# Transfer Learning for Operator Selection: A Reinforcement Learning Approach
## 4 Experimental Results
### Results and Discussions  
Tables 2-4 show comparisons among three variants in terms of solution quality. The column of _best_ is determined as the maximum value of the best solutions of thirty different runs. _Mean_ and _Std_ values are the average and standard deviation of them, respectively. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Set\({}_{1}\)**} & \multicolumn{4}{c}{**Set\({}_{2}\)**} & \multicolumn{4}{c}{**Set\({}_{3}\)**} \\ \hline ID & \(m\) & \(n\) & \(w\) & \(y\) & ID & \(m\) & \(n\) & \(w\) & \(y\) & ID & \(m\) & \(n\) & \(w\) & \(y\) \\ \hline
1\_1 & 100 & 85 & 0.10 & 0.75 & 2\_1 & 100 & 100 & 0.10 & 0.75 & 3\_1 & 85 & 100 & 0.10 & 0.75 \\
1\_2 & 100 & 85 & 0.15 & 0.85 & 2\_2 & 100 & 100 & 0.15 & 0.85 & 3\_2 & 85 & 100 & 0.15 & 0.85 \\
1\_3 & 200 & 185 & 0.10 & 0.75 & 2\_3 & 200 & 200 & 0.10 & 0.75 & 3\_3 & 185 & 200 & 0.10 & 0.75 \\
1\_4 & 200 & 185 & 0.15 & 0.85 & 2\_4 & 200 & 200 & 0.15 & 0.85 & 3\_4 & 185 & 200 & 0.15 & 0.85 \\
1\_5 & 300 & 285 & 0.10 & 0.75 & 2\_5 & 300 & 300 & 0.10 & 0.75 & 3\_5 & 285 & 300 & 0.10 & 0.75 \\
1\_6 & 300 & 285 & 0.15 & 0.85 & 2\_6 & 300 & 300 & 0.15 & 0.85 & 3\_6 & 285 & 300 & 0.15 & 0.85 \\
1\_7 & 400 & 385 & 0.10 & 0.75 & 2\_7 & 400 & 400 & 0.10 & 0.75 & 3\_7 & 385 & 400 & 0.10 & 0.75 \\
1\_8 & 400 & 385 & 0.15 & 0.85 & 2\_8 & 400 & 400 & 0.15 & 0.85 & 3\_8 & 385 & 400 & 0.15 & 0.85 \\
1\_9 & 500 & 485 & 0.10 & 0.75 & 2\_9 & 500 & 500 & 0.10 & 0.75 & 3\_9 & 485 & 500 & 0.10 & 0.75 \\
1\_10 & 500 & 485 & 0.15 & 0.85 & 2\_10 & 500 & 500 & 0.15 & 0.85 & 3\_10 & 485 & 500 & 0.15 & 0.85 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The SUKP benchmark instances. is the rank and \(S\) is the sign of Wilcoxon signed-rank test. The algorithms are ranked in terms of mean values. As can be seen from Table 2, RLABC provides the best place, (i.e., the first place) only for two instances 1_1 and 1_4. The average rank of RLABC over the set of problem is 2.2, and it has the worst ranking among three approaches. RLABC-TC is the second-best algorithm because the average of rank values is 2; it has left behind RLABC-T, which shows better performance than the others, reaching the mean rank value of 1.8. When the statistical results are examined, RLABC-T has produced a statistically meaningful result for less than half of the instances, whereas the results of RLABC-TC are statistically meaningful only for one instance. Table 3 presents comparative statistical performance of the three variants in terms of solution quality on Set\({}_{2}\) benchmark instances. Clearly, RLABC-T remains in the first position among the variants similar to the case of Set\({}_{1}\), where it achieves first place on the half of benchmark instances. It is observed that both RLABC-T and RLABC-TC perform better than RLABC with respect to _Best_ values, while RLABC takes first position in only two instances, 2_6 and 2_10. Table 4 shows the comparative statistical performance of three variants on Set\({}_{3}\) benchmark instances. The algorithms look more competitive on this set in comparison to the previous two sets. In fact, the average rank calculated for each is 2, 1.9, and 2.1 for RLABC, RLABC-T, and RLABC-TC, respectively. The comparative results suggest that the algorithms produce slightly different qualities of solutions. \begin{table}