# Improved Honey Badger Algorithm and Its Application to K-Means Clustering
## 5 Simulation Experiment and Analysis
### Experimental Comparative Analysis of Improved Honey Badger Algorithm

Table 3: _Cont._  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Functions** & **ATR** & **PSO** & **WOA** & **ARO** & **SWO** & **HBA** & **IHBA** \\ \hline \multirow{4}{*}{F1} & Avg & \(1.40\times 10^{1}\) & \(7.57\times 10^{-83}\) & \(9.08\times 10^{-59}\) & \(3.95\times 10^{2}\) & \(7.28\times 10^{-147}\) & 0 \\  & Std & \(2.29\) & \(4.11\times 10^{-82}\) & \(4.97\times 10^{-58}\) & \(7.91\times 10^{2}\) & \(8.43\times 10^{-146}\) & 0 \\  & Best & \(8.88\) & \(1.1\times 10^{-94}\) & \(1.27\times 10^{-71}\) & \(2.70\times 10^{-1}\) & \(6.06\times 10^{-152}\) & 0 \\  & Avg & \(1.64\times 10^{1}\) & \(1.62\times 10^{-54}\) & \(4.14\times 10^{-33}\) & 3.60 & \(7.34\times 10^{-77}\) & 0 \\  & Std & \(9.10\times 10^{-1}\) & \(6.34\times 10^{-54}\) & \(1.31\times 10^{-32}\) & 8.22 & \(3.63\times 10^{-76}\) & 0 \\  & Best & \(1.44\times 10^{1}\) & \(3.24\times 10^{-60}\) & \(4.93\times 10^{-37}\) & \(6.39\times 10^{-3}\) & \(7.47\times 10^{-81}\) & 0 \\  & Avg & \(5.60\times 10^{1}\) & \(2.79\times 10^{4}\) & \(6.43\times 10^{-47}\) & \(6.89\times 10^{2}\) & \(1.23\times 10^{-99}\) & 0 \\ F3 & Std & \(1.28\times 10^{1}\) & \(1.11\times 10^{4}\) & \(2.15\times 10^{-46}\) & \(1.35\times 10^{3}\) & \(5.85\times 10^{-99}\) & 0 \\  & Best & \(2.90\times 10^{1}\) & \(8.36\times 10^{3}\) & \(2.89\times 10^{-57}\) & \(9.09\times 10^{2}\) & \(1.22\times 10^{-109}\) & 0 \\  & Avg & \(1.52\) & \(3.54\times 10^{1}\) & \(2.89\times 10^{-25}\) & 4.15 & \(3.25\times 10^{-62}\) & 0 \\ F4 & Std & \(1.07\times 10^{1}\) & \(2.19\times 10^{1}\) & \(9.77\times 10^{-25}\) & 5.21 & \(6.05\times 10^{-62}\) & 0 \\  & Best & \(1.31\) & \(1.65\times 10^{-1}\) & \(2.86\times 10^{-31}\) & \(6.59\times 10^{-3}\) & \(6.09\times 10^{-65}\) & 0 \\  & Avg & \(1.68\times 10^{1}\) & \(7.85\times 10^{-54}\) & \(2.04\times 10^{-32}\) & 6.54 & \(1.90\times 10^{-75}\) & 0 \\ F5 & Std & \(1.56\) & \(1.58\times 10^{-53}\) & \(8.03\times 10^{-32}\) & 9.87 & \(3.27\times 10^{-75}\) & 0 \\  & Best & \(1.45\times 10^{1}\) & \(1.25\times 10^{-57}\) & \(2.64\times 10^{-37}\) & \(3.88\times 10^{-4}\) & \(2.25\times 10^{-78}\) & 0 \\  & Avg & \(2.14\times 10^{3}\) & \(5.78\times 10^{-89}\) & \(6.36\times 10^{-60}\) & \(7.03\times 10^{1}\) & \(2.00\times 10^{-139}\) & \(1.88\times 10^{-138}\) \\ F6 & Std & \(4.28\times 10^{2}\) & \(3.04\times 