# 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
\begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Crossover Method** & **70\%** & **60\%** & **50\%** & **Average** \\  & **Train/30\%** & **Train/40\%** & **Train/50\%** & **Accuracy** \\  & **Test** & **Test** & **Test** & \\ \hline GA + CGACell ECA & 0.9733 & 0.9644 & 0.9511 & 0.9629 \\ GA + Single-Point & 0.9321 & 0.9224 & 0.9108 & 0.9218 \\ GA + Two-Point & 0.9384 & 0.9282 & 0.9150 & 0.9272 \\ GA + Uniform & 0.9362 & 0.9260 & 0.9124 & 0.9249 \\ GA + PMX & 0.9475 & 0.9363 & 0.9227 & 0.9355 \\ GA + Order Crossover (OX) & 0.9400 & 0.9302 & 0.9161 & 0.9288 \\ GA + Average Crossover (AX) & 0.9290 & 0.9185 & 0.9040 & 0.9172 \\ GA + Shuffle Crossover & 0.9267 & 0.9150 & 0.8996 & 0.9138 \\ GA + Voting Recombination (VR) & 0.9411 & 0.9314 & 0.9175 & 0.9300 \\ GA + Masked Crossover (MRX) & 0.9233 & 0.9123 & 0.8988 & 0.9115 \\ GA + Heuristic Crossover (HX) & 0.9204 & 0.9075 & 0.8930 & 0.9070 \\ GA–CA Hybrid & 0.9588 & 0.9477 & 0.9342 & 0.9469 \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Accuracy comparison table—GA with 400 generations. established for the \(kn\) largest eigenvalues in their descending order), the Canonical Correlation Analysis (CCA), the GA-CA Hybrid algorithm, and the standard KNN algorithm. In the comparative study, three cases were considered regarding the number of classes of images: the classification of 3 classes of images, the classification of 7 classes of images, and all the classes (11) of images available in the database. For each case of the number of classes of images, the correctness percentages in the classification of images corresponding to the use of three, five, and eight training images from each class of images were established. In all three cases, the number of images used for the training stage is represented by the labels _Series1_--three training images, _Series2_--five training images, and _Series3_--eight training images--in Figures 28-31. Figure 31 shows the results obtained from the experimental analysis based on the Yale image database for the classification of images from 3, 7, and 11 face image classes by using a name of three, five, and eight training face images, respectively. Also, the numerical results obtained from the experimental analysis for the algorithm based on _CGACell_ crossover, using the Yale image database for classifying images from face image classes 3, 7, and 11  
Figure 31: Graphic representation of correct classification percents of face images for three, seven, and eleven classes of face images having three, five, and eight training images, respectively. Figure 30: Case III—image classification for eleven face image classes from the Yale face database. Figure 29: Case II—image classification for seven face image classes from the Yale face database. The symbols and variables used throughout the paper are summarized in Table 16. \begin{table}
\begin{tabular}{l l} \hline \hline
**Symbol/Notation** & **Definition** \\ \hline \(P(t)\) & Population of chromosomes at generation \(t\) in the genetic algorithm (GA) \\ \hline \(ch_{i}\) & The \(i\)-th chromosome in the population \\ \hline \(g_{iq}\) & The \(q\)-th gene of chromosome \(ch_{i}\), where \(g_{iq}\in\{0,1\}\) \\ \hline \(n_{c}\) & Number of chromosomes in the population \(P(t)\) \\ \hline \(n_{g}\) & Number of genes in each chromosome \\ \hline \(C_{s}\) & Set of chromosomes selected for crossover from population \(P(t)\) \\ \hline \(\gamma\) & Cellular automaton (CA) operator \\ \hline \(k\) & Dimensionality of the cellular automaton (1D, 2D,...) \\ \hline \(kD\ CA(C_{s},V_{h},\gamma)\) & Descendant chromosome generated using \(k\)-dimensional CA \\ \hline \(V_{h}\) & Neighborhood used in the CA; set of cell positions considered for local rule \\ \hline \(v_{i}\) & The \(i\)-th element of the neighborhood \(V_{h}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 15: Values of correct classification percents of face images from the Yale database for three, seven, and eleven classes of face images having three, five, and eight training images