# 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
Dev & 10.9094 & 0.0 & 0.0 & \(1.43\times 10^{-5}\) & \(2.03\times 10^{-5}\) & 0.0 & 0.0 \\ \hline \multirow{4}{*}{F19} & \multirow{4}{*}{\(-3.86\)} & Mean & \(-3.8536\) & \(-3.8628\) & \(-3.8548\) & \(-3.8615\) & \(-3.8587\) & \(-3.862\) & \(-3.86\) \\  & Best & \(-3.8626\) & \(-3.8628\) & \(-3.8613\) & \(-3.8628\) & \(-3.8628\) & \(-3.8628\) & \(-3.8628\) & \(-3.86\) \\  & Worst & \(-3.8405\) & \(-3.8628\) & \(-3.8512\) & \(-3.8549\) & \(-3.8277\) & \(-3.8552\) & \(-3.86\) \\  & Std. Dev & 0.0037 & 0.0 & 0.0024 & 0.0026 & 0.0065 & 0.0014 & 0.0 \\ \hline \multirow{4}{*}{F20} & \multirow{4}{*}{\(-3.32\)} & Mean & \(-3.0815\) & \(-3.2168\) & \(-3.006\) & \(-3.2532\) & \(-3.2412\) & \(-3.1334\) & \(-3.32\) \\  & Best & \(-3.1835\) & \(-3.3220\) & \(-3.1714\) & \(-3.322\) & \(-3.3219\) & \(-3.3111\) & \(-3.32\) \\  & Worst & \(-2.8472\) & \(-3.1376\) & \(-2.5881\) & \(-3.0604\) & \(-3.0807\) & \(-2.8095\) & \(-3.32\) \\  & Std. Dev & 0.0675 & 0.0448 & 0.1305 & 0.077 & 0.0915 & 0.0976 & 0.0 \\ \hline \multirow{4}{*}{F21} & \multirow{4}{*}{\(-10.153\)} & Mean & \(1.20\times 10^{-14}\) & \(2.00\times 10^{3}\) & 2.4136 & \(2.05\times 10^{-33}\) & \(5.28\times 10^{-85}\) & \(9.02\times 10^{-96}\) & \(3.16\times 10^{-16}\) \\  & 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}{*}{F22} & \multirow{4}{*}{\(-19.2085\)} & Mean & 0.0 & 31.5216 & 0.0100 & \(6.27\times 10^{-20}\) & \(4.56\times 10^{-53}\) & \(1.89\times 10^{-50}\) & \(1.68\times 10^{-30}\) \\  & Best & 0.0 & 0.1102 & \(9.06\times 10^{-5}\) & \(1.06\times 10^{-20}\) & \(1.07\times 10^{-61}\) & \(4.45\times 10^{-65}\) & \(2.13\times 10^{-9}\) \\  & Worst & 0.0 & 80.0085 & 0.0740 & \(2.05\times 10^{-19}\) & \(1.32\times 10^{-51}\) & \(9.29\times 10^{-49}\) & \(7.75\times 10^{-7}\) \\  & 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 \multirow{4}{*}{F23} & \multirow{4}{*}{\(-117.497\)} & 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}{*}{F24} & \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 & \(2.17\times 10^{-9}\) & \(9.20\times 10^{-5}\) & \(1.68\times 10^{-59}\) & \(0.0\) \\  & Worst & 0.0514 & \(77.9032\) & 58.7352 & \(1.37\timesThe unimodal function results show that the conventional HHO had a lead in reaching the global minima value more than the other algorithms. Surprisingly, GWO and WOA have an average performance compared to the newly developed AOA and SCA algorithms. The proposed HHAOA has notable performances in F4-F7 due to the arithmetic operators' and hawks' ability to narrow down the desired global minima and avoid further searching for the exploration locations. Meanwhile, the MFO performs poorly in these functions, which shows its inability to reach even for the singular objective functions.