## 5 Numerical Results
### Investigation of the Proposed Method's Performance on the IEEE 30-Bus System
Consequently, it can lead to a conclusion that the proposed method is very robust for finding solutions of the IEEE 30-bus system with TVD objective. According to Table 7 showing result comparison of \(L\) index objective, GSA in [29] for the case of continuous variables and four methods in [44] for the case of discrete variables reported the best results with the lowest \(L\) index, approximately 0.11 pu, while that of the proposed method is 0.1242 and 0.12437 pu, corresponding to continuous and discrete variables, respectively. However, the recalculated value of \(L\) index is 0.1247 and 0.1241 pu for GSA and ALO, which are higher and approximately equal to that of the proposed method. The verification of reported solutions from PSO-IPG [19] and QOTLBO [33] confirms that the two methods have reported accurate solutions; however, the two methods have the same solution quality with the proposed ICOA method. As compared to other remaining methods, the \(L\) index values indicate the proposed method can find the optimal solution with the improvement up to 17.1% and that value is 0.8% as compared to the COA method. Thus, the proposed method can find the solution with the same quality as other leading methods for the case of \(L\) index optimization for the IEEE 30-bus system. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multirow{2}{*}{**Min.**} & \multirow{2}{*}{**Avg.**} & \multicolumn{2}{c}{**Average**} & \multirow{2}{*}{\(N_{Iter}\)} & \multirow{2}{*}{\(N_{pop}\)} & \multirow{2}{*}{\(N_{\text{sage}}\)} & \multirow{2}{*}{**Tri (pu)**} & \multirow{2}{*}{**CV**} & \multirow{2}{*}{**DV**} & \multirow{2}{*}{**SR (\%)**} \\  & & & & & & & & & & & \\ \hline ICOA & 0.0888 & 0.1315 & 6.39 & 100 & 16 & 2000 & 1 & X & 100 \\ ICOA & 0.0905 & 0.1321 & 6.89 & 100 & 16 & 2000 & & & X & 100 \\ WCA & 0.116855 & 0.175071 & 8.5 & 100 & 20 & 2000 & 1.33 & X & & 100 \\ SSA & 0.1806 & 0.3392 & 6.3 & 100 & 20 & 2000 & 0.99 & X & & 92 \\ SFOA & 0.1588 & 0.2326 & 6.9 & 100 & 20 & 2000 & 1.08 & X & & 93 \\ COA & 0.122 & 0.2047 & 8.2 & 100 & 16 & 2000 & 1.28 & X & & 90 \\ COA1 & 0.1093 & 0.1828 & 7.2 & 100 & 16 & 2000 & 1.13 & X & 100 \\ COA2 & 0.0999 & 0.1795 & 7.8 & 100 & 16 & 2000 & 1.22 & X & 98 \\ PSO-AIW [19] & 0.1038 & 0.1597 & 12.25 & 200 & 20 & 4000 & 2.00 & X & - \\ PSO-AAC [19] & 0.2064 & 0.2376 & 12.88 & 200 & 20 & 4000 & 2.10 & X & - \\ SPSO-AAC [19] & 0.1354 & 0.1558 & 12.59 & 200 & 20 & 4000 & 2.05 & X & - \\ PSO-CF [19] & 0.1287 & 0.1557 & 12.94 & 200 & 20 & 4000 & 2.11 & X & - \\ PSO-PG [19] & 0.1202 & 0.144 & 12.45 & 200 & 20 & 4000 & 2.03 & X & - \\ PSO-SOWT [19] & 0.1614 & 0.1814 & 22.57 & 200 & 20 & 4000 & 3.68 & X & - \\ PSO-POSWT [19] & 0.1539 & 0.2189 & 22.32 & 200 & 20 & 4000 & 3.64 & X & - \\ PSO-IPG [19] & 0.0892 & 0.1078 & 9.724 & 200 & 20 & 4000 & 1.59 & X & - \\ DE [24] & 0.0911 & - & - & 500 & 150 & 75,000 & - & X & - \\ GSA [29] & 0.0676 & - & - & 200 & 100 & 20,000 & - & X & - \\ QOTLBO [33] & 0.0856 & 0.0872 & - & 100 & 50 & 10,000 & - & X & - \\ TLBO [33] & 0.0913 & 0.0934 & - & 100 & 50 & 10,000 & - & X & - \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Result comparison of TVD objective for the IEEE 30-bus system. For the comparison of solution search speed, the values of \(N_{sqe}\) and \(Ti\) are also summarized in Tables 5-7. Table 5 indicates that the proposed method is ranked the fastest method together with six other implemented methods by spending 2000 solution quality evaluations, while the values from other methods in other studies are 4000, 8000, 10,000, 15,000, 18,000, 20,000, and 75,000. For comparison of converted simulation time \(Ti\), the proposed is faster than other methods approximately from 1.3 times to 15 times. Similarly, Tables 6 and 7 also display the strong search speed of the proposed method once other methods have used \(N_{sqe}\) = 4000, 10,000, 20,000, and 75,000 for TVD objective and \(N_{sqe}\) = 4000, 8000, 10,000, 20,000, and 25,000 for \(L\) index objective.