# A Modified Artificial Bee Colony Algorithm Based on the Self-Learning Mechanism
## 4 Experiments and Results
### Experimental Results
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Functions** & **Metrics** & **ABC** & **MABC** & **GABC** & **distABC** & **SLABC** \\ \hline \multirow{6}{*}{\(f_{1}\)} & Best & \(2.39\times 10^{-10}\) & \(4.34\times 10^{-15}\) & \(1.37\times 10^{-19}\) & \(2.21\times 10^{-18}\) & \(\mathbf{1.99\times 10^{-29}}\) \\  & Median & \(1.85\times 10^{-9}\) & \(3.52\times 10^{-5}\) & \(7.20\times 10^{-19}\) & \(9.82\times 10^{-18}\) & \(\mathbf{8.70\times 10^{-29}}\) \\  & Worst & \(1.50\times 10^{-8}\) & \(2.36\times 10^{1}\) & \(3.13\times 10^{-18}\) & \(4.51\times 10^{-17}\) & \(\mathbf{4.59\times 10^{-28}}\) \\  & Mean & \(3.40\times 10^{-9}\) & \(2.32\times 10^{0}\) & \(9.29\times 10^{-19}\) & \(1.46\times 10^{-17}\) & \(\mathbf{1.25\times 10^{-28}}\) \\  & Std & \(4.09\times 10^{-8}\) & \(6.64\times 10^{0}\) & \(7.59\times 10^{-19}\) & \(1.26\times 10^{-17}\) & \(\mathbf{1.06\times 10^{-28}}\) \\ \hline \multirow{6}{*}{\(f_{2}\)} & Best & \(1.52\times 10^{-28}\) & \(6.94\times 10^{-36}\) & \(1.38\times 10^{-46}\) & \(1.42\times 10^{-41}\) & \(\mathbf{1.79\times 10^{-61}}\) \\  & Median & \(3.72\times 10^{-27}\) & \(1.46\times 10^{-23}\) & \(3.09\times 10^{-45}\) & \(1.59\times 10^{-40}\) & \(\mathbf{5.17\times 10^{-60}}\) \\  & Worst & \(7.55\times 10^{-26}\) & \(1.22\times 10^{-6}\) & \(2.74\times 10^{-44}\) & \(2.23\times 10^{-39}\) & \(\mathbf{2.17\times 10^{-58}}\) \\  & Mean & \(1.20\times 10^{-26}\) & \(7.83\times 10^{-8}\) & \(6.22\times 10^{-45}\) & \(2.85\times 10^{-40}\) & \(\mathbf{2.75\times 10^{-59}}\) \\  & Std & \(1.95\times 10^{-26}\) & \(2.79\times 10^{-7}\) & \(7.46\times 10^{-45}\) & \(4.87\times 10^{-40}\) & \(\mathbf{5.94\times 10^{-59}}\) \\ \hline \multirow{6}{*}{\(f_{3}\)} & Best & \(3.91\times 10^{-6}\) & \(1.21\times 10^{-8}\) & \(6.66\times 10^{-11}\) & \(1.06\times 10^{-9}\) & \(\mathbf{3.23\times 10^{-16}}\) \\  & Median & \(6.91\times 10^{-6}\) & \(8.46\times 10^{-7}\) & \(8.17\times 10^{-11}\) & \(2.02\times 10^{-9}\) & \(\mathbf{6.49\times 10^{-16}}\) \\  & Worst & \(1.27\times 10^{-5}\) & \(1.31\times 10^{0}\) & \(1.65\times 10^{-10}\) & \(4.96\times 10^{-9}\) & \(\mathbf{1.24\times 10^{-15}}\) \\  & Mean & \(7.55\times 10^{-6}\) & \(1.79\times 10^{-1}\) & \(9.41\times 10^{-11}\) & \(2.18\times 10^{-9}\) & \(\mathbf{6.75\times 