## 5 Numerical Results
### Investigation of the Proposed Method's Performance on 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} & \(\mathbf{N_{sqe}}\) & **Ti (pu)** & **CV** & **DV** & **SR (\%)** \\ \hline ICOA & 22.376 & 24.9062 & 21.4 & 6000 & 1.00 & X & 100 \\ ICOA & 22.383 & 25.046 & 21.8 & 6000 & & X & 100 \\ WCA & 26.0402 & 26.5319 & 27.4 & 6000 & 1.05 & X & 100 \\ SSA & 25.3854 & 27.0306 & 21.8 & 6000 & 1.02 & X & 88 \\ SFOA & 26.6541 & 28.4249 & 21.3 & 6000 & 1.00 & X & 67 \\ COA & 24.5358 & 26.8983 & 23.2 & 6000 & 1.08 & X & 74 \\ SGA [14] & 23.836 & - & & 18,000 & - & X & - \\ ALC-PSO [17] & 23.39 & 23.41 & 300.78 & 30,000 & 15.40 & X & - \\ PSO [21] & 24.7742 & - & 927 & 100,000 & 39.71 & - & - \\ ICA [21] & 24.1607 & - & 1018 & 100,000 & 43.61 & - & - \\ HPSO-ICA [21] & 24.1386 & - & 1450 & 100,000 & 62.11 & - & - \\ SGA [37] & 25.64 & 26.8378 & - & - & - & - & - \\ PSO [37] & 25.03 & 26.4742 & - & - & - & - & - \\ has [37] & 24.9059 & 26.9653 & - & - & - & - & - \\ KHA [38] & 23.41 & - & 303.15 & 10,000 & 15.52 & X & - \\ CKHA [38] & 23.38 & - & 301.12 & 10,000 & 15.42 & X & - \\ DSA [43] & 23.35 & - & - & 200,000 & - & X & - \\ GSA [45] & 24.4922 & - & - & - & - & X & - \\ PSO [45] & 24.3826 & - & - & - & - & X & - \\ CSA [45] & 24.2619 & - & - & - & - & X & - \\ WCA [46] & 24.82 & - & - & - & - & X & - \\ GBBWCA [46] & 23.27 & - & - & - & - & X & - \\ MFQ [48] & 24.5293 & - & - & 9000 & - & X & - \\ MOGWA [49] & 21.171 & - & - & - & - & - & - \\ GSA [29] & 23.46 & - & 321.4872 & & 16.46 & X & - \\ SGA [37] & 25.64 & 26.8378 & - & - & - & - & - \\ PSO [37] & 25.03 & 26.4742 & - & - & - & - & - \\ HAS [37] & 24.9059 & 26.9653 & - & - & - & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Result comparison of TPL for the IEEE 57-bus system. The performance of the proposed ICOA approach is also evaluated effectively and strongly as comparisons with other approaches are carried out and analyzed. In fact, the proposed ICOA approach can find out more effective optimal solutions than almost all methods for TPL optimization and all methods for TVD optimization. Only MOGWA [49] has shown TPL of 21.171 MW, which is less than that of the proposed ICOA approach; however, the verification implies that the optimal solution has not been shown in the study [49]. Other comparisons with the second-best solution and the worst solution indicate that the proposed ICOA approach can reduce TPL from 0.894 to 3.264 MW, corresponding to the improvement level from 3.99% to 14.59%. The proposed ICOA approach also finds less TVD than others from 0.0433 to 0.1258 pu, corresponding to the improvement level from 7.16% to 20.79%. The average of 50 runs found by the proposed ICOA approach is less than almost all methods excluding ALC-PSO [17]. However, it should be pointed out that the method has used a much higher value for \(N_{sqe}\) than the proposed ICOA approach. Namely, \(N_{sqe}\) is 30,000 for ALC-PSO [17] but 6000 for the proposed ICOA approach. The reported values of _Ti_ also lead to the same manner, since the proposed method can be faster than other methods by approximately 15-62 times for TPL optimization and approximately 21 times for TVD optimization. Consequently, there are enough evidences consisting of the best optimal solution, the best stabilization of search, and the fastest search ability to conclude that the proposed ICOA approach is the most effective solution for the ORPD problem with IEEE 57-bus system. Optimal solutions obtained by the proposed method for IEEE 57-bus system are given in Table 10 in Appendix A.