# An Improved Cuckoo Search Algorithm and Its Application in Robot Path Planning
## 4 Experiments and Analyses
### Performance Comparison Experiment and Result Analysis
\begin{tabular}{c c c c c c c c} \hline \hline
**Function** & **Index** & **CS** & **ICS** & **ASCSA** & **ECS** & **MCSA** & **BASCS** \\ \hline \multirow{2}{*}{\(f_{1}(x)\)} & mean & \(6.25\times 10^{-1}\) & \(3.13\times 10^{-3}\) & \(6.29\times 10^{-25}\) & \(2.74\times 10^{-81}\) & \(5.82\times 10^{0}\) & \(2.31\times 10^{-12}\) \\  & std & \(4.31\times 10^{-2}\) & \(6.89\times 10^{-4}\) & \(4.08\times 10^{-25}\) & \(4.04\times 10^{-81}\) & \(4.05\times 10^{0}\) & \(1.20\times 10^{-11}\) \\ \hline \multirow{2}{*}{\(f_{2}(x)\)} & mean & \(6.29\times 10^{1}\) & \(8.98\times 10^{-1}\) & \(1.39\times 10^{-13}\) & \(3.84\times 10^{-3}\) & \(2.77\times 10^{-1}\) & \(3.37\times 10^{-6}\) \\  & std & \(6.92\times 10^{1}\) & \(1.10\times 10^{-1}\) & \(5.14\times 10^{-13}\) & \(8.18\times 10^{-3}\) & \(1.73\times 10^{-1}\) & \(1.80\times 10^{-5}\) \\ \hline \multirow{2}{*}{\(f_{3}(x)\)} & mean & \(5.04\times 10^{0}\) & \(2.48\times 10^{-1}\) & \(9.03\times 10^{0}\) & \(1.11\times 10^{0}\) & \(2.45\times 10^{0}\) & \(1.04\times 10^{-3}\) \\  & std & \(7.03\times 10^{0}\) & \(7.70\times 10^{-2}\) & \(6.21\times 10^{0}\) & \(5.55\times 10^{-1}\) & \(7.03\times 10^{0}\) & \(9.10\times 10^{-4}\) \\ \hline \multirow{2}{*}{\(f_{4}(x)\)} & mean & \(2.04\times 10^{2}\) & \(6.40\times 10^{0}\) & \(2.19\times 10^{2}\) & \(2.62\times 10^{1}\) & \(1.44\times 10^{2}\) & \(1.68\times 10^{-1}\) \\  & std & \(1.54\times 10^{1}\) & \(1.42\times 10^{1}\) & \(1.52\times 10^{1}\) & \(5.26\times 10^{0}\) & \(2.16\times 10^{1}\) & \(8.80\times 10^{-1}\) \\ \hline \multirow{2}{*}{\(f_{5}(x)\)} & mean & \(9.79\times 10^{0}\) & \(2.95\times 10^{0}\) & \(3.03\times 10^{1}\) & \(2.93\times 10^{-1}\) & \(7.04\times 10^{0}\) & \(4.81\times 10^{-14}\) \\  & std & \(3.22\times 10^{0}\) & \(5.16\times 10^{-1}\) & \(2.88\times 10^{0}\) & \(1.77\times 10^{-1}\) & \(2.97\times 10^{0}\) & \(1.59\times 10^{-13}\) \\ \hline \multirow{2}{*}{\(f_{6}(x)\)} & mean & \(4.46\times 10^{0}\) & \(1.43\times 10^{0}\) & \(8.87\times 10^{-14}\) & \(7.00\times 10^{-64}\) & \(1.76\times 10^{1}\) & \(2.11\times 10^{-36}\) \\  & std & \(2.06\times 10^{-1}\) & \(3.50\times 10^{-1}\) & \(3.45\times 10^{-14}\) & \(1.03\times 10^{-63}\) & \(1.14\times 10^{1}\) & \(1.11\times 10^{-35}\) \\ \hline \multirow{2}{*}{\(f_{7}(x)\)} & mean & \(8.00\times 10^{-1}\) & \(3.04\times 10^{-3}\) & \(4.45\times 10^{-2}\) & \(2.76\times 10^{-2}\) & \(1.53\times 10^{0}\) & \(0.00\times 10^{0}\) \\  & std & \(1.26\times 10^{-1}\) & \(7.50\times 10^{-4}\) & \(8.86\times 10^{-3}\) & \(6.12\times 10^{-3}\) & \(9.94\times 10^{-1}\) & \(0.00\times 10^{0}\) \\ \hline \multirow{2}{*}{\(f_{8}(x)\)} & mean & \(4.51\times 10^{2}\) & \(1.11\times 10^{0}\) & \(5.69\times 10^{-22}\) & \(9.47\times 10^{-78}\) & \(7.60\times 10^{3}\) & \(4.57\times 10^{-6}\) \\  & std & \(5.11\times 10^{1}\) & \(2.21\times 10^{-4}\) & \(2.57\times 10^{-22}\) & \(3.01\times 10^{-77}\) & \(5.91\times 10^{3}\) & \(2.46\times 10^{-5}\) \\ \hline \multirow{2}{*}{\(f_{9}(x)\)} & mean & \(2.36\times 10^{1}\) & \(3.43\times 10^{-2}\) & \(0.00\times 10^{0}\) & \(7.50\times 10^{0}\) & \(6.70\times 10^{1}\) & \(3.79\times 10^{-15}\) \\  & std & \(1.41\times 10^{0}\) & \(1.34\times 10^{-1}\) & \(0.00\times 10^{0}\) & \(2.53\times 10^{0}\) & \(3.81\times 10^{1}\) & \(1.42\times 10^{-14}\) \\ \hline \multirow{2}{*}{\(f_{10}(x)\)} & mean & \(8.69\times 10^{0}\) & \(1.10\times 10^{-1}\) & \(2.61\times 10^{-1}\) & \(9.88\times 10^{-3}\) & \(1.85\times 10^{2}\) & \(2.50\times 10^{-9}\) \\  & std & \(1.15\times 10^{0}\) & \(1.79\times 10^{-2}\) & \(1.98\times 10^{-1}\) & \(4.32\times 10^{-3}\) & \(1.04\times 10^{2}\) & \(1.14\times 10^{-8}\) \\ \hline \hline \end{tabular}  \endThe calculation of confidence intervals revealed that BASCS exhibits substantial optimization advantages across multiple dimensions (50 and 100 dimensions), especially when addressing complex problems such as multimodal functions. Its lower and upper bounds for the best fitness are notably reduced, indicating enhanced stability and reliability.