## 4 Experimental Results and Discussion of IHSSAO Performance Verification
### Experiment I: Classical Benchmark Function
#### 4.1.3 Comparison with IHSSAO and Other Algorithms
For \(F_{18}\), the standard deviation of IHSSAO is second  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \(F_{\mathbf{s}}\) & **Metric** & **WOA** & **HHO** & **SSA** & **MVO** & **STOA** & **TSA** & **AO** & **IHSSAO** \\ \hline \(F_{1}\) & Avg & \(3.07\times 10^{-72}\) & \(3.72\times 10^{-94}\) & \(1.53\times 10^{-7}\) & \(1.17\times 10^{0}\) & \(8.28\times 10^{-7}\) & \(2.46\times 10^{-21}\) & \(1.56\times 10^{-104}\) & \(\mathbf{0.00\times 10^{0}}\) \\  & Std & \(1.37\times 10^{-71}\) & \(1.84\times 10^{-93}\) & \(1.29\times 10^{-7}\) & \(3.35\times 10^{-1}\) & \(1.41\times 10^{-6}\) & \(5.54\times 10^{-21}\) & \(8.52\times 10^{-104}\) & \(\mathbf{0.00\times 10^{0}}\) \\ \(F_{2}\) & Avg & \(2.06\times 10^{-51}\) & \(3.17\times 10^{-50}\) & \(2.32\times 10^{0}\) & \(9.27\times 10^{-1}\) & \(7.97\times 10^{-6}\) & \(1.06\times 10^{-13}\) & \(8.53\times 10^{-37}\) & \(\mathbf{0.00\times 10^{0}}\) \\  & Std & \(8.00\times 10^{-51}\) & \(9.82\times 10^{-50}\) & \(1.95\times 10^{0}\) & \(4.70\times 10^{-1}\) & \(6.96\times 10^{-6}\) & \(1.29\times 10^{-13}\) & \(3.76\times 10^{-56}\) & \(\mathbf{0.00\times 10^{0}}\) \\  & Avg & \(4.24\times 10^{4}\) & \(1.07\times 10^{-76}\) & \(1.72\times 10^{3}\) & \(1.92\times 10^{2}\) & \(8.82\times 10^{-2}\) & \(8.91\times 10^{-5}\) & \(1.58\times 10^{-101}\) & \(\mathbf{0.00\times 10^{0}}\) \\  & Std & \(1.51\times 10^{4}\) & \(5.82\times 10^{-76}\) & \(9.89\times 10^{2}\) & \(6.60\times 10^{1}\) & \(1.57\times 10^{-1}\) & \(2.42\times 10^{-4}\) & \(8.63\times 10^{-101}\) & \(\mathbf{0.00\times 10^{0}}\) \\ \(F_{4}\) & Avg & \(4.89\times 10^{1}\) & \(3.43\times 10^{-7}\) & \(1.15\times 10^{1}\) & \(1.81\times 10^{0}\) & \(6.38\times 10^{-2}\) & \(2.70\times 10^{-1}\) & \(9.68\times 10^{-54}\) & \(\mathbf{0.00\times 10^{0}}\) \\  & Std & \(2.95\times 10^{1}\) & \(1.87\times 10^{-46}\) & \(2.81\times 10^{0}\) & \(6.14\times 10^{-1}\) & \(8.84\times 10^{-2}\) & \(2.29\times 10^{-1}\) & \(3.16\times 10^{-53}\) & \(\mathbf{0.00\times 10^{0}}\) \\  & Avg & \(2.80\times 10^{1}\) & \(1.02\times 10^{-2}\) & \(2.76\times 10^{2}\) & \(6.11\times 10^{2}\) & \(2.84\times 10^{1}\) & \(2.81\times 10^{1}\) & \(5.80\times 10^{-3}\) & \(\mathbf{2.49\times 10^{-5}}\) \\  & Std & \(5.37\times 10^{-1}\) & \(1.14\times 10^{-2}\) & \(4.50\times 10^{2}\) & \(8.88\times 10^{2}\) & \(4.74\times 10^{-1}\) & \(7.85\times 10^{-1}\) & \(1.05\times 10^{-2}\) & \(\mathbf{1.11\times 10^{-4}}\) \\ \(F_{5}\) & Avg & \(4.42\times 10^{-1}\) & \(7.32\times 10^{-5}\) & \(\mathbf{4.68\times 10^{-7}}\) & \(1.22\times 10^{0}\) & \(2.65\times 10^{0}\) & \(3.74\times 10^{0}\) & \(7.58\times 10^{-4}\) & \(2.45\times 10^{-5}\) \\  & Std & \(2.25\times 10^{-1}\) & \(8.16\times 10^{-5}\) & \(\mathbf{1.41\times 10^{-6}}\) & \(4.04\times 10^{-1}\) & \(6.06\times 10^{-1}\) & \(7.28\times 10^{-1}\) & \(1.69\times 10^{-3}\) & \(3.68\times 10^{-5}\) \\  & Avg & \(2.53\times 10^{-3}\) & \(1.59\times 10^{-4}\) & \(1.89\times 10^{-1}\) & \(3.02\times 10^{-2}\) & \(5.66\times 10^{-3}\) & \(1.20\times 10^{-2}\) & \(1.08\times 10^{-4}\) & \(\mathbf{3.30\times 10^{-5}}\) \\  & Std & \(3.51\times 10^{-3}\) & \(1.20\times 10^{-4}\) & \(7.17\times 10^{-2}\) & \(1.29\times 10^{-2}\) & \(3.24\times 10^{-3}\) & \(4.71\times 10^{-3}\) & \(1.14\times 10^{-4}\) & \(\mathbf{3.86\times 10^{-5}}\) \\  & Avg & \(-10.228\)A0 & \(-12.542\)A9 & \(-43.759\)A9 & \(-7.419\)A26 & \(-5252.57\) & \(-5819.64\) & \(-9949.91\) & \(-\)**12.569.42** \\  & Std & \(1.86\times 10^{3}\) & \(1.11\times 10^{2}\) & \(7.84\times 10^{3}\) & \(6.31\times 10^{2}\) & \(6.62\times 10^{2}\) & \(6.81\times 10^{2}\) & \(3.65\times 10^{3}\) & \(\mathbf{1.30\times 10^{-1}}\) \\  & Avg & \(3.79\times 10^{-15}\) & \(\mathbf{0.00\times 10^{0}}\) & \(5.29\times 10^{1}\) & \(1.12\times 10^{2}\) & \(9.92\times 10^{0}\) & \(1.81\times 10^{2}\) & \(\mathbf{0.00\times 10^{0}}\) & \(\mathbf{0.00\times 10^{0}}\) \\  & Std & \(1.44\times 10^{-14}\) & \(\mathbf{0.00\timesonly to that of the SSA.