## 5 Numerical Results
### Investigation of the Proposed Method's Performance on the IEEE 118-Bus System  
In this section, the proposed ICOA is applied for the purpose of reducing TPL, improving voltage profile, and enhancing voltage stabilization of the IEEE 118-bus system. In addition, the application of SSA, WCA, SFOA, COA1, and COA2 methods for the system is also accomplished for further investigation of performance. The main comparison \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Method** & **Min.** & **Avg.** &
\begin{tabular}{c} **Average** \\ **Time (s)** \\ \end{tabular} & **CV** & **DV** & **SR (\%)** \\ \hline ICOA & 0.25169 & 0.26368 & 23.6 & X & & 96 \\ ICOA & 0.2583 & 0.2654 & 24.02 & & X & 92 \\ WCA & 0.2789 & 0.2824 & 29.6 & X & & 95 \\ SSA & 0.29 & 0.2991 & 24.1 & X & & 74 \\ SFO & 0.2831 & 0.2939 & 23.8 & X & & 61 \\ COA & 0.2757 & 0.2808 & 25.1 & X & & 63 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Result comparison of \(L\) index for the IEEE 57-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} & **\(N_{sqe}\)** & **_Ti (pu)_** & **CV** & **DV** & **SR (\%)** \\ \hline ICOA & 0.6051 & 0.7436 & 20.4 & 6000 & 1.00 & X & 100 \\ ICOA & 0.6155 & 0.7488 & 21 & 6000 & - & X & 100 \\ WCA & 0.7309 & 0.7913 & 27.2 & 6000 & 1.33 & X & 100 \\ SSA & 0.94 & 1.1736 & 20.9 & 6000 & 1.02 & X & 84 \\ SFO & 0.7913 & 0.9975 & 21.1 & 6000 & 1.03 & X & 70 \\ COA & 0.6711 & 0.8198 & 22.8 & 6000 & 1.12 & X & 72 \\ ALC-PSO [17] & 0.6634 & 0.6636 & 400.39 & 30,000 & 21.51 & X & - \\ KHA [38] & 0.6605 & - & 398.49 & 5000 & 21.41 & X & - \\ CKHA [38] & 0.6484 & - & 395.11 & 5000 & 21.22 & X & - \\ DSA [43] & 0.6589 & - & - & 100,000 & - & X & - \\ WCA [46] & 0.6631 & - & - & 50,000 & - & X & - \\ GBBWCA [46] & 0.6501 & - & - & 50,000 & - & X & - \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Result comparison of TVD for the IEEE 57-bus system. data consisting of minimum fitness, average fitness, \(N_{\text{\it{sage}}}\), and \(\text{\it{Ti}}\) together with others are reported in Table 11 for TPL objective, in Table 12 for TVD objective, and in Table 13 for \(L\) index objective. Other compared methods have set control variables to continuous values only and ignored the case of discrete values. Thus, analysis as well as discussion on results is only performed for the case of continuous variables. However, results from the proposed method for the case of discrete values are also reported in each comparison table. Comparisons of minimum and average fitness values among the proposed and implemented SSA, WCA, SFOA, COA, COA1, and COA2 methods shows that the proposed method is more effective in finding the best optimal solutions and more stable in the whole search process because the two values of the proposed method are less than those of these implemented ones for three objectives. The same values of \(N_{\text{\it{sage}}}\) and \(\text{\it{Ti}}\) confirm that all methods have been run on the same conditions and fair comparisons have been executed. Nevertheless, the proposed method is always superior to the methods, as observed in Figures 9-11. Approximately all runs of the proposed method could find better quality solutions for different objectives, and the fluctuations of the search process are very small, but very high fluctuations can be seen from the curves of other ones. Moreover, Figure 12 shows that nearly all loads of ICOA have voltage approximate with the reference value, 1 pu, while those from other ones are very different than 1 pu. The reported SR values in the three tables are useful for demonstrating the high potential of dealing with complicated constraints of the proposed method. For the three study cases, the proposed method handled all constraints as successfully as/more successfully than WCA, but its capability of dealing with constraints was better than other ones, especially much better than COA.