# Local Crossover: A New Genetic Operator for Grammatical Evolution
## 2 Materials and Methods
### Experimental Results
\begin{table}
\begin{tabular}{c c c c c c c} \hline
**DATASET** & **BFGS** & **GEN** & **RULE** & **NNC** & **RULE_CROSS** & **NNC_CROSS** \\ \hline APPENDICITS & 18.00\% & 24.40\% & 14.70\% & 13.70\% & 14.80\% & 14.40\% \\ \hline AUSTRALIAN & 38.13\% & 36.64\% & 14.27\% & 14.51\% & 14.46\% & 14.71\% \\ \hline BALANCE & 8.64\% & 8.36\% & 28.79\% & 22.11\% & 17.47\% & 14.32\% \\ \hline CIRULAR & 6.08\% & 5.13\% & 13.25\% & 13.64\% & 9.12\% & 7.49\% \\ \hline CLEVELAND & 77.55\% & 57.21\% & 48.24\% & 50.10\% & 47.52\% & 49.21\% \\ \hline DERMATOLOGY & 52.92\% & 16.60\% & 43.77\% & 25.06\% & 38.00\% & 12.92\% \\ \hline ECOLI & 69.52\% & 54.67\% & 55.18\% & 47.82\% & 53.48\% & 49.15\% \\ \hline FERT & 23.20\% & 28.50\% & 17.40\% & 19.00\% & 17.50\% & 19.20\% \\ \hline HABERMAN & 33.10\% & 27.80\% & 27.03\% & 28.03\% & 26.53\% & 28.37\% \\ \hline HAYES-ROTH & 56.54\% & 35.85\% & 39.39\% & 35.93\% & 38.08\% & 24.08\% \\ \hline HEART & 39.44\% & 26.41\% & 20.30\% & 15.78\% & 19.41\% & 15.33\% \\ \hline HEARTATTACK & 46.67\% & 29.03\% & 23.63\% & 19.33\% & 23.70\% & 18.73\% \\ \hline HOUSEVOTES & 7.13\% & 7.00\% & 3.48\% & 3.65\% & 4.51\% & 3.22\% \\ \hline GLASS & 69.95\% & 55.09\% & 58.10\% & 57.10\% & 54.81\% & 53.82\% \\ \hline IONOSHERE & 13.37\% & 18.03\% & 15.06\% & 11.12\% & 14.14\% & 9.25\% \\ \hline LIVERDISORDER & 42.59\% & 37.09\% & 37.09\% & 33.71\% & 35.68\% & 31.24\% \\ \hline MAMMOGRAPHIC & 29.54\% & 16.33\% & 19.00\% & 17.78\% & 18.10\% & 17.12\% \\ \hline PARKINSONS & 27.58\% & 16.58\% & 13.47\% & 12.21\% & 13.37\% & 11.47\% \\ \hline PIMA & 35.59\% & 34.21\% & 27.85\% & 27.99\% & 27.30\% & 25.95\% \\ \hline POPFAILURES & 5.24\% & 4.17\% & 5.44\% & 6.74\% & 5.02\% & 6.41\% \\ \hline REGIONS2 & 36.28\% & 33.53\% & 29.13\% & 25.52\% & 29.26\% & 24.46\% \\ \hline SAHEART & 37.48\% & 34.85\% & 30.20\% & 30.52\% & 31.00\% & 28.64\% \\ \hline SEMENT & 68.97\% & 46.30\% & 71.51\% & 54.99\% & 61.99\% & 35.82\% \\ \hline SPIRAL & 47.99\% & 47.67\% & 50.06\% & 48.39\% & 49.08\% & 48.04\% \\ \hline STUDENT & 4.90\% & 6.75\% & 11.08\% & 5.78\% & 7.23\% & 5.06\% \\ \hline TRANSFUSION & 25.59\% & 24.01\% & 25.19\% & 25.34\% & 24.46\% & 24.44\% \\ \hline WDBC & 29.91\% & 7.87\% & 7.66\% & 6.95\% & 6.43\% & 6.48\% \\ \hline WINE & 59.71\% & 22.88\% & 15.35\% & 14.35\% & 12.47\% & 9.88\% \\ \hline Z\_F\_S & 39.37\% & 24.60\% & 16.40\% & 14.17\% & 8.77\% & 10.23\% \\ \hline Z\_O\_N\_F\_S & 79.04\% & 64.26\% & 53.64\% & 49.18\% & 44.60\% & 42.30\% \\ \hline ZO\_NF\_S & 43.04\% & 21.54\% & 14.10\% & 14.14\% & 8.39\% & 9.12\% \\ \hline ZONF\_S & 15.62\% & 4.36\% & 2.76\% & 3.14\% & 2.06\% & 2.70\% \\ \hline ZOO & 12.10\% & 10.20\% & 14.80\% & 9.20\% & 11.10\% & 5.70\% \\ \hline
**AVERAGE** & **36.39\%** & **26.91\%** & **26.28\%** & **23.54\%** & **23.93\%** & **20.58\%** \\ \hline \end{tabular}
\end{table} 
Table 2: This table shows the average classification error as calculated on the corresponding test set for the classification datasets using all machine learning models. There is a clear indication from the experimental results that there is a significant reduction in the mean error using the new genetic operator in both machine learning models. In a wide range of datasets, the proposed technique drastically reduces the error of data classification or fitting, as it is also represented in Figures 5 and 6. These graphs show the number of datasets in which the application of the new genetic operator resulted in a drastic reduction in the corresponding error. Furthermore, the box plots for the classification cases are shown in Figures 7 and 8 for the rule construction model and the network construction model, respectively. Box plots for the same comparisons as deduced from the results using the series of regression datasets are shown in Figures 9 and 10, respectively. These figures confirm the significant improvement brought about by the use of the new operator in the effectiveness of the two techniques that utilize Grammatical Evolution. This improvement appears to be greater in the datasets used in data fitting.