## 5 Results and Discussion
### Evaluation of Different Algorithms Based on Computed Indexes  
Table 5 shows the comparison between generated hydropower and producible maximum hydropower (i.e., power plant capacity). The dry years were the most critical years, and the HJD hydropower plant was selected to analyze the results to avoid repetition. Thus, all of the mentioned analysis is for the HJD reservoir, hydropower plant, and dry years, and the results were the same for other years and hydropower plants. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{5}{c}{HJD (Dry Year)} \\ \hline \multirow{2}{*}{**Method**} & **Temporal Reliability Index** & **Volumetric Reliability Index** & **Vulnerability Index** & **RMSE** & **MAE** \\  & **Riley** & **Riley** & **Riley** & **MW** & **MW** \\ \hline CA & 38\% & 91\% & 20\% & 1.4 MW & 1.2 MW \\ MBF & 25\% & 83\% & 34\% & 2.3 MW & 2.1 MW \\ PSO & 18\% & 76\% & 39\% & 3.4 MW & 3.2 MW \\ GA & 14\% & 65\% & 41\% & 3.9 MW & 3.6 MW \\ \hline \multicolumn{5}{c}{**SFY (Dry Year)**} \\ \hline CA & 32\% & 90\% & 22\% & 1.6 MW & 1.2 MW \\ MBF & 29\% & 82\% & 36\% & 2.5 MW & 2.3 MW \\ PSO & 27\% & 75\% & 41\% & 3.6 MW & 3.4 MW \\ GA & 24\% & 63\% & 43\% & 4.1 MW & 4.0 MW \\ \hline \multicolumn{5}{c}{**DF (Dry Year)**} \\ \hline CA & 39\% & 92\% & 19\% & 1.2 MW & 1.1 MW \\ MBF & 27\% & 83\% & 32\% & 2.3 MW & 2.1 MW \\ PSO & 22\% & 77\% & 41\% & 3.1 MW & 3.0 MW \\ GA & 16\% & 67\% & 43\% & 3.9 MW & 3.7 MW \\ \hline \multicolumn{5}{c}{**WJD (Dry Year)**} \\ \hline CA & 41\% & 91\% & 19\% & 1.4 MW & 1.2 MW \\ MBF & 29\% & 84\% & 32\% & 2.1 MW & 2.0 MW \\ PSO & 19\% & 77\% & 40\% & 3.1 MW & 3.0 MW \\ GA & 16\% & 66\% & 42\% & 3.6 MW & 3.4 MW \\ \hline \multicolumn{5}{c}{**HJD (Normal Year)**} \\ \hline \multirow{2}{*}{**Method**} & **Temporal Reliability Index** & **Volumetric Reliability Index** & **Vulnerability Index** & **RMSE** & **MAE** \\ \hline CA & 42\% & 92\% & 17\% & 1.2 MW & 9.0 MW \\ MBF & 39\% & 91\% & 22\% & 1.5 MW & 1.3 MW \\ PSO & 27\% & 85\% & 28\% & 2.4 MW & 2.0 MW \\ GA & 29\% & 76\% & 31\% & 2.9 MW & 2.6 MW \\ \hline \multicolumn{5}{c}{**SFY (Normal Year)**} \\ \hline CA & 41\% & 91\% & 21\% & 1.3 MW & 1.2 MW \\ MBF & 38\% & 84\% & 29\% & 1.9 MW & 1.4 MW \\ PSO & 27\% & 82\% & 32\% & 2.8 MW & 2.6 MW \\ GA & 24\% & 75\% & 35\% & 2.6 MW & 2.1 MW \\ \hline \multicolumn{5}{c}{**DF (Normal Year)**} \\ \hline CA & 41\% & 92\% & 20\% & 1.3 MW & 1.0 MW \\ MBF & 35\% & 87\% & 24\% & 1.5 MW & 1.4 MW \\ PSO & 29\% & 81\% & 29\% & 2.3 MW & 2.1 MW \\ GA & 28\% & 79\% & 32\% & 2.9 MW & 2.6 MW \\ \hline \multicolumn{5}{c}{**WJD (Normal Year)**} \\ \hline CA & 42\% & 93\% & 17\% & 1.2 MW & 1.2 MW \\ MBF & 33\% & 92\% & 22\% & 1.6 MW & 1.5 MW \\ PSO & 26\% & 85\% & 26\% & 2.1 MW & 1.9 MW \\ GA & 30\% & 79\% & 28\% & 2.6 MW & 2.4 MW \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Computed indexes for generated power for dry years, normal years, and wet years. RMSE: Root mean square error; MAE: Mean absolute error. The temporal reliability index (TRI) for the CA based on dry years was 38%, which was 13%, 20%, and 24% more than via the MBF, PSO, and GA, respectively. The percent of this index represents the number of periods where the hydropower exceeded the set threshold (i.e., power plant capacity). Thus, there were no hydropower deficits during these periods due to a surplus of hydropower generation. When the TRI had a higher value, the system could generate hydropower for more periods, with a surplus capacity comparable to the hydropower plant capacity. Additionally, the volumetric reliability index (VRI) based on the CA during dry years was 91%, which was 8%, 15%, and 26% more than via the MBF, PSO, and GA, respectively. This result showed that the generated hydropower via the CA for more periods was closer to the hydropower plant capacity compared to via the MBF, GA, and PSO. The vulnerability index for the CA based on dry years was 20%, which was 14%, 19%, and 21% less than via the MBF (monarch butterfly algorithm), PSO, and GA, respectively.