## 5 Experimental Study
### Results
#### 5.2.2 Extended Terminal Set with Composite Features Determined by Frequency of Occurrence  
Based on the best individuals from the first phase of the experiments, we calculated the frequency of sub-expressions. The sub-expressions with more than 30 occurrences are listed in Table 6. It is interesting to note that only sub-expressions of size 3 occurred, whereas larger sub-expressions were rare in several trees. This shows that there did not \begin{table}
\begin{tabular}{l c c c c c c c c c} \hline \hline \multirow{2}{*}{**Iteration**} & \multicolumn{8}{c}{**Terminals**} \\ \cline{2-10}  & \(clk\) & \(dd\) & \(frma\) & \(ma\) & \(nrmach\) & \(nrel\) & \(pt\) & \(rel\) & \(w\) \\ \hline All nodes & & & & & & & & & \\ \hline
1 & 14.09 (\(\approx\)) & 16.36 (\(-\)) & **13.89 (\(\approx\))** & 18.78 (\(-\)) & 14.01 (\(\approx\)) & 14.12 (\(\approx\)) & 177.16 (\(-\)) & 13.88 (\(\approx\)) & 14.49 (\(-\)) \\
2 & 14.17 (\(\approx\)) & 16.52 (\(-\)) & - & 18.81 (\(-\)) & 13.89 (\(\approx\)) & 14.10 (\(\approx\)) & 178.45 (\(-\)) & **13.88 (\(+\))** & 14.49 (\(-\)) \\
3 & 13.88 (\(\approx\)) & 17.53 (\(-\)) & - & 18.83 (\(-\)) & **13.69 (\(+\))** & 13.71 (\(+\)) & 17.64 (\(-\)) & - & 14.38 (\(-\)) \\
4 & **13.81 (\(+\))** & 17.56 (\(-\)) & - & 19.31 (\(-\)) & - & 13.82 (\(+\)) & 17.61 (\(-\)) & - & 14.22 (\(\approx\)) \\
5 & - & 17.16 (\(-\)) & - & 18.69 (\(-\)) & - & **13.88 (\(\approx\))** & 17.468 (\(-\)) & - & 14.66 (\(-\)) \\
6 & - & 17.49 (\(-\)) & - & 18.59 (\(-\)) & - & - & 173.21 (\(-\)) & - & 14.57 (\(-\)) \\
7 & - & 25.82 (\(-\)) & - & **20.86 (\(-\))** & - & - & 283.27 (\(-\)) & - & - \\
8 & - & **44.62 (\(-\))** & - & - & - & - & 7755 (\(-\)) & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Results obtained by BSFs for the feature set outlined in Table 1. \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline
**all** & \(nrel\) & \(frma\) & \(rel\) & \(clk\) & \(nmach\) & \(pt\) & \(ma\) \\ \hline
14.08 & 14.13 (\(\approx\)) & 13.88 (\(\approx\)) & 13.84 (\(+\)) & 13.87 (\(+\)) & 13.84 (\(+\)) & 172.92 (\(-\)) & 4942.88 (\(-\)) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Results obtained by GP when selecting atomic features based on their frequency in the PFs. seem to be a larger, well-functioning sub-expression that could be reused; rather, the rules consisted of small, frequently repeated sub-expressions. The reason for this could be that either such a sub-expression did not exist or that GP had difficulty obtaining it with the given settings. If we examine which sub-expressions occurred most frequently, we can see that GP created certain sub-expressions that occurred frequently in manually created DRs. For example, the expression \(ma+pt\) was often used to determine how quickly the job would be completed on each machine, using information about when the machine was available and how long the job would take on the machine. Sub-expressions such as \(\frac{dd}{w}\) and \(\frac{pt}{w}\) were also common, as the purpose was to schedule jobs with a lower processing time or due date adjusted for the weight of the job. Based on this frequency of occurrence, seven new terminal nodes were designed and included in the previously optimised terminal set. Table 7 provides an overview of the results obtained through the additional use of the seven features described in Table 6. In this section, the results obtained are statistically compared with the optimised terminal set from Phase 1, the results of which are also included in the first row of the table. The results show that the inclusion of these composite features in the terminal set did not have a positive influence on the results compared to the optimised terminal set from Phase 1. In most cases, the results either remained the same or even deteriorated, which was confirmed by the statistical tests performed. The only node that seemed to have some effect on this terminal set was \(dd*dd\), which occurred most frequently in the PFs from Phase 1.