# Using Optimization Techniques in Grammatical Evolution
## 3 Results
### Experimental Results
\begin{table}
\begin{tabular}{c c c c c c c} \hline
**Dataset** & **ADAM** & **NEAT** & **GENETIC** & **RBF** & **NNC** & **NNC-S** \\ \hline APPENDICITIS & 16.50\% & 17.20\% & 18.10\% & 12.23\% & 14.40\% & 14.60\% \\ \hline AUSTRALIAN & 35.65\% & 31.98\% & 32.21\% & 34.89\% & 14.46\% & 14.90\% \\ \hline BALANCE & 7.87\% & 23.84\% & 8.97\% & 33.42\% & 22.13\% & **7.66\%** \\ \hline CIRCULAR & 3.94\% & 34.07\% & 5.99\% & 6.30\% & 14.26\% & **7.88\%** \\ \hline CLEVELAND & 67.55\% & 53.44\% & 51.60\% & 67.10\% & 49.93\% & **48.59\%** \\ \hline DERMATOLOGY & 26.14\% & 32.43\% & 30.58\% & 62.34\% & 24.80\% & **13.11\%** \\ \hline ECOI & 64.43\% & 43.24\% & 49.38\% & 59.50\% & 48.82\% & **44.88\%** \\ \hline HABERMAN & 29.00\% & 24.04\% & 28.66\% & 25.10\% & 28.33\% & 28.73\% \\ \hline HAYES ROTH & 59.70\% & 50.15\% & 56.18\% & 64.36\% & 37.23\% & **28.08\%** \\ \hline HEART & 38.53\% & 39.27\% & 28.34\% & 31.20\% & 15.78\% & 16.00\% \\ \hline HOUSEVOTES & 7.48\% & 10.89\% & 6.62\% & 6.13\% & 3.52\% & 3.74\% \\ \hline IONOSPHERE & 16.64\% & 19.67\% & 15.14\% & 16.22\% & 11.86\% & **10.03\%** \\ \hline LIVERDISORDER & 41.53\% & 30.67\% & 31.11\% & 30.84\% & 32.97\% & **32.82\%** \\ \hline MAMMOGRAPHIC & 46.25\% & 22.85\% & 19.88\% & 21.38\% & 18.22\% & **16.58\%** \\ \hline PARKINSONS & 24.06\% & 18.56\% & 18.05\% & 17.41\% & 13.21\% & **12.26\%** \\ \hline PIMA & 34.85\% & 34.51\% & 32.19\% & 25.78\% & 28.47\% & **25.26\%** \\ \hline POPFAILURES & 5.18\% & 7.05\% & 5.94\% & 7.04\% & 6.83\% & **5.52\%** \\ \hline REGIONS2 & 29.85\% & 33.23\% & 29.39\% & 38.29\% & 25.87\% & **24.47\%** \\ \hline SAHEART & 34.04\% & 34.51\% & 34.86\% & 32.19\% & 30.80\% & **29.52\%** \\ \hline SEGMENT & 49.75\% & 66.72\% & 57.72\% & 59.68\% & 54.89\% & **39.38\%** \\ \hline STUDENT & 5.13\% & 12.50\% & 5.61\% & 7.52\% & 5.70\% & **4.52\%** \\ \hline TRANSFUSION & 25.68\% & 24.87\% & 25.84\% & 27.36\% & 25.30\% & **24.33\%** \\ \hline WDBC & 35.35\% & 12.88\% & 8.56\% & 7.27\% & 7.27\% & **5.59\%** \\ \hline WINE & 29.40\% & 25.43\% & 19.20\% & 31.41\% & 13.53\% & **11.47\%** \\ \hline Z\_F\_S & 47.81\% & 38.41\% & 10.73\% & 13.16\% & 15.30\% & **7.93\%** \\ \hline Z\_O\_N\_F\_S & 78.79\% & 79.08\% & 64.81\% & 60.40\% & 50.48\% & **40.42\%** \\ \hline ZO\_NF\_S & 47.43\% & 43.75\% & 8.41\% & 9.02\% & 15.22\% & **6.60\%** \\ \hline ZONF\_S & 11.99\% & 5.44\% & 2.60\% & 4.03\% & 3.14\% & **2.36\%** \\ \hline ZOO & 14.13\% & 20.27\% & 16.67\% & 21.93\% & 9.10\% & **7.20\%** \\ \hline
**AVERAGE** & **32.23\%** & **30.72\%** & **24.94\%** & **28.74\%** & **22.13\%** & **18.43\%** \\ \hline \end{tabular}
\end{table} 
Table 2: Experimental results for the series of machine learning methods for the classification datasets. The numbers in cells are the average classification errors as measured in the test set. The bold values it is and indication if the suggested method outperforms the original NNC method. The above techniques were used in the experiments as they are widespread in machine learning, such as the Adam method [95; 96] and because they have a similar complexity to the present technique, such as Genetic Algorithms. As is evident, the proposed modification improves the efficiency of the proposed method in the majority of used datasets. This improvement on some datasets could be as much as an 80% percent error reduction on the test set. In all cases, the simple neural network construction technique outperforms other machine learning techniques and this is evident from the average result (the last row in experimental tables). However, the proposed method significantly reduces the classification error or the error in the data fitting sets in most of the cases where it was used. In fact, in order to show in which cases there was a reduction in the error, bold marking is used in the tables of results.