## 6 Analysis  
### Comparison of Results from Each Phase  
Table 11 gives an overview of the best results obtained with the validation set for each terminal set, as well as the best manually developed DRs, namely EDD, COVERT, and \begin{table}
\begin{tabular}{l l l l l l l} \hline \hline
**ph1** & **all** & \(payg\) & \(age\) & \(mr\) & \(pat\) & \(pmin\) \\ \hline
13.69 & 13.93 (\(\approx\)) & 13.90 (\(\approx\)) & 13.87 (\(\approx\)) & 13.71 (\(\approx\)) & 13.93 (\(\approx\)) & (\(\approx\)) \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Results obtained by GP when selecting manually designed composite features based on their frequency in the PFs. \begin{table}
\begin{tabular}{l l l l l l l l} \hline \hline
**ph1** & **all** & \(\frac{pt}{ma}\) & \(\frac{pt}{w}\) & \(ma*w\) & \(dd-pt\) & \(\frac{dd}{w}\) & \(ma1+pt\) \\ \hline
13.69 & 13.85 (\(\approx\)) & 14.05 (\(-\)) & 13.90 (\(\approx\)) & 13.84 (\(\approx\)) & 13.89 (\(\approx\)) & 13.79 (\(\approx\)) & 13.91 (\(\approx\)) \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Results obtained by GP when selecting automatically designed composite features based on their frequency in the PFs. \begin{table}
\begin{tabular}{l l l l l l l l} \hline \hline \multirow{2}{*}{**Iteration**} & \multicolumn{6}{c}{**Terminals**} \\ \cline{2-9}  & \(age\) & \(mr\) & \(pat\) & \(payg\) & \(pmin\) & \(sl\) \\ \hline Phase 1 optimised & \multicolumn{6}{c}{13.69} \\ \hline All terminals & \multicolumn{6}{c}{13.93 (\(\approx\))} \\ \hline
1 & **13.47** (\(\approx\)) & 13.88 (\(\approx\)) & 13.96 (\(\approx\)) & 13.87 (\(\approx\)) & 14.16 (\(-\)) & 14.15 (\(-\)) \\
2 & - & **13.77** (\(\approx\)) & 14.11 (\(-\)) & 13.95 (\(-\)) & 13.90 (\(-\)) & 14.30 (\(-\)) \\
3 & - & - & 14.01 (\(-\)) & 13.80 (\(\approx\)) & 13.95 (\(-\)) & **13.79** (\(\approx\)) \\
4 & - & - & 13.84 (\(\approx\)) & **13.66** (\(\approx\)) & 14.32 (\(-\)) & - \\
5 & - & - & **13.72** (\(\approx\)) & - & 13.80 (\(\approx\)) & - \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Results obtained using BSFS for the extended terminal set with features created based on their frequency of occurrence. ATC. The initial feature set from Table 1 is labelled as Phase 0, whereas Phase 2 + 3 refers to the combination of the best feature sets from Phase 2 and Phase 3, which was used to investigate whether the combination of these two feature sets led to an improvement in the results. In addition, the table shows the average rule size obtained when using each terminal set, which represents the average number of nodes in the expressions generated by GP. Compared to the manually generated DRs, we can see that GP achieved better DRs with the best terminal set obtained after each phase compared to the three manually generated ones. Only in the cases where no optimisation was performed, or when Phases 2 and 3 were combined, did GP fail to outperform the ATC rule. This shows that even for a terminal set with atomic terminal nodes, GP can reasonably combine them to outperform the existing rules. However, for more complex terminal nodes, GP can even increase the gap between manually and automatically created DRs. Figure 3 depicts the results from Table 11 as a box plot. The figure shows that the terminal node sets from Phase 1 and Phase 2 lead to the least scattered solutions. This is favourable, as it means that GP is more likely to produce a result close to the median. Therefore, the method is more reliable when it comes to generating solutions of expected quality. On the other hand, the solutions obtained when using the terminal node set obtained in Phase 3 are quite scattered. The results also show that GP is more likely to obtain better results with this terminal node set than with any other terminal node set. To determine whether there was a significant difference between the results, the statistical tests described above were used, and a \(p\)-value close to 0 was determined. This shows that there was a significant difference between the results obtained.