# An Improved Pied Kingfisher Optimizer for Maritime UAV Path Planning
## 3 Performance Validation of IPKO
Hybrid functions typically have complex structures and diverse characteristics, simulating the combined scenarios of various challenges encountered in real-world optimization problems. The fourth set of functions (f9-f12) includes composite functions that typically incorporate multiple complex characteristics to evaluate the overall performance of the algorithm in highly intricate optimization scenarios. Composite functions may feature multiple local optima, complex global structures, irregular search spaces, and other attributes, simulating highly complicated problems in real-world applications. The comparison algorithms employed for the algorithm effectiveness test in this study are the same as those used in CEC2005. To ensure fairness in testing, the maximum number of evaluations for the IPKO algorithm is set to 10,000 dim, where dim represents the problem dimension. To further analyze IPKO's performance across different dimensions, tests were conducted in 10-dimensional and 20-dimensional environments. The population size for each algorithm is uniformly set to 50 to ensure consistency in the results. Each experiment is independently run 30 times to minimize the impact of randomness on the test results and provide statistically more reliable data. The specific test results can be found in Tables 4 and 5, which present the performance data of IPKO and other comparison algorithms in both 10-dimensional and 20-dimensional environments. When analyzing these data, it is important to consider that the minimum value assesses the algorithm's best performance, while the average value reflects its overall stability and the standard deviation reveals the consistency and volatility of the results. These three metrics collectively provide a comprehensive overview of the algorithm's performance, facilitating a thorough understanding of IPKO's advantages across different dimensions. In order to further validate the significance of the performance differences between algorithms, this study conducted Wilcoxon and [PERSON] tests at a significance level of 0.05. These two statistical tests effectively analyze the significance of performance differences between algorithms, with '+' indicating IPKO's superiority over other comparison algorithms, '\(-\)' denoting inferiority, and '=' representing similar performance levels between IPKO and other algorithms. Figure 6: _Cont_. The results presented in Figures 7 and 8 clearly demonstrate the superior optimization performance of the IPKO algorithm in both 10-dimensional and 20-dimensional environments. In the 10-dimensional setting, IPKO achieved optimal outcomes in at least two performance metrics across tests f1, f2, f3, f4, f6, f9, f10, and f11. Similarly impressive advantages were observed for IPKO in the expansive domain of 20 dimensions encompassing tests f1-f7, f9, f11, and f12. This unwavering consistency across different dimensions underscores the robust optimization capabilities of IPKO. Notably, IPKO attained an average ranking of 2.3272 in the context of the 10-dimensional environment, which further improved to an outstanding score of 1.3452 when confronted with the 20-dimensional setting, thus firmly establishing its preeminent position in both scenarios. This progression  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**F** & **Index** & **IPKO** & **PKO** & **WOA** &  
serves as compelling evidence for the enduring efficacy exhibited by IPKO even amidst escalating problem dimensionality. IPKO algorithm consistently attained optimal values for functions f1-f3 in both 10-dimensional and 20-dimensional environments, showcasing its adaptability and efficiency across varying dimensions. It also exhibited exceptional accuracy and stability in optimization. In the 10-dimensional environment, IPKO outperformed other algorithms in most test functions except for f8, where it was slightly surpassed by the SO algorithm.