# An Improved Cuckoo Search Algorithm and Its Application in Robot Path Planning
## 4 Experiments and Analyses
### Performance Comparison Experiment and Result Analysis
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Function**} & \multirow{2}{*}{**Dimension**} & \multicolumn{2}{c}{**CS**} & \multicolumn{2}{c}{**ICS**} & \multicolumn{2}{c}{**ASCSA**} & \multicolumn{2}{c}{**ECS**} & \multicolumn{2}{c}{**MCSA**} & \multicolumn{2}{c}{**BASCS**} \\ \cline{3-13}  & & **Lower** & **Upper** & **Lower** & **Upper** & **Lower** & **Upper** & **Lower** & **Upper** & **Lower** & **Upper** & **Lower** & **Upper** \\ \hline \multirow{3}{*}{\(f_{1}(x)\)} & 50 & \(6.10\times\) & \(6.40\times\) & \(2.88\times\) & \(3.38\times\) & \(4.83\times\) & \(7.75\times\) & \(1.29\times\) & \(4.19\times\) & \(4.37\times\) & \(7.27\times\) & \(1.98\times\) & \(6.60\times\) \\  & \(10^{-1}\) & \(10^{-1}\) & \(10^{-1}\) & \(10^{-3}\) & \(10^{-25}\) & \(10^{-25}\) & \(10^{-25}\) & \(10^{-41}\) & \(10^{-81}\) & \(10^{0}\) & \(10^{-12}\) & \(10^{-12}\) \\  & \(100\) & \(4.15\times\) & \(4.31\times\) & \(1.00\times\) & \(1.00\times\) & \(0.00\times\) & \(0.00\times\) & \(0.00\times\) & \(5.17\times\) & \(7.67\times\) & \(0.00\times\) & \(0.00\times\) \\  & \(10^{0}\) & \(10^{0}\) & \(10^{-2}\) & \(10^{-2}\) & \(10^{0}\) & \(10^{0}\) & \(10^{0}\) & \(10^{0}\) & \(10^{0}\) & \(10^{0}\) & \(10^{0}\) & \(10^{0}\) \\ \hline \multirow{3}{*}{\(f_{2}(x)\)} & 50 & \(3.81\times\) & \(8.77\times\) & \(8.59\times\) & \(9.37\times\) & \(4.49\times\) & \(3.23\times\) & \(9.13\times\) & \(6.77\times\) & \(2.15\times\) & \(3.39\times\) & \(3.07\times\) & \(9.81\times\) \\  & \(10^{1}\) & \(10^{1}\) & \(10^{-1}\) & \(10^{-1}\) & \(10^{-14}\) & \(10^{-13}\) & \(10^{-4}\) & \(10^{-1}\) & \(10^{-1}\) & \(10^{-1}\) & \(10^{-1}\) & \(10^{-16}\) & \(10^{-16}\) \\  & \(100\) & \(2.09\times\) & \(3.93\times\) & \(1.98\times\) & \(2.14\times\) & \(0.00\times\) & \(0.00\times\) & \(0.00\times\) & \(3.00\times\) & \(7.50\times\) & \(8.90\times\) & \(0.00\times\) & \(0.00\times\) \\  & \(10^{2}\) & \(10^{2}\) & \(10^{2}\) & \(10^{2}\) & \(10^{2}\) & \(10^{2}\) & \(10^{2}\) & \(10^{2}\) & \(10^{2}\) & \(10^{2}\) & \(10^{2}\) & \(10^{2}\) & \(10^{2}\) \\ \hline \multirow{3}{*}{\(f_{3}(x)\)} & 50 & \(5.23\times\) & \(7.56\times\) & \(2.20\times\) & \(2.76\times\) & \(6.81\times\) & \(1.13\times\) & \(9.11\times\) & \(1.31\times\) & \(6.57\times\) & \(4.97\times\) & \(7.14\times\) & \(1.37\times\) \\  & \(100^{0}\) & \(10^{0}\) & \(10^{-1}\) & \(10^{-1}\) & \(10^{-1}\) & \(10^{0}\) & \(10^{0}\) & \(10^{-1}\) & \(10^{0}\) & \(10^{-2}\) & \(10^{0}\) & \(10^{-10}\) & \(10^{-10}\) \\  & \(100\) & \(3.02\times\) & \(6.90\times\) & \(1.05\times\) & \(1.47\times\) & \(1.99\times\) & \(1.99\times\) & \(3.84\times\) & \(4.46\times\) & \(4.95\times\) & \(6.07\times\) & \(0.00\times\) & \(0.00\times\) \\  & \(10^{0}\) & \(10^{0}\) & \(10^{0}\) & \(10^{0}\) & \(10^{0}\) & \(10^{0}\) & \(10^{0}\) & \(10^{0}\) & \(10^{0}\) & \(10^{0}\) & \(10^{0}\) & \(10^{0}\) & \(10^{0}\) & \(10^{0}\) \\ \hline \multirow{3}{*}{\(f_{4}(x)\)} & 50 & \(1.98\times\) & \(2.10\times\) & \(1.32\times\) & \(1.15\times\) & \(2.14\times\) & \(2.24\times\) & \(2.43\times\) & \(2.81\times\) & \(1.36\times\) & \(1.52\times\) & \(1.47\times\) & \(4.83\times\) \\  & \(10^{2}\) & \(10^{2}\) & \(10^{2}\) & \(10^{2}\) & \(10^{2}\) & \(10^{2}\) & \(10^{2}\) & \(10^{2}\) & \(10^{2}\) & \(10^{2}\) & \(10^{2}\) & \(10^{2}\) & \(10^{2}\) & \(10^{2}\) & \(10^{2}\) \\  & \(100\) & \(7.20\times\) & \(7.52\times\) & \(7.49\times\) & \(8.79\times\) & \(9.67\times\) & \(9.93\times\) & \(1.16\times\) & \(1.24\times\) & \(5.68\times\) & \(6.12\times\) & \(0.00\times\) & \(0.00\times\) \\  & \(10^{2}\) & \(10^{2}\) & \(10^{2}\) & \(10^{2}\) & \(10^{2}\) & \(10^{2}\) & \(10^{2}\) & \(10^{2}\) & \(10^{2}\) & \(10^{2}\) & \(10^{2}\) & \(10^{2}\) & \(10^{2}\) & \(10^{2}\) & \(10^{2}\) & \(10^{2}\) \\ \hline \multirow{3}{*}{\(f_{5}(x)\)} & 50 & \(6.44\times\) & \(1.09\times\) & \(2.77\times\) & \(As Figures 18-21 indicate, for both 50-dimension and 100-dimension, BASCS is capable of pinpointing the optimal solutions for multimodal functions \(f_{7}(\mathrm{x})\) and \(f_{9}(\mathrm{x})\).