## 6 Experimental Results
### Results
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**BenFun** & **Avg** & **StdDev** & **Med** & **Min** & **Opt** & **DMO** & **TPD** & **Max** \\ \hline \(f_{1}\) & \(4.4989\times 10^{-7}\) & \(1.6413\times 10^{-6}\) & \(4.4174\times 10^{-12}\) & \(4.9649\times 10^{-21}\) & 0 & \(4.9649\times 10^{-21}\) & N/A & \(8.3455\times 10^{-6}\) \\ \(f_{2}\) & \(3.0840\times 10^{-6}\) & \(6.4098\times 10^{-6}\) & \(2.4259\times 10^{-8}\) & \(1.5549\times 10^{-13}\) & 0 & \(1.5549\times 10^{-13}\) & N/A & \(2.0115\times 10^{-5}\) \\ \(f_{3}\) & \(5.2020\) & \(0.7963\) & \(5.5195\) & \(3.0218\) & 0 & \(3.0218\) & N/A & \(66.413\) \\ \(f_{4}\) & \(79.199\) & \(37.400\) & \(76.335\) & \(9.2776\) & 0 & \(9.2776\) & N/A & \(154.66\) \\ \(f_{5}\) & \(-1.2566\times 10^{4}\) & \(68.705\) & \(-1.2566\times 10^{4}\) & \(-1.2569\times 10^{4}\) & \(-12.569\times 10^{4}\) & \(-12.569\times 10^{4}\) & \(-12.569\times 10^{4}\) \\ \(f_{6}\) & \(34.583\) & \(17.886\) & \(30.845\) & \(4.9784\) & 0 & \(4.9748\) & N/A & \(69.647\) \\ \(f_{7}\) & \(3.1704\) & \(3.9211\) & \(0.80444\) & \(9.6590\times 10^{-10}\) & 0 & \(9.6590\times 10^{-10}\) & N/A & \(13.777\) \\ \(f_{8}\) & \(0.50737\) & \(0.50405\) & \(0.36998\) & \(1.9418\times 10^{-7}\) & 0 & \(1.9418\times 10^{-7}\) & N/A & \(1.1885\) \\ \(f_{9}\) & \(0.23693\) & \(0.28773\) & \(0.11216\) & \(1.8385\times 10^{-16}\) & \(1.8385\times 10^{-16}\) & N/A & \(1.0792\) \\ \(f_{10}\) & \(0.99800\) & \(2.5294\times 10^{-7}\) & \(0.99800\) & 0.99800 & 1 & \(-1.9962\times 10^{-3}\) & \(-01.9962\times 10^{-3}\) & \(0.99801\) \\ \(f_{11}\) & \(-1.10315\) & \(1.8408\times 10^{-4}\) & \(-1.0316\) & \(-1.0316\) & \(-1.0316285\) & \(0.000\) & \(0.0000\times 10^{-6}\) & \(-1.0310\) \\ \(f_{12}\) & \(0.39815\) & \(4.5697\times 10^{-4}\) & \(0.39794\) & \(0.39789\) & \(0.397887\) & \(1.0000\times 10^{-6}\) & \(2.5133\times 10^{-4}\) & \(0.39951\) \\ \(f_{3}\) & \(3.0097\) & \(1.6256\times 10^{-2}\) & \(3.0001\) & \(3.000\) & \(3.00\) & \(0.0000\) & \(0.0000\times 10^{-6}\) & \(3.0510\) \\ \(f_{44}\) & \(-3.8628\) & \(6.6880\times 10^{-5}\) & \(-3.8628\) & \(-3.8628\) & \(-3.8628\) & \(-2.7821\times 10^{-3}\) & \(7.2075\times 10^{-2}\) & \(-3.8624\) \\ \(f_{5}\) & \(-3.3179\) & \(2.1311\times 10^{-2}\) & \(-3.3220\) & \(-3.3220\) & \(-3.32\) & \(-1.9952\times 10^{-3}\) & \(6.0096\times 10^{-2}\) & \(-3.2031\) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Optimization results of mathematical functions tested; \(n=30\). \begin{table}
\begin{tabular}{c c c} \hline \hline
**BenFun** & **SeaSub** & **OptLoc** \\ \hline \(f_{1}\) & \([-100,100]^{30}\) & \([0]^{30}\) \\ \(f_{2}\) & \([-10,10]^{30}\) & \([0]^{30}\) \\ \(f_{3}\) & \([-1,1]^{30}\) & \([0]^{30}\) \\ \(f_{4}\) & \([-1,3]^{30}\) & \([1]^{30}\) \\ \(f_{5}\) & \([320,520]^{30}\) & \([420.9688]^{30}\) \\ \(f_{6}\) & \([-5.12,5.12]^{30}\) & \([0]^{30}\) \\ \(f_{7}\) & \([-32,32]^{30}\) & \([0]^{30}\) \\ \(f_{8}\) & \([-600,600]^{30}\) & \([0]^{30}\) \\ \(f_{9}\) & \([-50,50]^{30}\) & \([-1]^{30}\) \\ \(f_{10}\) & \([-65.536,65.536]^{2}\) & \((-31.98,-31.98)\) \\ \(f_{11}\) & \([-5,5]^{2}\) & \((0.08984,-0.7127)\) and \((-0.08984,0.7127)\) \\ \(f_{12}\) & \([-5,10]\) for \(x_{1}\) and \((-3.141,12.274)\), \((3.142,2.275)\) and \\ \([0,15]\) for \(x_{2}\) & \((9.425,2.475)\) \\ \(f_{13}\) & \([-2,2]^{2}\) & \((0.000,-1.000)\) \\ \(f_{14}\) & \([0,1]^{3}\) & \((0.115,0.556,0.853)\) \\ \(f_{15}\) & \([0,1]^{6}\) & \((0.202,0.146,0.477,0.275,0.312,0.657)\) \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Search subsets considered and the optimum locations obtained. Figure 17 shows the convergence graphics obtained by VLE for benchmark functions \(f_{1}\), \(f_{2}\), \(f_{7}\), \(f_{8}\), \(f_{10}\), and \(f_{12}\). Figure 18 shows the distribution graphics obtained by VLE for these functions.