## 3 Utilized Meta-Heuristic Algorithms
### Standard Genetic Algorithm
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Function** & **Definition** & **Class** & **Global Value** \\ \hline F21 & Sphere Function & Unimodal & \(-\)1400 \\ F22 & Different Powers Function & Unimodal & \(-\)1000 \\ F23 & Rotated Weierstrass Function & Multimodal & \(-\)600 \\ F24 & Rotated Griewank’s Function & Multimodal & \(-\)500 \\ F25 & Rastrigin’s Function & Multimodal & \(-\)400 \\ F26 & Schwefel’s Function & Multimodal & \(-\)100 \\ F27 & Rotated Schwefel’s Function & Multimodal & 100 \\ F28 & Rotated Katsurta Function & Multimodal & 200 \\ F29 & Lunacek Bi\_Rastrigin Function & Multimodal & 300 \\ F30 & Rotated Lunacek Bi\_Rastrigin Function & Multimodal & 400 \\ F31 & Expanded Griewank’s Plus Rosenbrock’s Function & Multimodal & 500 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Utilized CEC2014 test functions and their features. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Function** & **Definition** & **Class** & **Global Value** \\ \hline F32 & Shifted and Rotated Bent Cigar Function & Unimodal & 100 \\ F33 & Shifted and Rotated Rosenbrock’s Function & Multimodal & 300 \\ F34 & Shifted and Rotated Rastrigin’s Function & Multimodal & 400 \\ F35 & Shifted and Rotated Expanded Scaffer’s F6 Function & Multimodal & 500 \\ F36 & Shifted and Rotated Lunacek Bi\_Rastrigin Function & Multimodal & 600 \\ F37 & Shifted and Rotated Non-Continuous Rastrigin’s Function & Multimodal & 700 \\ F38 & Shifted and Rotated Levy Function & Multimodal & 800 \\ F39 & Shifted and Rotated Schwefel’s Function & Multimodal & 900 \\ F40 & Hybrid Function 1 (N = 3) & Hybrid & 1000 \\ F41 & Composition Function 2 (N = 3) & Composition & 2100 \\ F42 & Composition Function 3 (N = 4) & Composition & 2200 \\ F43 & Composition Function 4 (N = 4) & Composition & 2300 \\ F44 & Composition Function 5 (N = 5) & Composition & 2400 \\ F45 & Composition Function 6 (N = 5) & Composition & 2500 \\ F46 & Composition Function 7 (N = 6) & Composition & 2600 \\ F47 & Composition Function 8 (N = 6) & Composition & 2700 \\ F48 & Composition Function 9 (N = 3) & Composition & 2800 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Utilized CEC2018 test functions and their features. On the other hand, the Wilcoxon signed rank test is another non-parametric statistical test used to identify distinctions between two sets of data, which could represent samples or algorithms [40]. In the standard procedure, this test begins by calculating the differences between the outcomes of two algorithms, both of which consist of N observations (where N denotes the number of tests). These differences form a vector, which is then ranked from 1 to N. The smallest value receives a rank of 1. Subsequently, the test computes two values: \(R_{+}\) and \(R_{-}\). Based on these values, the test statistic, denoted as \(T\), is determined as the minimum of either \(R_{+}\) or \(R_{-}\). This \(T\) value is then used to compute the significant probability value (\(p\)) associated with the test. ### Results of the Test Functions

Table 4 shows the parameter settings of the meta-heuristic algorithms utilized. Based on standard parameter settings of SGA, DE, PSO, and GWO, respectively in [41], [33], [9] and [42], the parameter settings in Table 4 were chosen. Moreover, the number of iterations and population size (number of nests for CS) were accepted as 100. The code of RA, BIRA, SGA, and PSO were modeled by implementing Matlab 2019a, while the code of GWO, DE, and CS were taken from [42], [43], and [44], respectively. In order to minimize the effects of randomization, the tests were repeated with 30 runs that have 30 different random seeds. As a result of these 30 runs, the median and standard deviation values of the obtained results are shared in the result tables. The reason for utilizing the median value instead of the mean value is that a highly deviant outcome that may exist within 30 runs can seriously affect the average. The evaluation will be made taking into account the best performance of the compared algorithms.