# An Improved Pied Kingfisher Optimizer for Maritime UAV Path Planning
## 3 Performance Validation of IPKO
For the unimodal function f5, due to the PKO algorithm's unique characteristics, IPKO did not outperform the SO algorithm. However, for other functions, particularly optimizing multimodal functions such as f12-f13, it exceeds PKO by three orders of magnitude and other algorithms by several orders of magnitude. Although WOA performs better than IPKO on fixed-dimension multimodal function f15 based on results from other test functions, it can be concluded that IPKO's search performance is superior to WOA. Additionally, the Friedman test reveals that IPKO consistently demonstrates stable optimization capability, ranking highest with a score of 1.8383 among the compared algorithms, indicating its broad applicability. In summary, benchmark test results confirm that IPKO can consistently identify higher-quality solutions, validating its feasibility. Figure 6 presents the convergence curves of each algorithm on the 23 test functions, accompanied by visual representations of the functions and box plots for comparative analysis. In this 3D plot of the CEC function, the different colors represent varying values of the function across the search space. Typically, cooler colors (e.g., blue) indicate lower function values, while warmer colors (e.g., yellow) represent higher function values, helping visualize the landscape of the optimization problem. In the box plots, the red line represents the median, showing the central value of the fitness data, while the '' symbols indicate outliers, which are data points significantly different from the rest of the dataset,  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**F** & **Index** & **IPKO** & **PKO** & **WOA** & **SO** & **DOA** & **PSO** & **SCA** & **GWO** \\ \hline  & Min & \(0.000\times 10^{-00}\  
and different colored boxes represent different algorithms to enhance visualization This comprehensive visualization highlights the advantages of the improved algorithm. In terms of data comparison, IPKO not only converges to the optimal position in favorable test functions but also does so at a relatively faster speed, leading to the conclusion that IPKO exhibits superior performance. Additionally, the box plots clearly illustrate that IPKO has fewer outliers and greater stability, further demonstrating its robustness. The previous experiments have demonstrated the superior performance of IPKO across CEC2005 test sets. However, with the continuous advancement of technology, optimization problems are becoming increasingly difficult and complex. To further validate the performance of IPKO, this study conducted detailed tests on its performance using the challenging CEC2022 test set. The CEC2022 test set comprises four types of functions: unimodal functions, basic functions, hybrid functions, and composite functions. These diverse function types offer a comprehensive evaluation of the algorithm's performance in different problem scenarios. The first group of functions (f1) consists of unimodal functions with a single global optimum and relatively simple search space. Testing these unimodal functions primarily evaluates IPKO's global search capability in uniform search spaces by assessing how efficiently it converges to the single global optimum. Since unimodal functions lack complex local optima, the algorithm's efficiency in converging to the single global optimum is crucial. The second set of functions (f2-f5) comprises basic test functions, encompassing various optimization characteristics such as multimodal structures and separable and non-separable problems. These functions represent common types of fundamental optimization problems encountered in practical applications. The third set of functions (f6-f8) consists of hybrid functions composed of multiple sub-functions with different characteristics. Their aim is to assess the algorithm's adaptability and optimization efficiency in complex optimization problems.