## 6 Experimental Results
### Results
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**BenFun** & **Statistic** & **VLE** & **PSO** & **GSA** & **DE** & **WOA** \\ \hline \(f_{1}\) & Avg & \(4.4989\times 10^{-7}\) & \(1.3600\times 10^{-4}\) & \(2.5300\times 10^{-16}\) & \(8.2000\times 10^{-14}\) & \(1.4100\times 10^{-30}\) \\  & StdDev & \(1.413\times 10^{-6}\) & \(2.0200\times 10^{-4}\) & \(9.6700\times 10^{-17}\) & \(5.9000\times 10^{-14}\) & \(4.9100\times 10^{-30}\) \\ \(f_{2}\) & Avg & \(3.0840\times 10^{-6}\) & \(4.2144\times 10^{-2}\) & \(5.5655\times 10^{-2}\) & \(1.5000\times 10^{-9}\) & \(1.0600\times 10^{-21}\) \\  & StdDev & \(6.0498\times 10^{-6}\) & \(4.5421\times 10^{-2}\) & \(0.19407\) & \(9.9000\times 10^{-10}\) & \(2.3900\times 10^{-21}\) \\ \(f_{3}\) & Avg & \(5.2020\) & \(70.126\) & \(8.9653\times 10^{2}\) & \(6.8000\times 10^{-11}\) & \(5.3900\times 10^{-7}\) \\  & StdDev & \(0.79863\) & \(22.119\) & \(3.1896\times 10^{2}\) & \(7.4000\times 10^{-11}\) & \(2.9300\times 10^{-6}\) \\ \(f_{4}\) & Avg & \(79.199\) & \(96.718\) & \(67.543\) & \(0.0000\) & \(27.866\) \\  & StdDev & \(37.400\) & \(60.116\) & \(62.225\) & \(0.0000\) & \(0.76363\) \\ \(f_{5}\) & Avg & \(-1.2566\times 10^{4}\) & \(-4.8413\times 10^{3}\) & \(-2.8211\times 10^{3}\) & \(-1.1080\times 10^{4}\) & \(-5.0808\times 10^{3}\) \\  & StdDev & \(68.705\) & \(1.1528\times 10^{3}\) & \(4.9304\times 10^{2}\) & \(5.7470\times 10^{2}\) & \(6.9580\times 10^{2}\) \\ \(f_{6}\) & Avg & \(34.5830\) & \(46.704\) & \(25.968\) & \(69.200\) & \(0.0000\) \\  & StdDev & \(17.8860\) & \(11.629\) & \(7.4701\) & \(38.800\) & \(0.0000\) \\ \(f_{7}\) & Avg & \(3.1704\) & \(0.27602\) & \(6.2087\times 10^{-2}\) & \(9.7000\times 10^{-8}\) & \(7.4043\) \\  & StdDev & \(3.9211\) & \(0.50901\) & \(0.23628\) & \(4.2000\times 10^{-8}\) & \(9.8976\) \\ \(f_{8}\) & Avg & \(0.50737\) & \(9.2150\times 10^{-3}\) & \(27.702\) & \(0.0000\) & \(2.8900\times 10^{-4}\) \\  & StdDev & \(0.50405\) & \(7.7240\times 10^{-3}\) & \(5.0403\) & \(0.0000\) & \(1.5860\times 10^{-3}\) \\ \(f_{9}\) & Avg & \(0.23693\) & \(6.9170\times 10^{-3}\) & \(1.7996\) & \(7.9000\times 10^{-15}\) & \(0.33968\) \\  & StdDev & \(0.28773\) & \(2.6301\times 10^{-2}\) & \(0.95114\) & \(8.0000\times 10^{-15}\) & \(0.214864\) \\ \(f_{10}\) & Avg & \(0.99800\) & \(3.6272\) & \(5.8598\) & \(0.99800\) & \(2.1120\) \\  & StdDev & \(2.5294\times 10^{-7}\) & \(2.5608\) & \(3.8313\) & \(3.3000\times 10^{-16}\) & \(2.4986\) \\ \(f_{11}\) & Avg & \(-1.0315\) & \(-1.0316\) & \(-1.0316\) & \(-1.0316\) & \(-1.0316\) \\  & StdDev & \(1.8408\times 10^{-4}\) & \(6.2500\times 10^{-16}\) & \(4.8800\times 10^{-16}\) & \(3.1000\times 10^{-13}\) & \(4.2000\times 10^{-7}\) \\ \(f_{12}\) & Avg & \(0.39815\) & \(0.39789\) & \(0.39789\) & \(0.39789\) & \(0.39791\) \\  & StdDev & \(4.5697\times 10^{-4}\) & \(0.0000\) & \(0.0000\) & \(9.9000\times 10^{-9}\) & \(2.7000\times 10^{-5}\) \\ \(f_{13}\) & Avg & \(3.0097\) & \(3.0000\) & \(3.0000\) & \(3.0000\) & \(3.0000\) \\  & StdDev & \(1.6256\times 10^{-2}\) & \(1.3300\times 10^{-15}\) & \(4.1700\times 10^{-15}\) & \(2.0000\times 10^{-15}\) & \(4.2200\times 10^{-15}\) \\ \(f_{14}\) & Avg & \(-3.8628\) & \(-3.8628\) & \(-3.8628\) & N/A & \(-3.8562\) \\  & StdDev & \(6.6880\times 10^{-5}\) & \(2.5800\times 10^{-15}\) & \(2.2900\times 10^{-15}\) & N/A & \(2.7060\times 10^{-3}\) \\ \(f_{15}\) & Avg & \(-3.3179\) & \(-3.2663\) & \(-3.3178\) & N/A & \(-2.9811\) \\  & StdDev & \(2.1311\times 10^{-2}\) & \(6.0516\times 10^{-2}\) & \(2.3081\times 10^{-2}\) & N/A & \(0.37665\) \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Averages and standard deviations obtained by VLE, and published for PSO, GSA, DE and WOA, using the classical benchmark functions; \(n=30\).