# 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 & \(1.11\times 10^{-6}\) & \(3.72\times 10^{-6}\) & \(3.28\times 10^{-10}\) & \(2.29\times 10^{-10}\) & \(\mathbf{5.23\times 10^{-16}}\) \\  & Median & \(7.55\times 10^{-6}\) & \(3.45\times 10^{-1}\) & \(2.25\times 10^{-9}\) & \(2.10\times 10^{-9}\) & \(\mathbf{1.79\times 10^{-15}}\) \\  & Worst & \(4.46\times 10^{-5}\) & \(1.12\times 10^{2}\) & \(4.01\times 10^{-9}\) & \(2.71\times 10^{-7}\) & \(\mathbf{7.16\times 10^{-15}}\) \\  & Mean & \(1.25\times 10^{-5}\) & \(1.82\times 10^{1}\) & \(2.11\times 10^{-9}\) & \(1.82\times 10^{-8}\) & \(\mathbf{2.46\times 10^{-15}}\) \\  & Std & \(1.27\times 10^{-5}\) & \(3.55\times 10^{1}\) & \(1.02\times 10^{-9}\) & \(6.00\times 10^{-8}\) & \(\mathbf{1.87\times 10^{-15}}\) \\ \hline \multirow{6}{*}{\(f_{2}\)} & Best & \(7.38\times 10^{-17}\) & \(3.76\times 10^{-18}\) & \(1.21\times 10^{-25}\) & \(1.67\times 10^{-23}\) & \(\mathbf{4.98\times 10^{-35}}\) \\  & Median & \(9.25\times 10^{-16}\) & \(9.42\times 10^{-12}\) & \(4.18\times 10^{-25}\) & \(1.16\times 10^{-21}\) & \(\mathbf{3.08\times 10^{-34}}\) \\  & Worst & \(1.84\times 10^{-14}\) & \(1.48\times 10^{-3}\) & \(2.23\times 10^{-24}\) & \(5.76\times 10^{-21}\) & \(\mathbf{2.10\times 10^{-32}}\) \\  & Mean & \(3.04\times 10^{-15}\) & \(1.38\times 10^{-4}\) & \(5.64\times 10^{-25}\) & \(1.73\times 10^{-21}\) & \(\mathbf{2.68\times 10^{-33}}\) \\  & Std & \(4.56\times 10^{-15}\) & \(3.61\times 10^{-4}\) & \(4.75\times 10^{-25}\) & \(1.71\times 10^{-21}\) & \(\mathbf{5.43\times 10^{-33}}\) \\ \hline \multirow{6}{*}{\(f_{3}\)} & Best & \(1.79\times 10^{-3}\) & \(7.51\times 10^{-4}\) & \(6.21\times 10^{-6}\) & \(7.15\times 10^{-5}\) & \(\mathbf{3.87\times 10^{-9}}\) \\  & Median & \(2.71\times 10^{-3}\) & \(2.28\times 10^{-2}\) & \(1.39\times 10^{-5}\) & \(1.35\times 10^{-4}\) & \(\mathbf{9.02\times 10^{-9}}\) \\  & Worst & \(5.86\times 10^{-3}\) & \(8.83\times 10^{0}\) & \(3.36\times 10^{-5}\) & \(1.70\times 10^{-4}\) & \(\mathbf{2.08\times 10^{-8}}\) \\  & Mean & \(3.11\times 10^{-3}\) & \(8.79\times 10^{-1}\) & \(1.57\times 10^{-5}\) & \(1.30\times 10^{-4}\) & \(\mathbf{9.2\times 10^{-9}}\) \\  & Std & \(1.26\times 10^{-3}\) & \(2.25\times 10^{0}\) & \(6.59\times 10^{-6}\) & \(2.92\times 10^{-5}\) & \(\mathbf{3.57\times 10^{-9}}\) \\ \hline \multirow{6}{*}{\(f_{4}\)} & Best & \(9.12\times 10^{0}\) & \(1.46\times 10^{2}\) & \(2.95\times 10^{-1}\) & \(3.48\times 10^{0}\) & \(\mathbf{2.66\times 10^{-2}}\) \\  & Median & \(2.68\times 10^{1}\) & \(1.17\times 10^{3}\) & \(8.00\times 10^{1}\) & \(1.71\times 10^{1}\) & \(\mathbf{3.60\times 10^{0}}\) \\  & Worst & \(8.31\times 10^{1}\) & \(1.14\times 10^{4}\) & \(1.88\times 10^{2}\) & \(\mathbf{4.78\times 10^{1}}\) & \(1.45\times 10^{2}\) \\  & Mean & \(3.09\times 10^{1}\) & \(2.28\times 10^{3}\) & \(6.83\times 10^{1}\) & \(\mathbf{1.87\times 10^{1}}\) & \(2.23\times 10^{1}\) \\  & Std & \(1.83\times 10^{1}\) & \(2.88\times 10^{3}\) & \(5.76\times 10^{1}\) & \(\mathbf{1.11\times 10^{1}}\) & \(3.98\times 10^{1}\) \\ \hline \multirow{6}{*}{\(f_{5}\)} & Best & \(1.14\times 10^{1}\) & \(1.47\times 10^{-4}\) & \(1.08\times 10^{0}\) & \(8.46\times 10^{0}\) & \(\mathbf{1.11\times 10^{-10}}\) \\  & Median & \(1.70\times 10^{1}\) & \(7.63\times 10^{-1}\) & \(2.24\times 10^{0}\) & \(1.08\times 10^{1}\) & \(\mathbf{1.68\times 10^{-9}}\) \\  & Worst & \(2.24\times 10^{1}\) & \(6.76\times 10^{1}\) & \(4.04\times 10^{0}\) & \(1.30\times 10^{1}\) & \(\mathbf{2.98\times 10^{-8}}\) \\  & Mean & \(1.67\times 10^{1}\) & \(1.33\times 10^{1}\) & \(2.55\times 10^{0}\) & \(1.08\times 10^{1}\) & \(\mathbf{4.55\times 10^{-9}}\) \\  & Std & \(3.17\times 10^{0}\) & \(2.12\times 10^{1}\) & \(8.29\times 10^{-1}\) & \(1.23\times 10^{0}\) & \(\mathbf{7.09\times 10^{-9}}\) \\ \hline \multirow{6}{*}{\(f_{6}\)} & Best & \(2.46\times 10^{-6}\) & \(2.00\times 10^{-6}\) & \(4.27\times 10^{-10}\) & \(3.10\times 10^{-8}\) & \(\mathbf{1.77\times 10^{-13}}\) \\  & Median & \(2.45\times 10^{-5}\) & \(4.55\times 10^{-2}\) & \(2.05\times 10^{-9}\) & \(1.49\times 10^{-7}\) & \(\mathbf{1.49\times 10^{-12}}\) \\  & Worst & \(9.39\times 10^{-4}\) & \(2.44\times 10^{0}\) & \(6.47\times 10^{-7}\) & \(2.27\times 10^{-6}\) & \(\mathbf{1.18\times 10^{-11}}\) \\  & Mean & \(1.08\times 10^{-4}\) & \(6.46\times 10^{-1}\) &The distABC algorithm is better than SLABC algorithm on the convergence rate and the accuracy of the solution.