with _CGACell ECA_ crossover in a comparative study with GAs with other crossover methods mentioned above for the cases where the number of generations is equal to 100, 200, and 400, respectively. Finally, the results of ANOVA and Tukey HSD post hoc statistical tests are presented. The visual comparison in Figure 25 shows classification accuracy for the GA with _CGACell ECA_ crossover and other crossover strategies after 100 generations evaluated under three different data split conditions. The results, for this case with 100 generations, are in Table 10, and it was found that the _CGACell ECA_ consistently outperformed all other crossover operators in all three data splits; the GA-CA Hybrid and PMX were also strong performers, especially in higher training ratios, and the traditional methods like single-point, Shuffle, and Average Crossover showed noticeably lower performance, particularly under more challenging (50/50) splits. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Case** & **Training (\%)** & **Testing (\%)** \\ \hline Case 1 & 70\% & 30\% \\ Case 2 & 60\% & 40\% \\ Case 3 & 50\% & 50\% \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Train–test split configurations for Yale Face database experiments. Figure 25: GA with _CGACell ECA_ crossover and other crossover strategies after 100 generations. \begin{table}
\begin{tabular}{p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt}} \hline \hline
**Criterion** & **CGACell ECA (1D)** & **CGACell-kD CA** & **Single-Point Crossover** & **GA-CA Hybrid Analysis (CCA)** \\ \hline
**Category** & Evolutionary Crossover & Spatial Evolutionary Crossover & Standard Generic Operator & Hybrid Metaheuristic & Statistical Projection Method \\ \hline
**Operates On** & Binary chromosomes & Structured binary populations & Chromosome pairs & Population grid or lattice & Multi-view feature matrices \\ \hline
**Crossover Type** & Local recombination station using neighborhoods & Global segment swap & Evolving CA and GA rules & Not a crossover method \\ \hline
**CA Rule Usage** & Elementary CA (e.g., rule 90, 110) & General kD CA rules & None & CA rules evolve or guide operators & None \\ \hline
**Neighbored Dependency Dependency** & Triplets (left-center-right) & Flexible (Moore, von Neumann) & None (random cut point) & Yes—based on CA structure & No \\ \hline
**Time Complexity (per chromosome)** & \(O(n_{\varepsilon})\) & \(O(n_{r}\cdot n_{g})\) & \(O(n_{g})\) & \(O(n_{r}\cdot n_{g}+\text{GA steps})\) & \(O(\min(n,p,q)^{3})\) \\ \hline
**Space Complexity** & \(O(n_{\varepsilon}\cdot n_{g})\) & \(O(n_{c}\cdot n_{g})\) & \(O(n_{c}\cdot n_{g})\) & \(O(n_{c}\cdot n_{g})\) & \(O(n_{c}\cdot n_{g})\) & \(O(n_{p}+nq)\) \\ \hline
**Exploration Capability** & High & High (scalable to topology) & Moderate & High (adaptive via CA dynamics) & Low \\ \hline
**Parallelism Potential** & Very high & Very high & High & High & Low \\ \hline
**Implementation Complexity** & Low & Medium (topology/rules) & Very low & High (coupling mechanisms) & Medium (linear algebra) \\ \hline
**Performance Gap** & Improves GA diversity and robustness models & Improves local exploitation in spatial models & Fast but weak in local structure retention & Improved adaptability & Not directly applied \\ \hline
**Limitations** & Binary only, rule sensitivity & Rule/topology design needed & Weak in preserving gene dependencies & Model tuning and hybrid synchronization & Not part of evolution-ary framework \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Comparison of crossover and related mechanisms: CGACell ECA, CGACell-kD CA, single-point crossover, GA–CA Hybrid, and Canonical Correlation Analysis (CCA). Figure 26 shows the classification accuracy for the GA with _CGACell ECA_ crossover and other crossover strategies after 200 generations evaluated under three different data split conditions.