## 5 Numerical Results
### Investigation of the Proposed Method's Performance on the IEEE 118-Bus System
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Method** & **Min.** & **Avg.** &
\begin{tabular}{c} **Average** \\ **Time (s)** \\ \end{tabular} & \(N_{\text{\it{sage}}}\) & \(\text{\it{Ti}}\) (pu)** & **CV** & **DV** & **SR (\%)** \\ \hline ICOA & 114.8036 & 122.192 & 92.22 & 8000 & 1.00 & X & 94 \\ ICOA & 114.8623 & 123.764 & 93.6 & 8000 & & X & 90 \\ WCA & 118.3207 & 126.0165 & 129.34 & 8000 & 1.40 & X & 90 \\ SSA & 125.7288 & 131.4492 & 93.66 & 8000 & 1.02 & X & 65 \\ SFOA & 125.6801 & 129.0715 & 102.58 & 8000 & 1.11 & X & 57 \\ COA & 132.3341 & 137.7484 & 121.91 & 8000 & 1.32 & X & 52 \\ COA1 & 123.6867 & 128.4266 & 107.04 & 8000 & 1.16 & X & 90 \\ COA2 & 126.0426 & 130.8728 & 115.96 & 8000 & 1.26 & X & 64 \\ SARCGA [10] & 113.12 & 113.968 & - & 9000 & - & X & - \\ CLPSO [16] & 130.96 & - & - & 24,000 & - & X & - \\ PSO [16] & 131.99 & - & - & 24,000 & - & X & - \\ PSO-AIV [19] & 116.8976 & 118.2344 & 109.645 & 8000 & 1.30 & X & - \\ PSO-AAC [19] & 124.334 & 129.7494 & 96.32 & 8000 & 1.14 & X & - \\ SPSO-AAC [19] & 116.203 & 117.3553 & 96.45 & 8000 & 1.15 & X & - \\ PSO-CF [19] & 115.647 & 116.9863 & 95.86 & 8000 & 1.14 & X & - \\ PSO-PG [19] & 116.608 & 119.3968 & 96.11 & 8000 & 1.14 & X & - \\ PSO-SWT [19] & 124.1476 & 129.371 & 91.58 & 8000 & 1.09 & X & - \\ PGSWTPSO [19] & 119.427 & 122.781 & 95.17 & 8000 & 1.13 & X & - \\ PSO-IFPG [19] & 115.06 & 116.462 & 91.07 & 8000 & 1.08 & X & - \\ QOTLBO [33] & 112.2789 & 113.7693 & - & 10,000 & - & X & - \\ TLBO [33] & 116.4003 & 121.3902 & - & 10,000 & - & X & - \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Comparison of results obtained from the IEEE 118-bus system with power-loss optimization. Figure 10: TVD of 50 runs obtained by different methods for the IEEE 118-bus system. Figure 9: TPL of 50 runs obtained by different methods for the IEEE 118-bus system. The comparisons with other existing methods available in other studies can point out that the proposed method has a worse result than PSO-IPG [19], SARCGA [10], and QOTLBO [33] for TPL objective, and three PSO methods in [19] consisting of PSO-SWT, PSO-PGSWT, and PSO-IPG for \(L\) index objective. Nevertheless, it needs to confirm that not all the methods are really superior to the proposed method for the two objective functions. The verification of reported solutions can lead to the conclusion that SARCGA is not a good candidate for the proposed method. Figure 11: \(L\) index of 50 runs obtained by different methods for the IEEE 118-bus system. Figure 12: The voltage of all loads obtained by five implemented methods. real effective method, because there was no solution reported in [10]. QOTLBO [33] is only more effective than the proposed method for TPL objective but it is less effective for two cases of TVD and \(L\) index objectives. However, it should be noted that QOTLBO used a higher number of solution quality evaluations, 10,000, while that of the proposed method was only 8000. Thus, it can be said that the proposed method is more effective than QOTLBO. Among the rest of methods in [19], PSO-IPG is more effective than the proposed method for two cases of TPL and \(L\) index objective, but it is less effective than the proposed method for TVD objective. PSO-SWT and PSO-PGSWT used the same number of solution quality evaluations as the proposed method, but the two methods found less effective solutions for two cases of TPL and TVD objectives. However, it should be noted that these methods in [19] were run by setting upper bound of the load bus voltage to 1.1 pu, while the proposed method and other ones were run on the bound of 1.05 pu. Thus, we have continued to implement the proposed method by assigning the upper bound of load bus voltage to 1.1 pu.