## 3 Utilized Meta-Heuristic Algorithms
### Standard Genetic Algorithm
In each table, the values in bold indicate the best value found for that test function. #### 4.2.1 Comparing Three Versions of RA

In this section, the BIRA algorithm is compared with the IRA and BRA algorithms to show that BIRA is superior to the others. Table 5 shows the median values of the results obtained from tests with 30 random seeds for each function. When the results given in Table 5 are examined, it is seen that BIRA gives much more successful results than IRA and BRA. Considering the obtained results, we aimed to show the contribution of the BIRA algorithm to the literature by comparing it with the commonly used meta-heuristic algorithms in terms of performance. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Algorithm** & **Parameter** & **Value** \\ \hline \multirow{3}{*}{SGA} & Tournament size & 3 \\  & Crossover rate & 0.7 \\  & Mutation probability & 0.05 \\ \hline \multirow{2}{*}{DE} & Crossover rate & 0.7 \\  & Scaling factor & 0.8 \\ \hline \multirow{3}{*}{PSO} & w & 0.2 \\  & cl & 2 \\  & c2 & 2 \\ \hline \multirow{3}{*}{GWO} & A & \([-1,1]\) \\  & C & \([0,2]\) \\ \hline RA & Rooster’s size & 4 \\ \hline \multirow{2}{*}{BIRA} & Number of cages & 4 \\  & Bipolarity value & 0.25 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The parameter settings of the algorithms. F7, F8, F9, F10, F11, F14, F16, F19, and F20). In addition, when the performance of BIRA is compared with the performance of other algorithms, it is possible to observe that BIRA gives superior results compared to other algorithms, except for PSO. Table 7 shows the results of the algorithms in CEC2014 test functions. Although SGA, GWO, and RA display a much better performance in these test functions, they could not match the performance of BIRA. BIRA offered the best results in all tested functions. On the other hand, PSO could not show its success in the first test (shown in Table 6) and fell far behind SGA, GWO, RA, and BIRA algorithms. According to Table 8, which demonstrates the results of CEC2018 test functions, the BIRA algorithm manages to find the global values of the functions in 15 of the 17 test functions used (except F32 and F40) and introduces predominant results compared to all compared algorithms. Even though it provides the best result for F40, it could not reach the global value of 1000. The same problem can be seen for the F32 function. Although BIRA's inclusion of bad individuals in the selection process prevents local congestion, it can also cause deviation from the best in some cases, as with these functions. Furthermore, PSO performed better in this test than in the previous one; however, it still falls short of BIRA. Figure 2 demonstrates the convergence curves of the compared algorithms in benchmarks. Based on the figure, BIRA is able to find the best result for F1, F2, F6, F8, F11, F15, F17, and F21 in the first iteration. Hence, BIRA's convergence curve may not be seen in these test functions. When Figure 2 is examined, it can be seen that GWO and PSO give the closest performance to BIRA. Although CS and DE generally improve the best results they find during each iteration, they cannot approach the performance of BIRA. Although SGA and RA provide successful results in some test functions such as F10, they are generally stuck in the locals and cannot reach the global values. While Figure 3 displays the trajectory of the algorithms in the CEC2014 test functions, Figure 4 shows the convergence curves in tested CEC2018 functions. In Figure 3, all algorithms were able to find the best result in the first iteration for the functions of F22 and F28. Additionally, BIRA was able to discover the global value in the first 15 iterations in all functions, except F27 and F30 functions. Considering the performances of other algorithms as indicated in Figure 3, it is seen that DE and CS are stuck at the local minimums at the end of the first iterations and do not show any improvement.