# Transfer Learning for Operator Selection: A Reinforcement Learning Approach
## 4 Experimental Results
### Results and Discussions
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **RLABC** & \multicolumn{2}{c}{**RLABC-T**} & \multicolumn{2}{c}{**RLABC-TC**} \\ \hline
**Instance No** & **Rank** & **Rank** & **Sign** & **Rank** & **Sign** \\ \hline
1\_1 & 2 & 3 & + & 1 & - \\
1\_2 & 2 & 1 & + & 3 & - \\
1\_3 & 3 & 2 & + & 1 & + \\
1\_4 & 3 & 1 & + & 2 & + \\
1\_5 & 3 & 1 & + & 2 & + \\
1\_6 & 3 & 1 & + & 2 & + \\
1\_7 & 3 & 2 & + & 1 & + \\
1\_8 & 3 & 2 & + & 1 & + \\
1\_9 & 3 & 2 & + & 1 & + \\
1\_10 & 3 & 2 & + & 1 & + \\ \hline Mean: & 2.8 & 1.7 & & 1.5 & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The results of statistical analysis on computational for Set\({}_{1}\) with respect to computational time. Figure 5 presents the convergence graphs of methods through the search process; Figure 5a shows the algorithms' behaviour on a 400-dimensional problem, 2_7, and Figure 5b plots the performances on a 500-dimensional problem, 2_9. As can be seen in both figures, RLABC-T converges quicker than the other two but remains in local optima at around iteration 200. Meanwhile, RLABC-TC escapes that local optima in iterations such as 200, 300, and 350 in Figure 5a and in iterations around 80 and 250 in Figure 5b. On the other hand, RLABC gradually converges but stops after iteration 300 in both Figure 5a,b. This suggests that it is able to escape local optima at that points but cannot converge as RLABC-TC does. Both figures clarify that RLABC is outperformed by the other algorithms, while RLABC-TC converges better among all. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **RLABC** & **RLABC-T** & \multicolumn{2}{c}{**RLABC-TC**} \\ \hline  & **Rank** & **Rank** & **Sign** & **Rank** & **Sign** \\ \hline
2\_1 & 2 & 3 & + & 1 & + \\
2\_2 & 1 & 3 & - & 2 & - \\
2\_3 & 3 & 2 & + & 1 & + \\
2\_4 & 3 & 2 & + & 1 & + \\
2\_5 & 3 & 1 & + & 2 & + \\
2\_6 & 3 & 1 & + & 2 & + \\
2\_7 & 3 & 2 & + & 1 & + \\
2\_8 & 3 & 2 & + & 1 & + \\
2\_9 & 3 & 2 & + & 1 & + \\
2\_10 & 3 & 2 & + & 1 & + \\ \hline Mean: & 2.7 & 2 & & 1.3 & \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The results of statistical analysis for \(\text{Set}_{2}\) with respect to computational time. Figure 5: Convergence level attained by each operator while solving (**a**) 2_7 problem instance and (**b**) 2_9 problem instance. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **RLABC** & \multicolumn{2}{c}{**RLABC-T**} & \multicolumn{2}{c}{**RLABC-TC**} \\ \hline  & **Rank** & **Rank** & **Sign** & **Rank** & **Sign** \\ \hline
3\_1 & 1 & 3 & + & 2 & - \\
3\_2 & 3 & 1 & + & 2 & - \\
3\_3 & 3 & 2 & + & 1 & + \\
3\_4 & 1 & 3 & + & 2 & - \\
3\_5 & 3 & 1 & + & 2 & + \\
3\_6 & 3 & 1 & + & 2 & + \\
3\_7 & 3 & 2 & + & 1 & + \\
3\_8 & 3 & 2 & + & 1 & + \\
3\_9 & 3 & 2 & + & 1 & + \\
3\_10 & 3 & 2 & + & 1 & + \\ \hline Mean: & 2.6 & 1.9 & & 1.5 & \\ \hline \hline \end{tabular}
\end{table} 
Table 7: The results of statistical analysis for \(\text{Set}_{3}\) with respect to computational time. Figure 6 reflects the credit values gained by the three operators through iterations. As shown in the figure, all methods has slightly similar characteristics. _ibinABC_ has obtained more credit from the start to the 200 th iteration. The difference of methods is started from there. In the RLABC, _ibinABC_ always has the most credited operator, while RLABC and RLABC have changed to _DisABC_ and _binABC_. In overall comparison, RLABC is a powerful algorithm that shows good performance than most of the state-of-art methods that are applied to the same problem, as in [4]. However, it does not allow transfer learning in problem solving. RLABC-T and RLABC-TC have improved the results not only in terms of solution quality but also the algorithm's CPU time, demonstrating that the solution quality of the score is slightly better, while both RLABC-T and RLABC-TC significantly solve the problems much faster than RLABC. This experimentally approves the contribution of transfer learning in dynamically building an adaptive operator selection scheme.