## 6 Experiments on Benchmark Functions
### Comparison with Well-Established Algorithms  
The proposed MIARO is evaluated against the original ARO and seven well-established algorithms using benchmark functions: Harris Hawks Optimization (HHO) [53], Salp Swarm Algorithm (SSA) [54], Grey Wolf Optimizer (GWO), Whale Optimization Algorithm (WOA) [55], Meth-flame Optimization (MFO) [56], Sine Cosine Algorithm (SCA) [57], and Particle Swarm Optimization (PSO). For each algorithm, the parameters are adjusted consistently with the specifications provided in their respective original publications as detailed in Table 7. The findings in Table 8 reveal the mean solution from 30 independent experiments conducted for each algorithm, encompassing the average (avg) and standard deviation (std) of MIARO alongside eight additional algorithms. The terminal two data rows depict the median ranking for each algorithm and the statistical comparisons obtained from the Wilcoxon rank sum examination (statistical significance threshold \(\alpha=0.05\)), where \"\(+/-/=\)\" signifies that MIARO is stronger, weaker and on par with the compared algorithms. From the outcomes presented in Table 8, evidence suggests that the presented MIARO outperforms competing algorithms for functions F1-F7, F12-F13, F15, F20-F22. In addition, for F9-F11, F16-F19, F23, MIARO and some algorithms obtain the same optimal values, but for F17, F19, F23, MIARO surpasses their algorithms with regard to standard deviation. For F14, MIARO ranks second after SSA, and for F14, worse than HHO and WOA, it ranks third. The mean rank for MIARO stands at 1.1304, which is substantially lower compared to competing algorithms, which shows that MIARO achieves the highest performance relative to all algorithms. Also, the \"\(+/-/=\)\" in the bottom row of the table shows that MIARO significantly outperforms the other algorithms across the majority of functions. To clearly illustrate the performance of the MIARO algorithm, displayed in Figure 5 are the representative convergence curves for the chosen functions. As depicted in Figure 5, both the rate of convergence and precision are significantly superior in MIARO compared to the other algorithms across the chosen functions, with the exception of F5. For F5, the MIARO convergence speed is inferior to that of HHO in the early iteration period, but MIARO has a low tendency to become stuck in the local optimality during the latter part of the iterations and possesses higher accuracy compared to HHO. To appraise the practicality of the MIARO, this work performs an experimental evaluation of its time performance. During 30 separate trials on 23 evaluation functions, the mean execution time, best elapsed time, and standard deviation are recorded for each algorithm. The trial findings in Table 9 show that although MIARO is slightly inferior to algorithms ARO, SCA and PSO in terms of computational efficiency, MIARO reflects high reliability concerning the combined performance of the solution precision and convergence efficiency, which is valuable for practical applications [58]. \begin{table}
\begin{tabular}{l l} \hline \hline
**Method** & **Parameter Value** \\ \hline MIARO & \(r=(0,1),n=N(0,1),\beta=1.5,\lambda=(0,1),l=(-1,1)\) \\ ARO & \(r=(0,1),n=N(0,1)\) \\ HHO & \(\beta=1.5\) \\ SSA & \(c_{2}=[0,1],c_{3}=[0,1]\) \\ GWO & \(a=2\cdot\left(1-\frac{t}{t}\right)\) \\ WOA & \(a=2\cdot\left(1-\frac{1}{t}\right),b=1,l=[-1,1]\) \\ MFO & \(r=[-2,-1],t=[r,1],b=1\) \\ SCA & \(a=2,r_{2}=[0,2\pi],r_{3}=[0,2],r_{4}=[0,1]\) \\ PSO & \(c_{1}=2,c_{2}=2,v_{max}=6\) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Parameters of the algorithm.