## 4 Simulation Results and Discussions
### Single-Objective OPF Problem
#### 4.1.2 IEEE 118-Bus System  
The performance of the MaMPA in solving SOOPF problems is verified by testing in the large system which is the IEEE 118-bus system. The optimal system state variables together with the optimal solutions when each objective is chosen to be the objective function can be seen in Tables A2-A5 in Appendix A. The optimal solutions consisting of the objective values and time generated by MaMPA for cost, loss, and VSI objectives are compared with those of several algorithms as expressed in Tables 6-8 while the reference comparison of solving SOOPF by considering the emission objective could not be found. The objective value of the MaMPA when that objective was considered as the objective function are bold as in the Tables. The convergence curves generated by MaMPA for each objective, cases 5-8, are shown in Figure 3. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Algorithms** &
\begin{tabular}{c} **Cost** \\ **(USD/h)** \\ \end{tabular} & **Emis (ton/h)** & **Loss (MW)** & **VSI** & **Time (s)** \\ \hline DE [64] & 129,582.0000 & - & 79.41 & - & 89.5 \\ GWO [64] & 129,720.0000 & - & 79.58 & - & 101 \\ GSA [71] & 129,565.0000 & - & 76.19 & - & - \\ HSA [72] & 132,319.6000 & - & - & - & - \\ FHSA [72] & 132,138.3000 & - & - & - & - \\ ICBO [73] & 135,211.5704 & - & 62.73 & 0.0691 & - \\ MSA [74] & 129,640.7191 & - & 73.26 & 0.0615 & - \\ PSOGSA [75] & 129,733.5800 & - & 73.21 & - & 1280 \\ SCA [76] & 129,622.6500 & - & 76.50 & - & - \\ MSCA [76] & 129,620.2200 & - & 76.22 & - & - \\ TLBO [77] & 129,682.8440 & - & - & - & 1885 \\ DSA [77] & 129,691.6152 & - & - & - & - \\ SSA [78] & 129,675.0000 & - & 77.29 & - & 103.0 \\ ISSA [79] & 129,460.8351 & - & - & 0.0624 & - \\ SP-DE [80] & 135,055.7000 & - & 60.96 & - & 2400.0 \\ Rao-3 [81] & 129,220.6794 & - & 109.12 & - & 164.2 \\ AMTPG-Jaya [69] & 129,428.7030 & - & 76.05 & - & 94.3 \\ PSO [60] & 129,703.4800 & - & - & - & 1359.0 \\ BBO [60] & 129,734.0600 & - & - & - & 1595.0 \\ ABC [60] & 129,677.8300 & - & - & - & 1284.0 \\ TLBO [60] & 129,550.4900 & - & - & - & 741.8 \\ AGTLBO [60] & 129,543.5600 & - & 76.21 & - & 737.2 \\ MaMPA & **128,088.6942** & 6.8032 & 78.45 & 0.0625 & 171.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison results of case 5. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Algorithms** & **Cost (USD/h)** & **Emis (ton/h)** & **Loss (MW)** & **VSI** & **Time (s)** \\ \hline SSA [78] & 160,680.00 & - & 12.1930 & - & 103.0 \\ BBO [71] & 156,556,00 & - & 14.9200 & - & - \\ GSA [71] & 157,771.00 & - & 12.8800 & - & - \\ SP-DE [80] & 155,724.90 & - & 17.6946 & - & 2400.0 \\ MaMPA & 163,295.78 & 2.6964 & **11.1950** & 0.0665 & 172.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Comparison results of case 7. Figure 3: _Cont_. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Algorithms** & **Cost (USD/h)** & **Emis (ton/h)** & **Loss (MW)** & **VSI** & **Time (s)** \\ \hline NSGA-II [82] & - & - & - & 0.0690 & - \\ MNSGA-II [82] & - & - & - & 0.0660 & - \\ MaMPA & 150,972.30 & 4.9794 & 104.4672 & **0.0596** & 202.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Comparison results of case 8. In the IEEE 118-bus system, it is noticed that MaMPA provided significantly better feasible solutions for each objective than those of the various algorithms in the literature depicted in Tables 6-8. In particular, the cost value obtained by MaMPA was better than all compared algorithms for more than 1000 USD/h. The computational times of MaMPA are slower than some algorithms such as DE, GWO, SSA, Rao-3, and AMTPG-Jaya; however, they are faster than the other compared algorithms, especially PSOSA, TLBO, SP-DE, PSO, BBO, and ABC. From the convergence curves of each objective generated by MaMPA in Figure 3, it is noticeable that MaMPA could quickly converge on the feasible solution within one-fifth of the maximum iteration. Thus, MaMPA has a high performance in solving SOOPF problems in this large system.