# Transfer Learning for Operator Selection: A Reinforcement Learning Approach
## 4 Experimental Results
### Results and Discussions
\begin{tabular}{c c c c c c c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**RLABC**} & \multicolumn{3}{c}{**RLABC-T**} & \multicolumn{3}{c}{**RLABC-TC**} \\ \hline  & _Best_ & _Mean_ & _Std_ & \(R\) & _Best_ & _Mean_ & _Std_ & \(R\) & \(S\) & _Best_ & _Mean_ & _Std_ & \(R\) & \(S\) \\ \hline
1\_1 & 13,251 & 13,071.4 & 53.5 & 1 & 13,283 & 13,070.5 & 61.80 & 2 & - & 13,167 & 13,054.  
Figure 2 shows comparative results of the algorithms with respect to CPU time, while Table 5 tabulates the statistical analysis of the results, where both the table and the figure demonstrate clear improvement by RLABC-T and RLABC-TC except for the cases of 1_1 and 1_2 instances, which are smaller in size. The growing size of the instances ascertains further that RLABC could not compete with the other variants. This suggests that when the problem dimension increases, RLABC has shown worse performance in terms of computational time. The results also indicate that RLABC-T and RLABC-TC remain competitive, but RLABC-TC has done slightly better than RLABC-T. Almost for all benchmarks except two instances, improvements on time performance are statistically meaningful. A similar situation applies to Figures 3 and 4 and Tables 6 and 7, where the results by the algorithms applied to Set\({}_{2}\) and Set\({}_{3}\) are plotted and tabulated accordingly. These indicate that the comparisons with respect to the CPU time for all methods look similar to the cases of Set\({}_{1}\).  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**RLABC**} & \multicolumn{4}{c}{RLABC-T} & \multicolumn{4}{c}{**RLABC-TC**} \\ \hline  & _Best_ & _Mean_ & _Std_ & \(R\) & _Best_ & _Mean_ & _Std_ & \(R\) & \(S\) & _Best_ & _Mean_ & _Std_ & \(R\) & \(S\) \\ \hline
3\_1 & 12,045 & 11,632 & 191.489 & 3 & 12,020 & 11,697.3 & 148.956 & 1 & - & 12,020 & 11,651.9 & 152.747 & 2 & - \\
3\_2 & 12,369 & 12,205.2 & 149.614 & 1 & 12,369 & 12,101 & 263.167 & 3 & - & 12,369 & 12,196.8 & 201.196 & 2 & - \\
3\_3 & 13,609 & 13,352.2 & 130.039 & 2 & 13,609 & 13,399 & 99.6629 & 1 & - & 13,609 & 13,334.8 & 127.075 & 3 & - \\
3\_4 & 10,973 & 10,856.3 & 105.533 & 2 & 11,021 & 10,852.4 & 86.8795 & 3 & - & 11,298 & 10,859.1 & 140.543 & 1 & - \\
3\_5 & 11,538 & 11,240 & 169.691 & 3 & 11,538 & 11,308.8 & 210.61 & 1 & - & 11,538 & 11,287.8 & 194.904 & 2 & - \\
3\_6 & 11,377 & 11,077.2 & 189.324 & 1 & 11,377 & 11,017.5 & 178.618 & 2 & - & 11,377 & 10,997.4 & 202.552 & 3 & + \\
3\_7 & 10,181 & 9951.63 & 80.973 & 1 & 10,069 & 9932.27 & 67.0159 & 3 & - & 10,087 & 9946.9 & 76.4209 & 2 & - \\
3\_8 & 10,075 & 9403.8 & 177.593 & 3 & 10,077 & 9517.33 & 193.699 & 1 & + & 9749 & 9445.77 & 146.641 & 2 & - \\
3\_9 & 10,877 & 10,647.3 & 101.085 & 2 & 10,831 & 10,626.4 & 90.5375 & 3 & - & 10,987 & 10,668.8 & 122.98 & 1 & - \\
3\_10 & 9745 & 9426.57 & 136.45 & 2 & 10,220 & 9433.83 & 234.262 & 1 & - & 9649 & 9421.17 & 117.068 & 3 & - \\ \hline  & & & & & & & & & & & & & & \\ \end{tabular} Mean: & 2 & \multicolumn{4}{c}{Mean:} & 1.9 & \multicolumn{4}{c}{Mean:} & 2.1 \\ \hline \hline \end{tabular} 
\end{table}
Table 4: Comparative results in solution quality for Set\({}_{3}\) benchmarks. Figure 2: Comparative results with respect to computational time by all three (RLABC, RLABC-T, RLABC-TC) algorithms for Set\({}_{1}\) benchmarks. Figure 4: Comparative results with respect to computational time by all three (RLABC, RLABC-T), RLABC-TC) algorithms for Set\({}_{3}\) benchmarks. Figure 3: Comparative results with respect to computational time by all three (RLABC, RLABC-T), RLABC-TC) algorithms for Set\({}_{2}\) benchmarks.