10^{-88}\) & \(3.18\times 10^{-59}\) & \(1.43\times 10^{2}\) & \(1.10\times 10^{-138}\) & \(1.02\times 10^{-138}\) \\  & Best & \(1.33\times 10^{3}\) & \(1.0\times 10^{-99}\) & \(6.59\times 10^{-68}\) & \(1.79\times 10^{-4}\) & \(2.25\times 10^{-147}\) & \(7.84\times 10^{-204}\) \\  & Avg & \(1.03\times 10^{-1}\) & \(2.13\times 10^{-3}\) & \(5.30\times 10^{-4}\) & \(1.32\times 10^{-1}\) & \(1.32\times 10^{-4}\) & \(6.11\times 10^{-5}\) \\ F7 & Std & \(5.66\times 10^{-2}\) & \(2.32\times 10^{-3}\) & \(3.23\times 10^{-4}\) & \(1.20\times 10^{-1}\) & \(5.93\times 10^{-5}\) & \(4.76\times 10^{-5}\) \\  & Best & \(3.44\times 10^{-2}\) & \(2.47\times 10^{-5}\) & \(5.01\times 10^{-5}\) & \(7.51\times 10^{-3}\) & \(1.30\times 10^{-5}\) & \(3.08\times 10^{-6}\) \\  & Avg & \(1.73\times 10^{-5}\) & \(1.49\times 10^{-128}\) & \(4.14\times 10^{-4}\) & \(6.71\times 10^{-4}\) & 0 & 0 \\ F8 & Std & \(1.60\times 10^{-5}\) & \(8.17\times 10^{-128}\) & \(2.47\times 10^{-4}\) & \(3.20\times 10^{-3}\) & 0 & 0 \\  & Best & \(9.70\times 10^{-7}\) & \(1.50\times 10^{-163}\) & \(8.25\times 10^{-5}\) & 0 & 0 & 0 \\  & Avg & \(2.07\times 10^{2}\) & \(8.83\times 10^{-84}\) & \(5.11\times 10^{-4}\) & \(1.19\times 10^{2}\) & \(2.09\times 10^{-147}\) & 0 \\ F9 & Std & \(2.50\times 10^{1}\) & \(4.82\times 10^{-83}\) & \(4.40\times 10^{-4}\) & \(2.70\times 10^{2}\) & \(5.11\times 10^{-147}\) & 0 \\  & Best & \(1.79\times 10^{2}\) & \(7.70\times 10^{-96}\) & \(1.67\times 10^{-6}\) & 0 & \(5.67\times 10^{-154}\) & 0 \\  & Avg & \(-6.23\times 10^{3}\) & \(-5.31\times 10^{3}\) & \(-1.60\times 10^{4}\) & \(-3.90\times 10^{3}\) & \(-8.96\times 10^{3}\) & \(-1.08\times 10^{4}\) \\ F10 & Std & \(9.57\times 10^{2}\) & \(7.40\times 10^{2}\) & \(5.19\times 10^{2}\) & \(3.82\times 10^{2}\) & \(9.02\times 10^{2}\) & \(6.01\times 10^{2}\) \\  & Best & \(-7.94\times 10^{3}\) & \(-6.06\times 10^{3}\) & \(-1.14\times 10^{4}\) & \(-4.96\times 10^{3}\) & \(-1.02\times 10^{4}\) & \(-1.18\times 10^{4}\) \\  & Avg & \(2.19\times 10^{2}\) & \(3.79\times 10^{-15}\) & 0 & \  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Functions** & **ATR** & **PSO** & **WOA** & **ARO** & **SWO** & **HBA** & **IHBA** \\ \hline \multirow{4}{*}{F1} & avg & \(9.37\times 10^{3}\) & \(3.55\times 10^{-82}\) & \(2.88\times 10^{-51}\) & \(2.82\times 10^{3}\) &  
In the comparison of multi-modal test functions, IHBA showed a strong search ability; its performance was particularly outstanding, especially in the F12, F14, and F16 functions.