## 5 Experimental Study
### Results
#### 5.2.1 Simple Terminal Set  
In the first phase, the terminal set shown in Table 1 was used as the starting set for the construction of DRs. To determine which features were most important in this set, the BSFS and FBS methods were used to determine the optimised set of terminal nodes.  
The results obtained using BSFS in this phase are shown in Table 4. The columns in the table denote the results where the corresponding feature was removed from the feature set, whereas the rows denote the steps of the algorithm. The first row indicates the results obtained when all features were used. In each subsequent row, the best result is  
\begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter** & **Value** \\ \hline Population size & 1000 \\ Mutation probability & 0.3 \\ Tournament size & 3 \\ Crossover operators & subtree, uniform, context preserving, size fair, one point \\ Mutation operators & subtree, hoist, node complement, node replacement, permutation, shrink \\ Function set & addition, subtraction, multiplication, protected division (returns 1 if division by 0 is encountered), \(POS(x)=\max(x,0)\) \\ Termination criterion & 80,000 fitness evaluations \\ \hline \hline \end{tabular}
\end{table}
Table 3: GP parameters.  
indicated in bold, which also indicates which feature was removed from the feature set in the next iteration. In addition, each cell contains the results of the statistical test comparing the result presented in this cell with the result obtained with the entire terminal set. The symbol \(+\) means that significantly better results were achieved with the reduced set, \(-\) means that significantly worse results were achieved with the reduced set, and \(\approx\) means that there was no significant difference between the results. We can see from the table that removing certain nodes almost always led to a significant deterioration in the results. The nodes where this happened were \(dd\), \(ma\), \(pt\), and \(w\). From this, we can conclude that these nodes represent the minimum set of features that the GP needs to construct meaningful PFs. By using only these four terminal nodes, GP achieved a value of 13.88, which was lower but not statistically better than the value obtained when using all terminal nodes. Removing all other nodes from the terminal set did not have a significant impact on the results, or in some cases, even led to a significant improvement. The best overall result was obtained for the node set that included the \(clk\) and \(nrel\) nodes in addition to the four previously mentioned terminals. The \(clk\) nodes, in particular, seem to be important, as they provide information about the current time in the system, which can then be used in combination with other terminal nodes to determine when a job will become late and thus prioritiise it.  
Table 5 shows the results GP achieved when the terminal nodes were removed based on the frequency of their occurrence in the generated PFs. The first row lists the removed terminal nodes, whereas the second row shows the corresponding fitness values. Again, each cell contains the result of the statistical test comparing the results of the entire set with the reduced sets. We can see that the best overall result was obtained with two terminal sets: a smaller one with the nodes \(pt\), \(ma\), \(dd\), and \(w\), and a larger one with the nodes \(nnach\) and \(clk\) in addition to these nodes. In both cases, the results are significantly better than the results obtained with the entire terminal set. This shows that it is possible to make a meaningful selection of features depending on the frequency of the terminal nodes in the obtained expressions, especially since the four most important terminal nodes consistently have the highest frequency.