## 4 Simulation and Discussion
### Results
\begin{table}
\begin{tabular}{c 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 & \(2.0255\times 10^{-17}\) & **1.6060 \(\boldsymbol{\times 10^{-157}}\)** & \multirow{2}{*}{F\({}_{8}\)} & Avg & \(-2849.0724\) & \(\boldsymbol{-12532.65497}\) & F\({}_{14}\) & Avg & \(3.5913\) & \(0.9980\) \\  & std & \(1.1369\times 10^{-32}\) & **0** & std & \(1.0168\times 10\)-12 & **2.84717 \(\boldsymbol{\times 10\text{-}12}\)** & \multirow{2}{*}{F\({}_{14}\)} & \multirow{2}{*}{Avg} & \(3.5913\) & \(0.9980\) \\ \hline \multirow{2}{*}{F\({}_{2}\)} & Avg & \(2.3072\times 10^{-08}\) & **2.4203 \(\boldsymbol{\times 10^{-08}}\)** & \multirow{2}{*}{F\({}_{9}\)} & Avg & \(1.62675\) & \multirow{2}{*}{F\({}_{15}\)} & Avg & \(0.0024\) & \(8.0939\times 10^{-4}\) \\  & std & \(5.1789\times 10^{-24}\) & **8.3748 \(\boldsymbol{\times 10^{-36}}\)** & & & \(31.3776\times 10^{-15}\)** & **0** & & std & \(2.9902\times 10^{-19}\) & \(3.5153\times 10^{-28}\) \\ \hline \multirow{2}{*}{F\({}_{3}\)} & Avg & \(2.79349\) & **1.4902 \(\boldsymbol{\times 10^{-30}}\)** & \multirow{2}{*}{F\({}_{10}\)} & Avg & \(3.5673\times 10^{-09}\) & **4.3396 \(\boldsymbol{\times 10^{-33}}\)** & \multirow{2}{*}{F\({}_{16}\)} & Avg & \(-1.0316\) \\  & std & \(1.2075\times 10^{-13}\) & **5.4834 \(\boldsymbol{\times 10^{-46}}\)** & & std & \(3.6992\times 10^{-25}\) & **9.0314 \(\boldsymbol{\times 10^{-29}}\)** & & std & \(5.9580\times 10^{-16}\) & \(6.4545\times 10^{-34}\) \\ \hline \multirow{2}{*}{F\({}_{4}\)} & Avg & \(3.2547\times 10^{-9}\) & **7.1301 \(\boldsymbol{\times 10^{-71}}\)** & \multirow{2}{*}{F\({}_{11}\)} & Avg & \(3.7375\) & **0.0311** & \multirow{2}{*}{F\({}_{17}\)} & Avg & \(0.3978\) & **0.3978** \\  & std & \(2.0346\times 10^{-24}\) & **3.5969 \(\boldsymbol{\times 10^{-87}}\)** & & std & \(2.7804\times 10^{-15}\) & **0** & & std & \(9.9301\times 10^{-17}\) & **0** \\ \hline \multirow{2}{*}{F\({}_{5}\)} & Avg & \(36.10695\) & **23.1212** & \multirow{2}{*}{F\({}_{12}\)} & Avg & \(0.0362\) & \(\boldsymbol{2.319\times 10^{-27}}\)** & \multirow{2}{*}{F\({}_{18}\)} & Avg & \(3\) & **3** \\  & std & \(3.0982\times 10^{-14}\) & **5.5608 \(\boldsymbol{\times 10^{-15}}\)** & & std & \(6.2063\times 10^{-18}\) & **1.0829 \(\boldsymbol{\times 10^{-27}}\)** & & std & \(6.9511\times 10^{-16}\) & \(1.2909\times 10^{-35}\) \\ \hline \multirow{2}{*}{F\({}_{6}\)} & Avg & \(0\) & **0** & \multirow{2}{*}{F\({}_{13}\)} & Avg & \(0.0020\) & \(\boldsymbol{2.5758\times 10^{-26}}\)** & \multirow{2}{*}{F\({}_{19}\)} & Avg & \(-3.8627\) & \(-3.8627\) \\  & std & \(0\) & **0** & & std & \(4.2617\times 10^{-14}\) & **7.7006 \(\boldsymbol{\times 10^{-26}}\)** & & std & \(8.3413\times 10^{-15}\) & \(6.3248\times 10^{-29}\) \\ \hline \multirow{2}{*}{F\({}_{7}\)} & Avg & \(0.0206\) & **7.4501 \(\boldsymbol{\times 10^{-4}}\)** & \multirow{2}{*}{F\({}_{20}\)} & Avg & \(-3.0396\) & \(-3.3219\) \\  & std & \(2.7152\times 10^{-18}\) & **1.9394 \(\boldsymbol{\times 10^{-29}}\)** & & & & std & \(2.1846\times 10^{-14}\) & \(\boldsymbol{1.9860\times 10^{-25}}\) \\ \hline \multirow{2}{*}{F\({}_{21}\)} & Avg & \(-5.1486\) & \multirow{2}{*}{F\({}_{10.1531}\)} & Avg & \(-5.1486\) & \multirow{2}{*}{**-10.1531**} \\  & std & \(2.2970\times 10^{-16}\) & & & & & \(2.2970\times 10^{-16}\) & \(1.1916\times 10^{-24}\) \\ \hline \multirow{2}{*}{F\({}_{22}\)} & Avg & \(-9.0239\) & \multirow{2}{*}{**-10.4029**} & \multirow{2}{*}{**-10.4029**} \\  & std & \(1.6484\times 10^{-12}\) & **1.3505 \(\boldsymbol{\times 10^{-34}}\)** & & & \(2.3505\times 10^{-34}\) \\ \hline \multirow{2}{*}{F\({}_{23}\)} & Avg & \(-8.9045\) & \multirow{2}{*}{**-10.5364**} & \multirow{2}{*}{**-10.5364**} \\  & std & \(7.1497\times 10^{-14}\) & & & \(7.1497\times 10^{-14}\) & **5.95808 \(\boldsymbol{\times 10^{-48}}\)** \\ \hline \end{tabular}
\end{table}