## 5 Simulation Results and Discussion
### Test Systems and Results
#### 5.1.3 Test System 3  
A test system with 110 generating units possessing quadratic fuel cost characteristics is utilized. The details of the input parameters were taken from [41]. The load demand is assumed to be 15,000 MW. The best solution obtained by the proposed RLGWO can be seen in Table 5. A comparison of the convergence characteristics of 110 generators between the GWO and RLGWO methods with respect to fitness value is presented in Figure 8.  
The maximum, minimum, and average achieved over 50 trials are given in Table 6. Figure 9 presents a visualization of Table 6. The RLGWO produced the lowest cost among the five algorithms and was able to find the minimum cost the most times (as can be seen from Figure 9b). Still, it is the fastest algorithm among the five algorithms tested.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Generation Costs**} & \multicolumn{1}{c}{**Time (s)**} & \multicolumn{1}{c}{**No. of Hits of the**} \\ \cline{2-5}
**Method** & **Max** & **Min** & **Average** & **Minimum Solution** \\ \hline RLGWO & 136,548.3499 & 136,548.3499 & 136,548.3499 & 8.6 & 50 \\ ORCCRO & 136,855.19 & 136,855.19 & 136,855.19 & 14 & 50 \\ OIWO & 136,452.677 & 136,452.677 & 136,452.677 & 10.7 & 46 \\ DE/BBO & 137,150.77 & 136,950.77 & 137,116.58 & 32 & 45 \\ BBO & 137,587.82 & 137,026.82 & 137,116.58 & 40 & 41 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Comparison between different methods taken after 50 trials (40-unit system with loss).  
Figure 6: Comparative convergence characteristics of the original GWO and the proposed RLGWO algorithms for the 40-unit system.  
Figure 7: Results for different methods for the 40-unit system (50 trials): (**a**) boxplot of the final generation cost; (**b**) time and number of hits of the minimum solution.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Generation Costs**} & \multicolumn{2}{c}{**No. of Hits of the**} \\ \cline{2-7}
**Method** & **Max** & **Min** & **Average** & **Minimum Solution** \\ \hline RLGWO & 197,952.88 & 197,952.36 & 197,952.62 & 28 & 49 \\ ORCCRO & 198,016.89 & 198,016.29 & 198,016.32 & 45 & 48 \\ OIIWO & 197,989.93 & 197,989.14 & 197,989.41 & 31 & 46 \\ DE/BBO & 198,828.57 & 198,231.06 & 198,326.66 & 132 & 43 \\ BBO & 199,102.59 & 198,241.166 & 198,413.45 & 115 & 41 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Comparison between different methods taken after 50 trials (110-unit system with loss).  
Figure 8: Comparative convergence characteristics of the original GWO and the proposed RLGWO algorithms for the 110-unit system.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Unit**} & \multicolumn{2}{c}{**Power Output**} & \multirow{2}{*}{**Unit**} & \multicolumn{2}{c}{**Power Output**} & \multirow{2}{*}{**Unit**} & \multicolumn{2}{c}{**Power Output**} & \multirow{2}{*}{**Unit**} & \multicolumn{2}{c}{**Power Output**} \\  & & & **(MW)** & & **(MW)** & & **(MW)** & & **(MW)** & **(MW)** \\ \hline  
\$/h) & \\
23 & 68.89 & 46 & 619.5389 & 69 & 70.0006 & 92 & 98.38849 & & \\ \hline \hline \end{tabular}
\end{table}
Table 5: Best simulation results for the 110-unit system with loss (\(P_{D}=15,000\) MW).