# Using Optimization Techniques in Grammatical Evolution
## 3 Results
### Experimental Results
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Dataset** & **NNC-S (\(g=2\))** & **NNC-S (\(g=5\))** & **NNC-S (\(g=10\))** & **NNC-S (\(g=20\))** \\ \hline APPENDICITIS & 14.90\% & 15.00\% & 14.60\% & 14.50\% \\ \hline AUSTRALIAN & 14.59\% & 14.85\% & 14.90\% & 15.04\% \\ \hline BALANCE & 8.53\% & 7.68\% & 7.66\% & 7.56\% \\ \hline CIRCULAR & 10.49\% & 8.81\% & 7.88\% & 7.50\% \\ \hline CLEVELAND & 48.41\% & 48.31\% & 48.59\% & 48.10\% \\ \hline DERMATOLOGY & 15.09\% & 13.80\% & 13.11\% & 13.29\% \\ \hline ECOLI & 45.30\% & 45.12\% & 44.88\% & 44.36\% \\ \hline HABERMAN & 27.80\% & 27.97\% & 28.73\% & 27.83\% \\ \hline HAYES ROTH & 29.85\% & 28.85\% & 28.08\% & 29.15\% \\ \hline HEART & 16.11\% & 15.04\% & 16.00\% & 14.78\% \\ \hline HOUSEVOTES & 3.70\% & 4.22\% & 3.74\% & 3.70\% \\ \hline IONOSPHERE & 10.54\% & 10.09\% & 10.03\% & 10.00\% \\ \hline LIVERDISORDER & 31.41\% & 33.15\% & 32.82\% & 33.29\% \\ \hline MAMMCGRAPHIC & 17.16\% & 17.25\% & 16.58\% & 16.99\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Experiments with the parameter \(g\) used in the modified Simulated Annealing method. Furthermore, another experiment was executed by varying the parameter \(R\) of the proposed Simulated Annealing variant. This parameter controls the range of changes performed in any given chromosome. The results for this experiment are shown in Table 5. This time the method appeared quite robust in its performance, without large variations in the error as measured in the test set. \begin{table}
\begin{tabular}{c c c c c} \hline
**Dataset** & **NNC-S (\(g=2\))** & **NNC-S (\(g=5\))** & **NNC-S (\(g=10\))** & **NNC-S (\(g=20\))** \\ \hline PARKINSONS & 12.32\% & 12.89\% & 12.26\% & 12.11\% \\ \hline PIMA & 26.12\% & 25.96\% & 25.26\% & 25.92\% \\ \hline POPFAILURES & 5.58\% & 6.00\% & 5.52\% & 5.68\% \\ \hline REGIONS2 & 24.71\% & 24.05\% & 24.47\% & 24.66\% \\ \hline SAHEART & 30.04\% & 29.67\% & 29.52\% & 29.07\% \\ \hline SEGMENT & 46.94\% & 42.37\% & 39.38\% & 41.19\% \\ \hline STUDENT & 4.60\% & 4.73\% & 4.52\% & 4.48\% \\ \hline TRANSFUSION & 24.28\% & 24.34\% & 24.33\% & 24.03\% \\ \hline WDBC & 6.23\% & 6.22\% & 5.59\% & 5.68\% \\ \hline WINE & 12.59\% & 11.30\% & 11.47\% & 9.24\% \\ \hline Z\_F\_S & 9.57\% & 9.60\% & 7.93\% & 8.10\% \\ \hline Z\_O\_N\_F\_S & 46.04\% & 43.36\% & 40.42\% & 41.54\% \\ \hline ZO\_NF\_S & 9.69\% & 8.54\% & 6.60\% & 6.44\% \\ \hline ZONF\_S & 2.58\% & 2.28\% & 2.36\% & 2.36\% \\ \hline ZOO & 6.90\% & 7.00\% & 7.20\% & 7.70\% \\ \hline
**AVERAGE** & **19.38\%** & **18.91\%** & **18.43\%** & **18.42\%** \\ \hline \end{tabular}
\end{table} 
Table 4: _Cont._ \begin{table}
\begin{tabular}{c c c c c} \hline
**Dataset** & **NNC-S (\(R=2\))** & **NNC-S (\(R=5\))** & **NNC-S (\(R=10\))** & **NNC-S (\(R=20\))** \\ \hline APPENDICITIS & 14.40\% & 14.90\% & 14.60\% & 15.20\% \\ \hline AUSTRALIAN & 14.77\% & 14.78\% & 14.90\% & 14.70\% \\ \hline BALANCE & 7.66\% & 7.74\% & 7.66\% & 7.66\% \\ \hline CIRCULAR & 8.39\% & 8.29\% & 7.88\% & 7.78\% \\ \hline CLEVELAND & 49.45\% & 49.28\% & 48.59\% & 47.11\% \\ \hline DERMATOLOGY & 14.09\% & 12.54\% & 13.11\% & 11.34\% \\ \hline ECOLI & 44.24\% & 46.30\% & 44.88\% & 44.48\% \\ \hline HABERMAN & 27.33\% & 28.10\% & 28.73\% & 28.04\% \\ \hline HAYES ROTH & 29.15\% & 27.92\% & 28.08\% & 26.46\% \\ \hline HEART & 15.67\% & 15.52\% & 16.00\% & 15.15\% \\ \hline HOUSEVOTES & 4.00\% & 3.62\% & 3.74\% & 4.52\% \\ \hline IONOSPHERE & 10.14\% & 10.03\% & 10.03\% & 10.71\% \\ \hline LIVERDISORDER & 32.80\% & 32.12\% & 32.82\% & 32.29\% \\ \hline \end{tabular}
\end{table} 
Table 5: Experiments with the parameter \(R\) of the modified Simulated Annealing algorithm. The parameter \(g\) was set to 10. As a practical application of the suggested method, we consider the dataset proposed in [97], which relates alcohol consumption and EEG recordings. The proposed method was applied on this dataset and it is compared against the original neural network construction technique; the results are outlined in Figure 8.