# An Improved Cuckoo Search Algorithm and Its Application in Robot Path Planning
## 4 Experiments and Analyses
### Performance Comparison Experiment and Result Analysis  
This study conducted comparative experiments on BASCS, CS, and four CS variants to evaluate their performance across 10 benchmark functions. The experiments were performed in 50 and 100 dimensions, with each algorithm running independently 30 times, capped at 5000 iterations per run. Extensive experiments in [16] demonstrate that \(N=15\)-40, \(Pa=0.25\), \(\lambda=1.5\), and \(\alpha=0.01\) are sufficient for most optimization tasks. In this manuscript, \(N\) is set to 25 to balance time cost and search accuracy, with the fixed step size and elimination probability replaced by adaptive versions to enhance performance. Detailed algorithm parameters are provided in Table 3.  
Tables 4 and 5 summarize the optimization results for both dimensions. The performance metrics include the mean and standard deviation (std) of the best fitness values obtained across the 30 runs. The mean reflects the algorithm's accuracy, where a lower mean indicates higher accuracy. The std measures the algorithm's stability, with a smaller std indicating greater stability. Key observations from Tables 4 and 5 are as follows:  
1. For both 50-dimension and 100-dimension, BASCS is less accurate than ASCSA and ECS on unimodal functions \(f_{1}(x)\), \(f_{2}(x)\), and multimodal functions \(f_{6}(x)\) and \(f_{8}(x)\)  
Figure 11: The function \(f_{10}(x)\). \begin{table}
\begin{tabular}{c c} \hline \hline
**Algorithm** & **Parameter** \\ \hline BASCS & \(N=25\), \(\lambda=1.5\), \(Pa_{\min}=0.1\), \(Pa_{\max}=0.75\) \\ CS & \(N=25\), \(\lambda=1.5\), \(Pa=0.25\), \(\alpha=0.01\) \\ MCSA & \(N=25\), \(\lambda=1.5\), \(Pa=0.25\), \(\alpha_{\min}=0.1\), \(\alpha_{\max}=1.5\) \\ ASCSA & \(N=25\), \(\lambda=1.5\), \(Pa=0.25\) \\ ICS & \(N=25\), \(\lambda=1.5\), \(Pa=0.25\), \(\alpha=0.01\) \\ ECS & \(N=25\), \(\lambda=1.5\), \(Pa=0.25\), \(\alpha=0.01\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The parameter settings of comparative experiments. But, in unimodal functions \(f_{3}(x)\), \(f_{4}(x)\), and \(f_{5}(x)\) and multimodal functions \(f_{7}(x)\) and \(f_{10}(x)\), BASCS shows the best computational accuracy. 2. On the multimodal function \(f_{7}(x)\), for both 50-dimension and 100-dimension, only BASCS converges to the theoretical optimal solution, whereas the other five algorithms do not. 3. For both 50-dimension and 100-dimension cases, BASCS exhibits the best stability on the unimodal functions \(f_{3}(x)\), \(f_{4}(x)\), and \(f_{5}(x)\), as well as on the multimodal function \(f_{10}(x)\). 4. On the unimodal functions \(f_{4}(x)\) and \(f_{5}(x)\), for both 50-dimension and 100-dimension, none of the six algorithms converge to the theoretically optimal solution. However, the optimization results obtained by BASCS are far superior to those obtained by the other five algorithms. 5. On the unimodal functions \(f_{3}(x)\), \(f_{4}(x)\), and \(f_{5}(x)\) and the multimodal functions \(f_{7}(x)\), \(f_{9}(x)\), and \(f_{10}(x)\), BASCS achieves the lowest mean and std across both 50 and 100 dimensions, indicating its superior accuracy and stability on multimodal functions. 6. In 100-dimension, BASCS delivers optimal optimization results for all functions except the multimodal \(f_{8}(x)\), demonstrating superior capability in handling various types of objective functions compared to the other five algorithms. 7. BASCS exhibits high accuracy on the unimodal functions, whereas a well-calibrated global search ratio in the multimodal function can effectively avoid local optima and enhance performance. To further explore the performance differences and reliability among the algorithms, confidence intervals were employed to assess whether significant differences exist between BASCS, CS, and its four variants. Table 6 presents the test results, derived from the mean and standard deviation of the best fitness values shown in Tables 4 and 5. The \"Lower\" and \"Upper\" columns indicate the lower and upper bounds of the confidence intervals, respectively. \begin{table}