## 4 Simulation Results and Discussions
### Single-Objective OPF Problem
#### 4.1.1 IEEE 30-Bus System  
In the IEEE 30-bus system, the results including the system state variables and objective values of solving SOOPF by MaMPA for cases 1-4 are provided in Table 11 in Appendix A. The comparison results of MaMPA including real power generations, each objective value, and time with those of various methods for each considered objective are presented in Tables 2-5 where the objective value of the MaMPA when that objective was considered as the objective function are bold. The convergence curves of the MaMPA for cases 1-4 are presented in Figure 2. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Case Study** & **Objectives** & **System** \\ \hline
1 & Cost & IEEE 30-bus \\
2 & Emission & IEEE 30-bus \\
3 & Loss & IEEE 30-bus \\
4 & VSI & IEEE 30-bus \\
5 & Cost & IEEE 118-bus \\
6 & Emission & IEEE 118-bus \\
7 & Loss & IEEE 118-bus \\
8 & VSI & IEEE 118-bus \\
9 & Cost, Emission & IEEE 30-bus \\
10 & Cost, Loss & IEEE 30-bus \\
11 & Cost, VSI & IEEE 30-bus \\
12 & Emission, Loss & IEEE 30-bus \\
13 & Cost, Emission, Loss & IEEE 30-bus \\
14 & Cost, Emission, VSI & IEEE 30-bus \\
15 & Cost, Emission & IEEE 118-bus \\
16 & Cost, Loss & IEEE 118-bus \\
17 & Cost, Emission, Loss & IEEE 118-bus \\
18 & Cost, Emission, VSI & IEEE 118-bus \\
19 & Cost, Emission, Loss, VSI & IEEE 30-bus \\
20 & Cost, Emission, Loss, VSI & IEEE 118-bus \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Case study presented in this work. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Algorithms** & \(P_{gt}\) (MW) & \(P_{gt}\) (MW) & \(P_{gt}\) (MW) & \(P_{gt}\) (MW) & \(P_{gt}\) (MW) & \(P_{gt}\) (USD/h) & \(P_{gt}\) (10/h) & \(\mathbf{Cost}\) (MW) & \(\mathbf{Cost}\) (10/h) & \(\mathbf{Cost}\) (10/h) \\ \hline EP [16] & 173.8480 & 49.9980 & 21.3860 & 22.6300 & 12.9280 & 12.0000 & 802.6200 & 0.357217 & 9.3900 & - & 51.4 \\ EP-OPF [59] & 175.0297 & 48.9522 & 21.4200 & 22.7020 & 12.9040 & 12.1035 & 803.5710 & 0.360125 & 9.7114 & - & - \\ ACO [17] & 181.9450 & 47.0010 & 21.4596 & 21.4460 & 13.2070 & 12.0134 & 802.5780 & 0.38200 & 9.8520 & - & - \\ SGA [18] & 179.3607 & 44.2400 & 24.6100 & 19.9000 & 10.7100 & 14.0900 & 803.6990 & 0.371129 & 9.5177 & - & - \\ GOA [19] & - & 48.0194 & 20.9145 & 20.2342 & 15.7260 & 13.5828 & 809.7410 & - & 10.0900 & - & - \\ HHO [19] & - & 47.4072 & 17.3766 & 17.8064 & 13.1780 & 17.1314 & 804.1407 & - & 7.9700 & - & - \\ MVO [19] & - & 51.1890 & 21.3110 & 21.1730 & 22.6990 & 16.5870 & 810.9011 & - & 7.6800 & - & - \\ PSO [19] & - & 31.9013 & 15.0000 & 10.0000 & 29.9951 & 12.0000 & 828.1315 & - & 8.3502 & - & - \\ ABC [60] & - & - & - & - & - & 800.6802 & - & - & - & 25.1 \\ BBO [60] & - & - & - & - & - & - & 800.9527 & - & - & - & 28.9 \\ PSO [60] & - & - & - & - & - & - & 800.7016 & - & - & - & 27.0 \\ TLDG [60] & - & - & - & - & - & - & 800.6735 & - & - & - & 26.6 \\ ACTLBO [60] & 177.1160 & 48.7445 & 21.3225 & 21.2933 & 11.9442 & 12.0017 & 80.8411 & 0.366200 & 9.0222 & - & 26.7 \\ MaMPA & 176.2376 & 48.8430 & 21.5184 & 22.1248 & 12.2011 & 12.0000 & **802.5449** & 0.363619 & 9.5249 & 0.1388 & 25.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison results of case 1.