# Determining Optimal Power Flow Solutions Using New Adaptive Gaussian TLBO Method
## 4 Numerical Results
### Discussion on Results
\begin{table}
\begin{tabular}{l l l l l l} \hline \hline \multirow{2}{*}{**Optimizer**} & \multicolumn{1}{l}{**Min**} & \multicolumn{1}{l}{**Mean**} & \multicolumn{1}{l}{**Max**} & \multicolumn{1}{l}{**Std.**} & \multicolumn{1}{l}{**Time (s)**} \\ \cline{2-5}  & \multicolumn{1}{l}{**Case 1**} & & & & \\ \hline AGTLBO & 800.4811 & 800.5316 & 800.5587 & 0.076 & 26.7 \\ TLBO & 800.6735 & 800.8705 & 801.1324 & 0.542 & 26.6 \\ ABC & 800.6802 & 800.9642 & 802.1506 & 1.819 & 25.1 \\ BBO & 800.9527 & 802.3304 & 805.3919 & 3.994 & 28.9 \\ PSO & 800.7016 & 801.4378 & 803.8826 & 2.075 & 27.0 \\ \hline \multirow{2}{*}{**Optimizer**} & \multicolumn{1}{l}{**Min**} & \multicolumn{1}{l}{**Mean**} & \multicolumn{1}{l}{**Max**} & \multicolumn{1}{l}{**Std.**} & \multicolumn{1}{l}{**Time (s)**} \\ \cline{2-5}  & \multicolumn{1}{l}{**Case 2**} & & & \\ \hline AGTLBO & 646.4511 & 646.6973 & 646.9005 & 0.094 & 26.8 \\ TLBO & 647.1344 & 647.8260 & 648.4326 & 0.927 & 26.7 \\ ABC & 647.4256 & 648.2013 & 648.8591 & 1.748 & 26.4 \\ BBO & 647.7739 & 649.2835 & 651.7072 & 3.690 & 29.0 \\ PSO & 647.6495 & 648.9424 & 650.6625 & 2.514 & 27.3 \\ \hline \multirow{2}{*}{**Optimizer**} & \multicolumn{1}{l}{**Min**} & \multicolumn{1}{l}{**Mean**} & \multicolumn{1}{l}{**Max**} & \multicolumn{1}{l}{**Std.**} & \multicolumn{1}{l}{**Time (s)**} \\ \cline{2-5}  & \multicolumn{1}{l}{**Case 3**} & & & & \\ \hline AGTLBO & 0.20482 & 0.20483 & 0.20484 & 0.000 & 27.0 \\ TLBO & 0.20484 & 0.20490 & 0.20495 & 0.006 & 27.0 \\ ABC & 0.20484 & 0.20505 & 0.20557 & 0.009 & 26.2 \\ BBO & 0.20490 & 0.20532 & 0.20603 & 0.010 & 29.1 \\ PSO & 0.20484 & 0.20496 & 0.20551 & 0.009 & 27.5 \\ \hline \multirow{2}{*}{**Optimizer**} & \multicolumn{1}{l}{**Min**} & \multicolumn{1}{l}{**Mean**} & \multicolumn{1}{l}{**Max**} & \multicolumn{1}{l}{**Std.**} & \multicolumn{1}{l}{**Time (s)**} \\ \cline{2-5}  & \multicolumn{1}{l}{**Case 4**} & & & & \\ \hline AGTLBO & 3.0906 & 3.0911 & 3.0920 & 0.000 & 27.5 \\ TLBO & 3.1104 & 3.1133 & 3.1275 & 0.062 & 27.3 \\ ABC & 3.1314 & 3.1682 & 3.2074 & 0.103 & 26.8 \\ BBO & 3.1725 & 3.2490 & 3.3178 & 0.199 & 29.5 \\ PSO & 3.1709 & 3.1770 & 3.2235 & 0.071 & 27.7 \\ \hline \multirow{2}{*}{**Optimizer**} & \multicolumn{1}{l}{**Min**} & \multicolumn{1}{l}{**Mean**} & \multicolumn{1}{l}{**Max**} & \multicolumn{1}{l}{**Std.**} & \multicolumn{1}{l}{**Time (s)**} \\ \cline{2-5}  & \multicolumn{1}{l}{**Case 5**} & & & & \\ \hline AGTLBO & 832.1624 & 832.2364 & 832.3047 & 0.402 & 27.4 \\ TLBO & 832.5325 & 832.8761 & 833.4422 & 0.953 & 27.3 \\ ABC & 832.5860 & 833.0923 & 833.4986 & 1.046 & 26.9 \\ BBO & 832.9234 & 834.7060 & 836.6011 & 2.814 & 29.4 \\ PSO & 832.5966 & 832.9648 & 834.5746 & 1.983 & 28.0 \\ \hline \multirow{2}{*}{**Optimizer**} & \multicolumn{1}{l}{**Min**} & \multicolumn{1}{l}{**Mean**} & \multicolumn{1}{l}{**Max**} & \multicolumn{1}{l}{**Std.**} & \multicolumn{1}{l}{**Time (s)**} \\ \cline{2-5}  & \multicolumn{1}{l}{**Case 9**} & & & & \\ \hline AGTLBO & 41,678.310 & 41,684.744 & 41,692.19 & 24.36 & 71.3 \\ TLBO & 41,679.890 & 41,690.376 & 41,710.38 & 38.15 & 72.5 \\ ABC & 41,681.704 & 41,695.058 & 41,712.74 & 45.90 & 83.8 \\ BBO & 41,697.552 & 41,728.918 & 41,765.75 & 133.4 & 107.6 \\ PSO & 41,683.951 & 41,697.120 & 41,714.54 & 75.62 & 88.9 \\ \hline \multirow{2}{*}{**Optimizer**} & \multicolumn{1}{l}{**Min**} & \multicolumn{1}{l}{**Mean**} & \multicolumn{1}{l}{**Max**} & \multicolumn{1}{l}{**Std.**} & \multicolumn{1}{l}{**Time (s)**} \\ \cline{2-5}  & \multicolumn{1}{l}{**Case 12**} & & & & \\ \hline AGTLBO & 129,545.56 & 129,552.92 & 129,562.3 & 8.53 & 740.2 \\ TLBO & 129,550.49 & 129,607.63 & 129,691.0 & 72.14 & 741.8 \\ ABC & 129,677.83 & 129,732.46 & 130,896.6 & 446.8 & 1284 \\ BBO & 129,734.06 & 129,985.25 & 132,268.8 & 995.2 & 1595 \\ PSO & 129,703.48 & 129,867.01 & 131,573.7 & 610.7 & 1359 \\ \hline \hline \end{tabular}
\end{table} 
Table 18: Statistical results to show the performance of proposed AGTLBO and other algorithms. Figure 8: Convergence of algorithms for Case 2. Figure 7: Convergence of algorithms for Case 1.