# An Improved Cuckoo Search Algorithm and Its Application in Robot Path Planning
## 4 Experiments and Analyses
### Performance Comparison Experiment and Result Analysis
Moreover, on the multimodal function \(f_{10}(\mathrm{x})\), BASCS significantly outperforms the rest by persistently evading local optima during mid-iterations. On functions \(f_{7}(\mathrm{x})\), \(f_{8}(\mathrm{x})\), and \(f_{10}(\mathrm{x})\), BASCS also demonstrates a swifter optimization rate compared to the other algorithms. \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{3-11}  & & **Wilcox** & **Rank** & **Wilcox** & **Rank** & **Wilcox** & **Rank** & **Wilcox** & **Rank** & **Wilcox** & **Rank** & **Rank** \\ \hline \multirow{2}{*}{\(f_{1}(x)\)} & 50 & + & 5 & + & 4 & \(-\) & 2 & \(-\) & 1 & + & 6 & 3 \\  & 100 & + & 6 & + & 4 & + & 3 & \(-\) & 1 & + & 5 & 2 \\ \hline \multirow{2}{*}{\(f_{2}(x)\)} & 50 & + & 6 & + & 5 & \(-\) & 1 & + & 3 & + & 4 & 2 \\  & 100 & + & 6 & + & 5 & + & 2 & + & 3 & + & 4 & 1 \\ \hline \multirow{2}{*}{\(f_{3}(x)\)} & 50 & + & 5 & + & 2 & + & 6 & + & 3 & + & 4 & 1 \\  & 100 & + & 4 & + & 2 & + & 6 & + & 3 & + & 5 & 1 \\ \hline \multirow{2}{*}{\(f_{4}(\mathrm{x})\)} & 50 & + & 5 & + & 2 & + & 6 & + & 3 & + & 4 & 1 \\  & 100 & + & 4 & + & 5 & + & 6 & + & 2 & + & 3 & 1 \\ \hline \multirow{2}{*}{\(f_{5}(x)\)} & 50 & + & 5 & + & 3 & + & 6 & + & 2 & + & 4 & 1 \\  & 100 & + & 4 & + & 3 & + & 6 & + & 2 & + & 5 & 1 \\ \hline \multirow{2}{*}{\(f_{6}(x)\)} & 50 & + & 5 & + & 4 & + & 3 & \(-\) & 1 & + & 6 & 2 \\  & 100 & + & 5 & + & 4 & + & 3 & \(-\) & 1 & + & 6 & 2 \\ \hline \multirow{2}{*}{\(f_{7}(x)\)} & 50 & + & 5 & + & 2 & + & 4 & + & 3 & + & 6 & 1 \\  & 100 & + & 6 & + & 2 & + & 4 & + & 3 & + & 5 & 1 \\ \hline \multirow{2}{*}{\(f_{8}(x)\)} & 50 & + & 5 & + & 4 & \(-\) & 2 & \(-\) & 1 & + & 6 & 3 \\  & 100 & + & 5 & + & 4 & + & 3 & \(-\) & 1 & + & 6 & 2 \\ \hline \multirow{2}{*}{\(f_{9}(x)\)} & 50 & + & 5 & + & 3 & \(-\) & 1 & + & 4 & + & 6 & 2 \\  & 100 & + & 5 & + & 3 & + & 2 & + & 4 & + & 6 & 1 \\ \hline \multirow{2}{*}{\(f_{10}(x)\)} & 50 & + & 5 & + & 3 & + & 4 & + & 2 & + & 6 & 1 \\  & 100 & + & 4 & + & 3 & + & 6 & + & 2 & + & 5 & 1 \\ \hline \multirow{2}{*}{
\begin{tabular}{} \end{tabular} } & 50 & + & 5 & 3.4 & & 3.75 & & 2.25 & & 5.1 & 2.18 \\  & & 5 & & 3 & & 4 & & 2 & & 6 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: The Wilcoxon rank-sum test results. Figure 12: The function \(f_{1}(x)\). Figure 14: The function \(f_{3}(x)\). Figure 15: The function \(f_{4}(x)\). Figure 16: The function \(f_{5}(x)\). Figure 17: The function \(f_{6}(x)\). Figure 18: The function \(f_{7}(x)\). In [25; 26; 27; 28], ICS, ECS, ASCSA, and MCSA demonstrate superior performance over PSO and Genetic Algorithms (GA) across various optimization tasks. These algorithms integrate advanced mechanisms--such as dynamic parameter adjustments, enhanced exploration--exploitation balance, and adaptive search strategies--addressing the known  
Figure 19: The function \(f_{8}(x)\). Figure 20: The function \(f_{9}(x)\). weaknesses of PSO and GA, such as premature convergence and poor adaptability in complex search spaces. ICS utilizes Levy flight with dynamic radius adjustments, significantly enhancing global search capabilities and reducing the likelihood of getting stuck in local optima--a common challenge for PSO and GA. This adaptability allows ICS to explore the search space efficiently and converge on better solutions. ECS refines CS with faster convergence and improved stability. It performs especially well in large-scale or multimodal problems, where PSO and GA often struggle due to limited exploration capabilities and susceptibility to local optima entrapment. ASCSA's adaptive step-size mechanism enables it to adjust dynamically during different search phases.