# A Novel Hybrid Harris Hawk-Arithmetic Optimization Algorithm for Industrial Wireless Mesh Networks
## 4 Results and Discussion
### Performance Analysis on Benchmark Functions
#### 4.1.3 Quantitative Analysis  
In this section, the efficiency of each algorithm was evaluated by measuring how closely the statistical data match the global minimum of the benchmark function being tested. HHAOA performs better than other algorithms, as it has significant performance outcomes. However, this also means that HHAOA can identify a better optimal solution with fewer iterations and is closer to the objective function, as evidenced by its lower mean value. In contrast, a lower standard deviation (Stdv) signifies more excellent convergence stability, effectiveness, and reliability. Consequently, HHAOA is capable of avoiding local optima with great success. Table 6 show the numerical comparison for all the optimization techniques. Here, the abbreviated terms are \(Func\).--Benchmark Functions, \(G_{m}\)--Global minima, and \(Std\).Dev--Standard deviation. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Func.** & \(G_{m}\) & **Statistics** & **AOA** & **MFO** & **SCA** & **GWO** & **WOA** & **HHO** & **HHAOA** \\ \hline \multirow{4}{*}{F1} & \multirow{4}{*}{1} & Mean & \(1.20\times 10^{-14}\) & \(2.00\times 10^{3}\) & 2.4136 & \(2.05\times 10^{-33}\) & \(5.28\times 10^{-85}\) & \(9.02\times 10^{-96}\) & \(3.16\times 10^{-6}\) \\  & & Best & \(1.40\times 10^{-270}\) & 0.2900 & 0.0036 & \(6.88\times 10^{-35}\) & \(1.47\times 10^{-96}\) & \(1.75\times 10^{-121}\) & \(6.84\times 10^{-17}\) \\  & & Worst & \(6.00\times 10^{-13}\) & \(2.00\times 10^{4}\) & \(27.5418\) & \(1.10\times 10^{-32}\) & \(1.62\times 10^{-83}\) & \(4.51\times 10^{-94}\) & \(1.99\times 10^{-12}\) \\  & & Std. Dev & \(8.49\times 10^{-14}\) & \(4.95\times 10^{3}\) & \(4.3477\) & \(2.80\times 10^{-33}\) & \(2.34\times 10^{-84}\) & \(2.34\times 10^{-84}\) & \(5.19\times 10^{-13}\) \\ \hline \multirow{4}{*}{F2} & \multirow{4}{*}{0} & Mean & 0.0 & 31.5216 & 0.0100 & \(6.27\times 10^{-20}\) & \(4.56\times 10^{-53}\) & \(1.89\times 10^{-50}\) & \(1.68\times 10^{-20}\) \\  & & Best & 0.0 & 0.1102 & \(9.06\times 10^{-5}\) & \(1.06\times 10^{-20}\) & \(1.07\times 10^{-61}\) & \(4.45\times 10^{-65}\) & \(2.13\times 10^{-9}\) \\ \cline{1-1}  & & Worst & 0.0 & 80.0085 & 0.0740 & \(2.05\times 10^{-19}\) & \(1.32\times 10^{-51}\) & \(9.29\times 10^{-49}\) & \(7.75\times 10^{-7}\) \\ \cline{1-1}  & & Std. Dev & 0.0 & 21.6905 & 0.0140 & \(4.19\times 10^{-20}\) & \(2.20\times 10^{-52}\) & \(1.31\times 10^{-49}\) & \(1.71\times 10^{-7}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Quantitative analysis of the different benchmark functions for all the optimization algorithms. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Func. ** & \(G_{m}\) & **Statistics** & **AOA** & **MFO** & **SCA** & **GWO** & **WOA** & **HHO** & **HHAOA** \\ \hline \multirow{4}{*}{F3} & \multirow{4}{*}{0} & Mean & 0.0055 & \(1.99\times 10^{4}\) & \(6.44\times 10^{3}\) & \(3.42\times 10^{-8}\) & \(2.75\times 10^{4}\) & \(5.34\times 10^{-81}\) & \(1.09\times 10^{-7}\) \\  & & Best & \(3.63\times 10^{-224}\) & \(1.73\times 10^{3}\) & \(381.3511\) & \(3.48\times 10^{-12}\) & \(3.72\times 10^{3}\) & \(3.05\times 10^{-103}\) & \(4.51\times 10^{-13}\) \\  & & Worst & 0.0711 & \(4.71\times 10^{4}\) & \(2.33\times 10^{4}\) & \(4.48\times 10^{-7}\) & \(4.97\times 10^{4}\) & \(1.85\times 10^{-79}\) & \(2.06\times 10^{-6}\) \\  & & Std. Dev & 0.0138 & \(1.27\times 10^{4}\) & \(5.13\times 10^{3}\) & \(8.42\times 10^{-8}\) & \(1.11\times 10^{4}\) & \(2.75\times 10^{-80}\) & \(3.61\times 10^{-7}\) \\ \hline \multirow{4}{*}{F4} & \multirow{4}{*}{0} & Mean & 0.0221 & \(56.8052\) & \(25.9687\) & \(2.23\times 10^{-8}\) & \(40.4751\) & \(3.71\times 10^{-51}\) & \(7.87\times 10^{-8}\) \\  & & Best & \(7.89\times 10^{-95}\) & \(31.0704\) & \(4.4921\) & \(2.17\times 10^{-9}\) & \(9.20\times 10^{-5}\) & \(1.68\times 10^{-99}\) & \(0\) \\  & & Worst & 0.0514 & \(77.9037\) & \(58.7352\) & \(1.37\times 10^{-7}\) & \(8.80\times 10^{4}\) & \(6.46\times 10^{-50}\) & \(3.62\times 10^{-7}\) \\  & & Std.