10^{-16}}\) \\  & Std & \(2.44\times 10^{-6}\) & \(3.58\times 10^{-1}\) & \(2.77\times 10^{-11}\) & \(9.43\times 10^{-10}\) & \(\mathbf{2.71\times 10^{-16}}\) \\ \hline \multirow{6}{*}{\(f_{5}\)} & Best & \(1.84\times 10^{-1}\) & \(7.88\times 10^{0}\) & \(\mathbf{1.97\times 10^{-2}}\) & \(1.15\times 10^{-1}\) & \(4.53\times 10^{-2}\) \\  & Median & \(2.25\times 10^{0}\) & \(1.46\times 10^{2}\) & \(\mathbf{3.26\times 10^{-1}}\) & \(8.01\times 10^{-1}\) & \(2.48\times 10^{0}\) \\  & Worst & \(8.50\times 10^{0}\) & \(7.63\times 10^{2}\) & \(8.43\times 10^{1}\) & \(\mathbf{2.17\times 10^{0}}\) & \(8.20\times 10^{1}\) \\  & Mean & \(2.74\times 10^{0}\) & \(2.32\times 10^{2}\) & \(1.03\times 10^{1}\) & \(\mathbf{8.82\times 10^{-1}}\) & \(1.07\times 10^{-1}\) \\  & Std & \(2.41\times 10^{0}\) & \(2.24\times 10^{2}\) & \(2.45\times 10^{1}\) & \(\mathbf{5.49\times 10^{-1}}\) & \(2.43\times 10^{-1}\) \\ \hline \multirow{6}{*}{\(f_{6}\)} & Best & \(2.59\times 10^{-9}\) & \(2.52\times 10^{-13}\) & \(3.55\times 10^{-15}\) & \(1.21\times 10^{-11}\) & \(\mathbf{0.00\times 10^{0}}\) \\  & Median & \(9.13\times 10^{-2}\) & \(1.87\times 10^{-9}\) & \(4.35\times 10^{-14}\) & \(6.74\times 10^{-5}\) & \(\mathbf{0.00\times 10^{0}}\) \\  & Worst & \(1.99\times 10^{0}\) & \(1.46\times 10^{1}\) & \(1.03\times 10^{-12}\) & \(9.95\times 10^{-1}\) & \(\mathbf{0.00\times 10^{0}}\) \\  & Mean & \(4.89\times 10^{-1}\) & \(9.33\times 10^{-1}\) & \(1.79\times 10^{-13}\) & \(1.09\times 10^{-1}\) & \(\mathbf{0.00\times 10^{0}}\) \\  & Std & \(5.92\times 10^{-1}\) & \(3.33\times 10^{0}\) & \(2.92\times 10^{-13}\) & \(3.04\times 10^{-1}\) & \(\mathbf{0.00\times 10^{0}}\) \\ \hline \multirow{6}{*}{\(f_{7}\)} & Best & \(2.04\times 10^{-10}\) & \(8.48\times 10^{-14}\) & \(\mathbf{0.00\times 10^{0}}\) & \(\mathbf{0.00\times 10^{0}}\) & \(\mathbf{0.00\times 10^{0}}\) \\  & Median & \(1.51\times 10^{-9}\) & \(9.96\times 10^{-5}\) & \(2.78\times 10^{-16}\) & \(1.67\times 10^{-16}\) & \(\mathbf{0.00\times 10^{0}}\) \\  & Worst & \(1.50\times 10^{-8}\) & \(1.31\times 10^{0}\) & \(4.86\times 10^{-10}\) & \(6.00\times 10^{-15}\) & \(\mathbf{6.66\times 10^{-16}}\) \\  & Mean & \(3.98\times 10^{-9}\) & \(3.71\times 10^{-1}\) & \(2.64\times 10^{-11}\) & \(7.94\times 10^{-16}\) & \(\mathbf{5.55\times 10^{-17}}\) \\  & StdFigures 2-4 show how the mean of the best solution for each algorithm changes with the number of iterations times.