## 5 Computational Results and Discussion
In Table 7 it is possible to note significant improvements, especially in the average and standard deviation. The minimum values were equal, but our maximum was lower. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**MH** & \(\mathbf{n}\) & \(\mathbf{Sn}\) & \(\mathbf{MaxFail}\) & **Stopping Criteria** \\ \hline \multirow{4}{*}{ABC} & 10 & 75 & 1250 & 2000 \\  & 15 & 1750 & 3000 \\  & 20 & 2000 & 3500 \\  & 30 & 125 & 4000 \\  & 50 & & 2250 & 4500 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Values of artificial bee colony parameters. \(\mathbf{Sn}\) is the size of the population. \(\mathbf{MaxFail}\) is the maximum failures allowed. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Min Value** & **Max Value** & **Average** & \(\mathbf{\sigma}\) \\ \hline Previous results & 0.07 & 0.57 & 0.3792 & 0.13217 \\ Racing & 0.08 & 0.53 & 0.3474 & 0.11834 \\ CBR & 0.09 & 0.50 & 0.3388 & 0.10736 \\ Racing + CBR & 0.07 & 0.48 & 0.3142 & 0.10999 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Descriptive analysis of the \(C_{max}\) ratio for all approaches, including the obtained minimum values, maximum values, averages and standard deviations. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**MH** & \(\mathbf{n}\) & \(\mathbf{Part}\) & **Stopping Criteria** & \(\mathbf{mIn}\) & \(\mathbf{MIn}\) & \(\mathbf{c1}\) & \(\mathbf{c2}\) & \(\mathbf{mVel}\) & \(\mathbf{MVel}\) \\ \hline \multirow{4}{*}{PSO} & 10 & 30 & 1000 & & & & & & \\  & 15 & 25 & 1500 & & & & & \\  & 20 & & 1750 & 40\% & 95\% & 2 & 2 & \(-4\) & 4 \\  & 30 & 75 & 3500 & & & & & & \\  & 50 & & 4500 & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Values of particle swarm optimization parameters. \(\mathbf{Part}\) is the number of particles. \(\mathbf{mIn}\) is the minimum inertia. \(\mathbf{MIn}\) is the maximum inertia. \(\mathbf{c1}\) and \(\mathbf{c2}\) are learning factors. \(\mathbf{mVel}\) is the minimum velocity. \(\mathbf{MVel}\) is the maximum velocity. Analyzing the statistical significance of these findings becomes critical at this stage. When comparing the previous published results and the results of the hybrid approach (Table 8), one can claim, with a 95% confidence level, that there are statistically significant differences between the results obtained initially (without learning) and the results obtained by the racing + CBR approach, allowing one to infer as to the benefit of its use. The same conclusions are possible to find about the comparison of the hybrid method against the results of racing and CBR approaches separately. To complete the study, in Figure 7 the average execution times achieved by Auto-DynAgents system with the inclusion of the racing + CBR approach are presented. By comparing the average execution times of all approaches, it is possible to show that the hybrid approach significantly improved compared to previous published results, and also there was a slight improvement in the racing based approach. However, there is no evidence of improvements in efficiency compared to CBR. Thus, in addition to improving the effectiveness of the results, the racing + CBR approach also allowed us to improve system efficiency, especially when compared to the previous results (without learning). \begin{table}
\begin{tabular}{c c c c c c} \hline  & **Average** & \(\sigma\) & \(t\) & **DoF** & \(p\) \\ \hline Previous vs. Racing + CBR & 0.06496 & 0.06499 & 5.475 & 29 & 0.000 \\ Racing vs. Racing + CBR & 0.03314 & 0.03582 & 5.068 & 29 & 0.000 \\ CBR vs. Racing + CBR & 0.02454 & 0.05208 & 2.581 & 29 & 0.015 \\ \hline \end{tabular}
\end{table} 
Table 8: Student’s \(t\) test for paired samples. Figure 6: Comparison average results from all approaches. A total of 30 instances from OR-Library were considered and solved using each of the four approaches: previous; CBR; racing; racing + CBR. Therefore, four paired samples of 30 observations each were obtained. The results were normalized. The statistical analysis was conducted using R [73].