# Improved Honey Badger Algorithm and Its Application to K-Means Clustering
## 5 Simulation Experiment and Analysis
### Experimental Comparative Analysis of Improved Honey Badger Algorithm
\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}{*}{F17} & Avg & \(6.66\times 10^{-1}\) & \(4.82\times 10^{-2}\) & \(9.64\times 10^{-2}\) & \(2.56\) & \(7.33\times 10^{-3}\) & \(0\) \\  & Std & \(3.38\times 10^{-1}\) & \(4.99\times 10^{-2}\) & \(7.84\times 10^{-3}\) & \(1.78\) & \(2.79\times 10^{-2}\) & \(0\) \\  & Best & \(1.54\times 10^{-1}\) & \(0\) & \(6.56\times 10^{-2}\) & \(1.52\times 10^{-1}\) & \(0\) & \(0\) \\  & Avg & \(-2.06\) & \(-2.06\) & \(-2.06\) & \(-2.06\) & \(-2.06\) & \(-2.06\) & \(-2.06\) \\ F18 & Std & \(9.41\times 10^{-6}\) & \(6.95\times 10^{-10}\) & \(1.04\times 10^{-11}\) & \(1.23\times 10^{-3}\) & \(9.03\times 10^{-16}\) & \(8.84\times 10^{-19}\) \\  & Best & \(-2.06\) & \(-2.06\) & \(-2.06\) & \(-2.06\) & \(-2.06\) & \(-2.06\) & \(-2.06\) \\  & Avg & \(2.04\times 10^{-5}\) & \(1.38\times 10^{-4}\) & \(9.06\times 10^{-20}\) & \(1.09\times 10^{-6}\) & \(8.57\times 10^{-14}\) & \(0\) \\ F19 & Std & \(2.75\times 10^{-5}\) & \(7.14\times 10^{-4}\) & \(2.43\times 10^{-19}\) & \(5.94\times 10^{4}\) & \(6.28\times 10^{-14}\) & \(0\) \\  & Best & \(1.53\times 10^{-7}\) & \(1.25\times 10^{-21}\) & \(1.58\times 10^{-50}\) & \(5.00\times 10^{-6}\) & \(9.28\times 10^{-33}\) & \(0\) \\  & Avg & \(6.63\times 10^{-8}\) & \(2.55\times 10^{-5}\) & \(0\) & \(3.67\times 10^{-2}\) & \(0\) & \(0\) \\ F20 & Std & \(8.27\times 10^{-8}\) & \(1.39\times 10^{-4}\) & \(0\) & \(5.87\times 10^{-2}\) & \(0\) & \(0\) \\  & Best & \(2.40\times 10^{-9}\) & \(4.36\times 10^{-34}\) & \(0\) & \(0\) & \(0\) & \(0\) \\  & Avg & \(6.69\times 10^{-6}\) & \(6.08\times 10^{-225}\) & \(8.84\times 10^{-78}\) & \(3.44\times 10^{-4}\) & \(0\) & \(0\) \\ F21 & Std & \(6.97\times 10^{-6}\) & \(0\) & \(2.87\times 10^{-77}\) & \(6.27\times 10^{-4}\) & \(0\) & \(0\) \\  & Best & \(8.62\times 10^{-7}\) & \(8.28\times 10^{-254}\) & \(6.93\times 10^{-85}\) & \(0\) & \(0\) & \(0\) \\  & Avg & \(6.63\times 10^{-5}\) & \(2.30\times 10^{-95}\) & \(9.85\times 10^{-100}\) & \(1.57\times 10^{-3}\) & \(0\) & \(0\) \\ F22 & Std & \(6.17\times 10^{-5}\) & \(8.49\times 10^{-95}\) & \(2.52\times 10^{-99}\) & \(3.09\times 10^{-3}\) & \(0\). & \(0\) \\  & Best & \(3.68\times 10^{-7}\) & \(1.49\times 10^{-114}\) & \(9.17\times 10^{-106}\) & \(0\) & \(0\) & \(0\) \\  & Avg & \(1.52\) & \(1.98\) & \(8.86\times 10^{-20}\) & \(1.11\) & \(2.62\) & \(1.62\) \\ F23 & Std & \(8.23\times 10^{-1}\) & \(2.66\) & \(2.86\times 10^{-19}\) & \(1.02\) & \(2.88\) & \(1.99\) \\  & Best & \(7.02\times 10^{-1}\) & \(1.24\times 10^{-3}\) & \(2.33\times 10^{-26}\) & \(7.98\times 10^{-2}\) & \(2.40\times 10^{-2}\) & \(5.19\times 10^{-2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Error statistics (average, standard deviation, best) for 30 runs of the IHBA and comparison algorithms on fixed-dimension test functions. reached the optimal standard deviation, indicating the stability of IBHA on F18. In the F23, ARO demonstrated the highest level of integration, while the IHBA exhibited a slightly lower performance in comparison to the ARO. In summary, IHBA performed well on multiple test functions and demonstrated superiority over the comparison algorithm regarding solution quality and robustness. Figure 6 is a convergence diagram of the IHBA on the benchmark function. To ensure fairness, a population \(N=50\), a maximum number of iterations \(t_{max}=500\), and a dimension \(D=30\) was set in the experiment. Each algorithm was run independently 30 times. Due to the limited space, this paper selected some test functions for convergence analysis and comparison. F1-F5 in single-peak test function; F10, F12, F14, and F16 in multi-peak test function; and F17, F19, F21, and F22 in constant-dimension test function were selected, respectively. Figure 6: _Cont._  
Figure 6: \(Cont\). As illustrated in Figure 6, for the unimodal test functions, IHBA demonstrated the fastest convergence speed among the five algorithms.