## 4 Experimental Studies
### Statistical Testing of iaABC
#### 4.1.3 iaABC's Performance on CEC 2022 Benchmark Functions  
The statistical performance of iaABC on CEC 2022 benchmark functions is analyzed based on error. The error is the difference between the global optimum value for the function and the best value produced by the algorithm. The results of the errors of the 10-dimensional experiments with the algorithms are given in Table 4, while the convergence error lines are given in Figure 3. The results regarding the errors and the convergence error lines obtained for the 20-dimensional experiments are presented in Table 5 and Figure 4, respectively. When the error is 1E-8 or less, it is evaluated as 0. The results obtained with Co-PPSO are taken from [39]. Figure 3: Convergence error curves of the compared algorithms for 10D. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline
**No** & **Method** & **Best** & **Worst** & **Median** & **Mean** & **SD** & **No** & **Method** & **Best** & **Worst** & **Median** & **Mean** & **SD** \\ \hline F1 & Co-PPSO & 0.00E+00 & 0.00E+00 & 0.00E+00 & 0.00E+00 & 0.00E+00 & F7 & Co-PPSO & 2.04E+08 & 2.20E  
\begin{table}
\begin{tabular}{l l l l l l l l l l l l l l l} \hline
**No** & **Method** & **Best** & **Worst** & **Median** & **Mean** & **SD** & **No** & **Method** & **Best** & **Worst** & **Median** & **Mean** & **SD** \\ \hline F3 & Co-PPSO & 0.00E+00 & 0.00E+00 & 0.00E+00 & 0.00E+00 & 0.00E+00 & F9 & Co-PPSO & 2.00E+02 & 2.00E+02 & 2.30E+0  
Figure 4: _Cont._  
According to the statistical results for the 10-D case presented in Table 4, the iaABC algorithm achieved more successful outcomes than other algorithms in 8 out of 12 test functions. Examining the convergence error graphs for the algorithms, shown in Figure 3, indicates that the proposed method demonstrates effective convergence performance. For the unimodal function, iaABC, like many other algorithms, produced the best solution in all trials. In this context, the proposed method has excellent performance and good robustness. iaABC produces successful solutions for the basic functions used for comparison, and the  
Figure 4: Convergence error curves of the compared algorithms for 20D. error curves in Figure 3 prove that iaABC has a more efficient convergence performance than other algorithms. The Rosenbrock function is not convex and contains many narrow hillocks. Because the hillocks are very sharp, metaheuristic methods cannot identify points that can be advanced in the problem [43]. However, iaABC produces solutions with the most successful mean and SD values for F2 and reaches a convergence accuracy of 1E-3. However, it also produces the optimal result for the F3 and F5 functions. Regarding the compared hybrid functions, iaABC produced the optimal result for the F7 function and achieved 1E-1 convergence accuracy for the F8 function. Composition functions are formed by combining various complex functions, each of which may have multiple local optima. This complexity presents a challenge for the optimization capabilities of metaheuristic algorithms. The proposed method successfully identifies the optimal result for the F11 function, which is one of the composition functions. However, it does not achieve optimal results for the F9, F10, or F12 functions. However, when looking at each function from the perspective of 30 trials, the convergence accuracy of iaABC reached 1E+2. When these results are evaluated, it can be said that iaABC has a certain ability for global exploration. Table 5 displays the results achieved by the algorithms for the 20-dimensional case. Expanding the solution vector poses a challenge for these algorithms. However, the global optimum solution obtained by iaABC matches the target value for the unimodal function F1. When the mean and standard deviation data calculated for 30 trials are examined, it is proven that the algorithm has good robustness. The solution spaces of the basic functions have wavy surfaces. Especially in the Rosenbrock function, the curves are very sharp.