# Local Crossover: A New Genetic Operator for Grammatical Evolution
## 2 Materials and Methods
### Experimental Results
The outcomes obtained from this experiment are depicted in Table 5.  
The lowest average classification error is observed for \(N_{cr}=100\); however, no major changes are observed in the classification errors as the parameter increases. Furthermore, we expected the average execution time to increase as the value \(N_{cr}\) increases, and this is demonstrated in Figure 12, where the computation time for the neural network construction method is plotted with respect to the \(N_{cr}\). Figure 11: Statistical test for all the improved machine learning methods and the original methods. The methods were tested on the classification datasets. Figure 10: Box plot used to compare the original neural network construction model and the improved one that utilizes the new crossover operator for the regression datasets. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**DATASET** & **RULE** & \(p_{cr}=0.025\) & \(p_{cr}=0.05\) & \(p_{cr}=0.075\) \\ \hline APPENDICITIS & 14.70\% & 15.80\% & 14.80\% & 15.10\% \\ \hline AUSTRALIAN & 14.27\% & 13.96\% & 14.46\% & 14.03\% \\ \hline BALANCE & 28.79\% & 20.18\% & 17.47\% & 18.07\% \\ \hline CIRCULAR & 13.25\% & 11.00\% & 9.12\% & 9.78\% \\ \hline CLEVELAND & 48.24\% & 48.24\% & 47.52\% & 46.07\% \\ \hline DERMATOLOGY & 43.77\% & 38.60\% & 38.00\% & 36.00\% \\ \hline ECOLI & 55.18\% & 52.49\% & 53.48\% & 48.83\% \\ \hline FERT & 17.40\% & 16.70\% & 17.50\% & 18.50\% \\ \hline HABERMAN & 27.03\% & 27.57\% & 26.53\% & 26.87\% \\ \hline HAYES-ROTH & 39.39\% & 35.69\% & 38.08\% & 36.77\% \\ \hline HEART & 20.30\% & 20.48\% & 19.41\% & 20.37\% \\ \hline HEARTATTACK & 23.63\% & 22.83\% & 23.70\% & 22.53\% \\ \hline HOUSEVOTES & 3.48\% & 3.48\% & 4.51\% & 3.13\% \\ \hline GLASS & 58.10\% & 55.62\% & 54.81\% & 52.76\% \\ \hline IONOSPHERE & 15.06\% & 15.14\% & 14.14\% & 14.14\% \\ \hline LIVERDISORDER & 37.09\% & 34.79\% & 35.68\% & 33.50\% \\ \hline MAMMOGRAPHIC & 19.00\% & 18.34\% & 18.10\% & 17.90\% \\ \hline PARKINSONS & 13.47\% & 13.95\% & 13.37\% & 13.21\% \\ \hline PIMA & 27.85\% & 27.80\% & 27.30\% & 27.84\% \\ \hline POPFAILURES & 5.44\% & 5.33\% & 5.02\% & 5.32\% \\ \hline REGIONS2 & 29.13\% & 28.82\% & 29.26\% & 28.00\% \\ \hline SAHEART & 30.20\% & 30.00\% & 31.00\% & 30.18\% \\ \hline SEGMENT & 71.51\% & 67.36\% & 61.99\% & 63.91\% \\ \hline SPIRAL & 50.06\% & 50.42\% & 49.08\% & 49.60\% \\ \hline STUDENT & 11.08\% & 7.50\% & 7.23\% & 6.07\% \\ \hline TRANSFUSION & 25.19\% & 24.20\% & 24.46\% & 24.68\% \\ \hline WDBC & 7.66\% & 5.79\% & 6.43\% & 6.41\% \\ \hline WINE & 15.35\% & 15.47\% & 12.47\% & 13.59\% \\ \hline Z\_F\_S & 16.40\% & 11.63\% & 8.77\% & 9.10\% \\ \hline Z\_O\_N\_F\_S & 53.64\% & 47.14\% & 44.60\% & 44.04\% \\ \hline ZO\_NF\_S & 14.10\% & 10.50\% & 8.39\% & 8.42\% \\ \hline ZONF\_S & 2.76\% & 2.64\% & 2.06\% & 2.14\% \\ \hline ZOO & 14.80\% & 11.30\% & 11.10\% & 8.70\% \\ \hline
**AVERAGE** & **26.28\%** & **24.57\%** & **23.93\%** & **23.50\%** \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The effect of a series of values of \(p_{cr}\) to the rule model with application on the classification datasets. The average computation time increases dramatically as the critical parameter \(N_{cr}\) increases, which is something that is expected, since the crossings increase significantly with the increase in this parameter. This dramatic increase in required execution time can be reduced by incorporating modern parallel libraries. These programming techniques may include the application of the Message Passing Interface (MPI) library [95] or the incorporation of the OpenMP library [96].