## 4 Simulation and Discussion
### Results
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Unimodal**} & \multicolumn{3}{c}{**Multimodal**} & \multicolumn{3}{c}{**Fixed-Dimension Multimodal**} \\  & \multicolumn{2}{c}{**Original**} & \multicolumn{2}{c}{**DM**} & \multicolumn{2}{c}{**Original**} & \multicolumn{2}{c}{**DM**} & \multicolumn{2}{c}{**Original**} & \multicolumn{2}{c}{**DM**} \\ \hline \multirow{2}{*}{F\({}_{1}\)} & Avg & \(1.09\times 10^{-88}\) & \(\mathbf{2.84\times 10^{-278}}\) & \(\mathbf{F_{8}}\) & Avg & \(-5885.1172\) & \(\mathbf{-11901.9832}\) & F\({}_{14}\) & Avg & \(3.7408\) & \(\mathbf{1.3948}\) \\  & std & \(5.1413\times 10^{-74}\) & \(\mathbf{0}\) & \(\mathbf{0}\) & std & \(2.0336\times 10^{-12}\) & \(\mathbf{4.8808\times 10^{-41}}\) & & std & \(6.4545\times 10^{-15}\) & \(\mathbf{8.44062\times 10^{-16}}\) \\ \hline \multirow{2}{*}{F\({}_{2}\)} & Avg & \(1.2952\times 10^{-34}\) & \(\mathbf{1.6523\times 10^{-137}}\) & F\({}_{9}\) & Avg & \(8.5265\times 10^{-15}\) & \(\mathbf{0}\) & F\({}_{15}\) & Avg & \(0.0063\) & \(\mathbf{0.0043}\) \\  & std & \(1.9127\times 10^{-10}\) & \(\mathbf{1.2275\times 10^{-182}}\) & \(\mathbf{F_{9}}\) & Avg & \(5.54646\times 10^{-30}\) & \(\mathbf{0}\) & \(\mathbf{0}\) & \(1.1636\times 10^{-18}\) & \(\mathbf{3.10317\times 10^{-28}}\) \\ \hline \multirow{2}{*}{F\({}_{3}\)} & Avg & \(7.4091\times 10^{-15}\) & \(\mathbf{1.0362\times 10^{-30}}\) & Avg & \(1.7053\times 10^{-14}\) & \(\mathbf{1.0835\times 10^{-14}}\) & F\({}_{16}\) & Avg & \(-1.0316\) & \(\mathbf{-1.0316}\) \\  & std & \(5.6446\times 10^{-30}\) & \(\mathbf{1.2533\times 10^{-15}}\) & std & \(2.7517\times 10^{-29}\) & \(\mathbf{2.8223\times 10^{-30}}\) & & std & \(3.9720\times 10^{-16}\) & \(\mathbf{5.9580\times 10^{-26}}\) \\ \hline \multirow{2}{*}{F\({}_{4}\)} & Avg & \(1.2599\times 10^{-14}\) & \(\mathbf{2.5914\times 10^{-47}}\) & \multirow{2}{*}{F\({}_{11}\)} & Avg & \(0.0037\) & \(\mathbf{0.0014}\) & \multirow{2}{*}{F\({}_{17}\)} & Avg & \(0.3978\) & \(\mathbf{0.3978}\) \\  & std & \(1.0583\times 10^{-29}\) & \(\mathbf{2.1742\times 10^{-43}}\) & & std & \(1.2606\times 10^{-18}\) & \(\mathbf{0}\) & std & \(8.6888\times 10^{-17}\) & \(\mathbf{1.2412\times 10^{-19}}\) \\ \hline \multirow{2}{*}{F\({}_{5}\)} & Avg & \(26.8607\) & \(\mathbf{4.9282}\) & & \(0.0372\) & \(\mathbf{1.0468\times 10^{-90}}\) & & \(\mathbf{1.03}\) & \(\mathbf{3.0000}\) \\  & std & \(0\) & \(\mathbf{0}\) & & std & \(4.3444\times 10^{-17}\) & \(\mathbf{3.2368\times 10^{-25}}\) & & std & \(2.0853\times 10^{-15}\) & \(\mathbf{2.0853\times 10^{-18}}\) \\ \hline \multirow{2}{*}{F\({}_{6}\)} & Avg & \(0.6423\) & \(\mathbf{9.6762\times 10^{-69}}\) & F\({}_{13}\) & Avg & \(5.5763\) & \(\mathbf{9.4403\times 10^{-90}}\) & & \(-3.8621\) \\  & std & \(6.2063\times 10^{-17}\) & \(\mathbf{7.3985\times 10^{-24}}\) & std & \(2.4825\times 10^{-16}\) & \(\mathbf{3.6992\times 10^{-34}}\) & & std & \(2.4825\times 10^{-15}\) & \(\mathbf{0}\) \\ \hline \multirow{2}{*}{F\({}_{7}\)} & Avg & \(0.0008\) & \(\mathbf{0.0005}\) & & & & & \(-3.2523\) & \(\mathbf{-3.2982}\) \\  & std & \(7.2730\times 10^{-20}\) & \(\mathbf{1.3934\times 10^{-29}}\) & & & & & \(2.1846\times 10^{-15}\) & \(\mathbf{1.8867\times 10^{-30}}\) \\ \hline \multirow{2}{*}{F\({}_{2}\)} & Avg & \(9.6452\) & \(-\mathbf{10.1531}\) & Avg & \(9.6452\) & \(-\mathbf{10.1531}\) & \(\mathbf{1.1916\times 10^{-32}}\) \\  & std & \(6.538\times 10^{-15}\) & \(\mathbf{1.1916\times 10^{-32}}\) & & & & \(\mathbf{1.1916\times 10^{-32}}\) \\ \hline \multirow{2}{*}{F\({}_{22}\)} & Avg & \(-10.4025\) & \(-\mathbf{10.4029}\) & \(\mathbf{1.0429}\) & \(\mathbf{1.0429}\) & \(\mathbf{1.0429}\) \\  & std & \(1.9860\times 10^{-15}\) & \(\mathbf{1.1519\times 10^{-25}}\) & \(\mathbf{1. Figure 3: The convergence curves of GA for original and “modified by DM” versions. Figure 4: The convergence curves of PSO for original and “modified by DM” versions. Figure 5: The convergence curves of GSA for original and “modified by DM” versions. Figure 6: The convergence curves of TLBO for original and “modified by DM” versions.