## 5 Numerical Results
### Investigation of the Proposed Method's Performance on the IEEE 30-Bus System
Accordingly, the proposed method is faster than these compared methods approximately from 1.6 to 3.5 times for TVD objective and approximately from 2 to 11 times for \(L\) index objective. All in all, the proposed method is more powerful than other compared methods available in previous studies in terms of solution search speed. Compared to other implemented methods, the proposed method and these methods have approximately the same search speed due to the same setting of adjustment parameters; however, the proposed method has converged to optimal solutions with high quality, while others have not yielded the achievement. As shown in Section 5.2, the proposed method has reached a success rate of up to 100% for TPL and TVD cases and 98% for \(L\) index case, while the implemented methods have not reached the same success rate. For TPL case, only WCA has achieved SR with 100%, while SSA and SFOA have reached SR with 89% and 87%. SR of the three methods was, respectively, 100%, 92%, and 93% for TVD case and was, respectively, 90%, 78%, and 81% for \(L\) index case. Clearly, the proposed method is more capable of handling all constraints of the IEEE 30-bus system. One again, the conclusion can be confirmed via the best fitness of 50 runs plotted in Figures 5-7 for TPL, TVD, and \(L\) index objective, respectively. In Figure 5, all applied methods have high fluctuations, but only the proposed ICOA reaches many better solutions with less power loss than other methods. In Figures 6 and 7, the proposed ICOA has smaller fluctuation than other methods, and it also find solutions with much lower values of TVD and \(L\) index \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} & \(N_{sqe}\) & \(Ti\) (pu)** & **CV** & **DV** & **SR (\%)** \\ \hline ICOA & 0.1242 & 0.1264 & 6.9 & 2000 & 1.00 & X & 94 \\ ICOA & 0.12437 & 0.1271 & 6.9 & 2000 & 1.0 & X & 92 \\ WCA & 0.124754 & 0.127404 & 8.9 & 2000 & 1.29 & X & 90 \\ SSA & 0.1313 & 0.148 & 7 & 2000 & 1.01 & X & 78 \\ SFOA & 0.1275 & 0.1384 & 7.3 & 2000 & 1.06 & X & 81 \\ COA & 0.1252 & 0.1267 & 9.4 & 2000 & 1.36 & X & 76 \\ COA1 & 0.1246 & 0.1266 & 7.9 & 2000 & 1.14 & X & 92 \\ COA2 & 0.1252 & 0.1299 & 8.3 & 2000 & 1.20 & X & 88 \\ PSO-AIW [19] & 0.1258 & 0.127 & 14.42 & 4000 & 2.18 & X & - \\ PSO-AAC [19] & 0.1499 & 0.1513 & 14.53 & 4000 & 2.19 & X & - \\ SPSO-AAC [19] & 0.1271 & 0.1285 & 14.05 & 4000 & 2.12 & X & - \\ PSO-CF [19] & 0.1261 & 0.1279 & 14.39 & 4000 & 2.17 & X & - \\ PSO-PG [19] & 0.1264 & 0.1297 & 14.84 & 4000 & 2.24 & X & - \\ PSO-SOSWT [19] & 0.1488 & 0.1634 & 18.99 & 4000 & 2.87 & X & - \\ PSO-POSWT [19] & 0.1394 & 0.1537 & 19.107 & 4000 & 2.88 & X & - \\ PSO-IPG [19] & 0.1241 & 0.1266 & 13.75 & 4000 & 2.08 & X & - \\ DE [24] & 0.1246 & - & - & 25,000 & - & X & - \\ GSA [29] & 0.1161 & - & - & 20,000 & - & X & - \\ QOTLBO [33] & 0.1242 & 0.1245 & - & 10,000 & - & X & - \\ TLBO [33] & 0.1252 & 0.1254 & - & 10,000 & - & X & - \\ BA [44] & 0.1191 & - & 94.65 & 4000 & 10.29 & X & - \\ GWO [44] & 0.118 & - & 104.29 & 4000 & 11.34 & & X & - \\ ABC [44] & 0.1161 & - & 105.04 & 8000 & 11.42 & & X & - \\ ALO [44] & 0.1161 & - & 97.92 & 4000 & 10.64 & & X & - \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Result comparison of \(L\) index for the IEEE 30-bus system.