# An Improved Cuckoo Search Algorithm and Its Application in Robot Path Planning
## 4 Experiments and Analyses
### Ablation Experiments and Results Analysis  
To affirm the viability of our enhanced strategy, ablation studies on the tent chaotic map and random migration strategy were performed. The test functions and parameters are detailed in Tables 1 and 2, where BASCS1 indicates CS with the tent chaotic map, BASCS2 with random migration, and BASCS3 with their combined strategy.  
The experimental setup included a population size of 25, a maximum of 5000 iterations, and 30 independent runs to ensure data reliability. The resulting convergence curves are depicted in Figures 2-11. Figures 2-7 illustrate the convergence of the algorithms on unimodal benchmarks across 50 and 100 dimensions. Figures 8-11 display the convergence of the algorithms on multimodal benchmarks under the same dimensional conditions.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**The Name of** & **Expression** & **Solution Space** & **Dimension** & **Optimal Solution** \\ \hline Sum Squares & & & & \\ (Unimodal function) & & & & \\ \hline Bohachevsky & & & & \\ (Unimodal function) & & & & \\ \hline Powell & & & & \\ (Unimodal function) & & & & \\ \hline Griewank & & & \\ (Multimodal function) & & & & \\ \hline Ackley & & & \\ (Multimodal function) & & & & \\ \hline Rastrigin & & & \\ (Multimodal function) & & & & \\ \hline Alpine & & & \\ (Multimodal function) & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 1: _Cont._  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Algorithm** & **Parameter** \\ \hline BASCS1 & \(N=25\), \(\lambda=1.5\), \(Pa=0.25\), \(\alpha=0.01\) \\ BASCS2 & \(N=25\), \(\lambda=1.5\), \(Pa=0.25\), \(\alpha=0.01\) \\ BASCS3 & \(N=25\), \(\lambda=1.5\), \(Pa=0.25\), \(\alpha=0.01\) \\ CS & \(N=25\), \(\lambda=1.5\), \(Pa=0.25\), \(\alpha=0.01\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: The parameter settings of ablation experiments.  
Figure 4: The function \(f_{3}(x)\).  
Figure 3: The function \(f_{2}(x)\).  
Figure 2: The function \(f_{1}(x)\).  
Figure 5: The function \(f_{4}(x)\).  
Figure 6: The function \(f_{5}(x)\).  
Figure 7: The function \(f_{6}(x)\).  
Figure 8: The function \(f_{7}(x)\).  
Figure 10: The function \(f_{9}(x)\).  
As seen in Figures 2-7, for both 50-dimension and 100-dimension, BASCS3 outperforms BASCS1 and CS on the unimodal functions \(\mathrm{f_{1}(x)}\), \(\mathrm{f_{2}(x)}\), \(\mathrm{f_{4}(x)}\), \(\mathrm{f_{5}(x)}\), and \(\mathrm{f_{6}(x)}\) and outperforms BASCS2 on \(\mathrm{f_{4}(x)}\); only for 50-dimension, BASCS3 is inferior to others on \(\mathrm{f_{3}(x)}\). As seen in Figures 8-11, for both 50-dimension and 100-dimension, BASCS3 is superior to BASCS1 and CS on the multimodal functions \(\mathrm{f_{7}(x)}\), \(\mathrm{f_{8}(x)}\), \(\mathrm{f_{9}(x)}\), and \(\mathrm{f_{10}(x)}\), superior to BASCS2 on \(\mathrm{f_{8}(x)}\), \(\mathrm{f_{9}(x)}\), and \(\mathrm{f_{10}(x)}\), and similar to BASCS2 only on \(\mathrm{f_{7}(x)}\).  
Therefore, to validate the approach, combining tent chaotic mapping with random migration for initial population generation in CS is notably more effective than using either strategy alone.