# 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 & \(3.68\times 10^{-26}\) & \(2.53\times 10^{-38}\) & \(9.03\times 10^{-46}\) & \(4.21\times 10^{-42}\) & \(\mathbf{3.49\times 10^{-65}}\) \\  & Median & \(1.55\times 10^{-25}\) & \(2.96\times 10^{-20}\) & \(3.83\times 10^{-45}\) & \(3.06\times 10^{-40}\) & \(\mathbf{3.32\times 10^{-64}}\) \\  & Worst & \(2.91\times 10^{-24}\) & \(2.23\times 10^{-1}\) & \(1.89\times 10^{-44}\) & \(1.82\times 10^{-37}\) & \(\mathbf{1.25\times 10^{-62}}\) \\  & Mean & \(4.25\times 10^{-25}\) & \(1.12\times 10^{-2}\) & \(6.50\times 10^{-45}\) & \(9.71\times 10^{-39}\) & \(\mathbf{1.33\times 10^{-63}}\) \\  & Std & \(6.73\times 10^{-24}\) & \(4.99\times 10^{-2}\) & \(5.98\times 10^{-45}\) & \(4.06\times 10^{-38}\) & \(\mathbf{2.83\times 10^{-63}}\) \\ \hline \multirow{6}{*}{\(f_{2}\)} & Best & \(2.18\times 10^{-64}\) & \(7.26\times 10^{-81}\) & \(8.34\times 10^{-99}\) & \(3.47\times 10^{-88}\) & \(\mathbf{6.50\times 10^{-133}}\) \\  & Median & \(6.66\times 10^{-63}\) & \(9.75\times 10^{-53}\) & \(3.13\times 10^{-97}\) & \(1.70\times 10^{-85}\) & \(\mathbf{3.47\times 10^{-130}}\) \\  & Worst & \(4.85\times 10^{-61}\) & \(1.21\times 10^{-9}\) & \(9.61\times 10^{-96}\) & \(7.77\times 10^{-80}\) & \(\mathbf{6.18\times 10^{-128}}\) \\  & Mean & \(3.86\times 10^{-62}\) & \(6.06\times 10^{-11}\) & \(1.35\times 10^{-96}\) & \(4.24\times 10^{-81}\) & \(\mathbf{5.81\times 10^{-129}}\) \\  & Std & \(1.06\times 10^{-61}\) & \(2.71\times 10^{-10}\) & \(2.42\times 10^{-96}\) & \(1.73\times 10^{-80}\) & \(\mathbf{1.51\times 10^{-128}}\) \\ \hline \multirow{6}{*}{\(f_{3}\)} & Best & \(4.66\times 10^{-15}\) & \(1.32\times 10^{-20}\) & \(1.75\times 10^{-24}\) & \(1.13\times 10^{-21}\) & \(\mathbf{2.89\times 10^{-35}}\) \\  & Median & \(8.28\times 10^{-15}\) & \(2.70\times 10^{-20}\) & \(4.49\times 10^{-24}\) & \(4.02\times 10^{-21}\) & \(\mathbf{7.69\times 10^{35}}\) \\  & Worst & \(1.46\times 10^{-14}\) & \(5.83\times 10^{-6}\) & \(8.59\times 10^{-24}\) & \(7.47\times 10^{-18}\) & \(\mathbf{2.50\times 10^{-34}}\) \\  & Mean & \(8.86\times 10^{-15}\) & \(2.92\times 10^{-7}\) & \(4.52\times 10^{-24}\) & \(4.75\times 10^{-19}\) & \(\mathbf{8.31\times 10^{-35}}\) \\  & Std & \(3.05\times 10^{-15}\) & \(1.30\times 10^{-6}\) & \(1.44\times 10^{-24}\) & \(1.70\times 10^{-18}\) & \(\mathbf{5.02\times 10^{-35}}\) \\ \hline \multirow{6}{*}{\(f_{4}\)} & Best & \(4.79\times 10^{-3}\) & \(6.89\times 10^{-2}\) & \(1.19\times 10^{-3}\) & \(8.89\times 10^{-3}\) & \(\mathbf{1.50\times 10^{-4}}\) \\  & Median & \(9.91\times 10^{-2}\) & \(2.54\times 10^{0}\) & \(9.07\times 10^{-2}\) & \(\mathbf{6.26\times 10^{-2}}\) & \(1.09\times 10^{-1}\) \\  & Worst & \(1.01\times 10^{0}\) & \(1.59\times 10^{2}\) & \(2.40\times 10^{0}\) & \(\mathbf{2.98\times 10^{-1}}\) & \(7.54\times 10^{1}\) \\  & Mean & \(1.34\times 10^{-1}\) & \(2.16\times 10^{0}\) & \(3.32\times 10^{-1}\) & \(\mathbf{8.84\times 10^{-2}}\) & \(9.87\times 10^{0}\) \\  & Std & \(2.10\times 10^{-1}\) & \(4.19\times 10^{1}\) & \(5.44\times 10^{-1}\) & \(\mathbf{8.88\times 10^{-2}}\) & \(2.24\times 10^{1}\) \\ \hline \multirow{6}{*}{\(f_{5}\)} & Best & \(\mathbf{0.00\times 10^{0}}\) & \(\mathbf{0.00\times 10^{0}}\) & \(\mathbf{0.00\times 10^{0}}\) & \(\mathbf{0.00\times 10^{0}}\) & \(\mathbf{0.00\times 10^{0}}\) \\  & Median & \(\mathbf{0.00\times 10^{0}}\) & \(6.21\times 10^{-13}\) & \(\mathbf{0.00\times 10^{0}}\) & \(\mathbf{0.00\times 10^{0}}\) & \(\mathbf{0.00\times 10^{0}}\) \\  & Worst & \(3.55\times 10^{-15}\) & \(1.15\times 10^{-1}\) & \(\mathbf{0.00\times 10^{0}}\) & \(\mathbf{0.00\times 10^{0}}\) & \(\mathbf{0.00\times 10^{0}}\) \\  & Mean & \(5.33\times 10^{-16}\) & \(9.82\times 10^{-3}\) & \(\mathbf{0.00\times 10^{0}}\) & \(\mathbf{0.00\times 10^{0}}\) & \(\mathbf{0.00\times 10^{0}}\) \\  & Std & \(1.01\times 10^{-15}\) & \(2.87\times 10^{-2}\) & \(\mathbf{0.00\times 10^{0}}\) & \(\mathbf{0.00\times 10^{0}}\) & \(\mathbf{0.00\times 10^{0}}\) \\ \hline \multirow{6}{*}{\(f_{6}\)} & Best & \(\mathbf{0.00\times 10^{0}}\) & \(\mathbf{0.00\times 10^{0}}\) & \(\mathbf{0.00\times 10^{0}}\) & \(\mathbf{0.00\times 10^{0}}\) & \(\mathbf{0.00\times 10^{0}}\) & \(\mathbf{0.00\times 10^{0}}\) \\  & Median & \(3.00\times 10^{-15}\) & \(1.94\times 10^{-15}\) & \(\mathbf{0.00\times 10^{0}}\) & \(\mathbf{0.00\times 10^{0}}\) & \(\mathbf{0.00\times 10^{0}}\) \\  & Worst & \(3.08\times 10^{-8}\) & \(5.47\times 10^{-1}\) & \(1.55\times 10^{-15}\) & \(\mathbf{0.00\times 10^{0}}\) & \(\mathbf{0.