# K-Means Clustering Algorithm Based on Chaotic Adaptive Artificial Bee Colony
## 4 Numerical Experiments
### CAABC Performance Analysis
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**No.** & **Mean/Std.** & **ABC** & **IABC** & **HABC** & **CAABC** & **DFSABC\_elite** & **CAABC1** & **CAABC2** \\ \hline \multirow{4}{*}{\(f_{1}\)} & Mean & \(1.52\times 10^{-14}\) & \(4.93\times 10^{-17}\) & \(4.53\times 10^{-19}\) & \(\mathbf{2.78\times 10^{-22}}\) & \(1.04\times 10^{-19}\) & \(5.36\times 10^{-20}\) & \(3.61\times 10^{-19}\) \\ \cline{2-8}  & Std. & \(2.99\times 10^{-14}\) & \(2.06\times 10^{-17}\) & \(6.22\times 10^{-19}\) & \(\mathbf{2.16\times 10^{-22}}\) & \(6.17\times 10^{-19}\) & \(3.17\times 10^{-19}\) & \(8.03\times 10^{-19}\) \\ \cline{2-8}  & CPUtime(s) & 34.36 & 11.55 & 12.25 & **8.09** & 9.99 & 7.56 & 11.03 \\ \hline \multirow{4}{*}{\(f_{2}\)} & Mean & \(3.92\times 10^{-210}\) & \(6.88\times 10^{-61}\) & \(7.14\times 10^{-20}\) & \(\mathbf{9.17\times 10^{-253}}\) & \(5.45\times 10^{-240}\) & \(2.80\times 10^{-240}\) & \(4.63\times 10^{-220}\) \\ \cline{2-8}  & Std. & \(\mathbf{0.00}\) & \(1.70\times 10^{-61}\) & **0.00** & **0.00** & **0.00** & **0.00** & **0.00** \\ \cline{2-8}  & CPUtime & 25.40 & 11.23 & 13.60 & **5.69** & 7.32 & 8.92 & 11.04 \\ \hline \multirow{4}{*}{\(f_{3}\)} & Mean & \(4.54\times 10^{-179}\) & \(4.45\times 10^{-2}\) & \(5.96\times 10^{-178}\) & \(\mathbf{2.26\times 10^{-181}}\) & \(8.32\times 10^{-180}\) & \(4.40\times 10^{-180}\) & \(3.92\times 10^{-178}\) \\ \cline{2-8}  & Std. & \(\mathbf{0.00}\) & \(5.29\times 10^{-3}\) & **0.00** & **0.00** & **0.00** & **0.00** & **0.00** \\ \cline{2-8}  & CPUtime & 27.50 & 13.64 & 15.63 & **8.97** & 10.43 & 12.55 & 15.32 \\ \hline \multirow{4}{*}{\(f_{4}\)} & Mean & \(2.03\times 10^{-4}\) & \(1.22\times 10^{-4}\) & \(6.04\times 10^{-4}\) & \(\mathbf{2.02\times 10^{-4}}\) & \(2.04\times 10^{-4}\) & \(2.09\times 10^{-4}\) & \(2.09\times 10^{-4}\) \\ \cline{2-8}  & Std. & \(3.36\times 10^{-7}\) & \(9.67\times 10^{-7}\) & \(9.54\times 10^{-6}\) & \(\mathbf{6.08\times 10^{-7}}\) & \(2.11\times 10^{-7}\) & \(4.21\times 10^{-7}\) & \(6.32\times 10^{-6}\) \\ \cline{2-8}  & CPUtime & 80.47 & 39.21 & 37.43 & **20.33** & 26.42 & 30.02 & 34.53 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison with other improved Artificial Bee Colony in 60-dimensions. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**No. ** & **Mean/Std. ** & **ABC** & **IABC** & **HABC** & **CAABC** & **DFSABC\_elite** & **CAABC1** & **CAABC2** \\ \hline \multirow{4}{*}{\(f_{10}\)} & Mean & \(2.21\times 10^{-5}\) & \(2.73\times 10^{-5}\) & \(3.36\times 10^{-268}\) & \(\mathbf{1.09\times 10^{-297}}\) & \(3.39\times 10^{-226}\) & \(1.22\times 10^{-228}\) & \(2.22\times 10^{-205}\) \\ \cline{2-8}  & Std. & \(1.32\times 10^{-6}\) & \(1.90\times 10^{-6}\) & **0.00** & **0.00** & **0.00** & **0.00** & **0.00** \\ \cline{2-8}  & CPUtime & 34.75 & 15.75 & 14.75 & **12.82** & 16.43 & 15.76 & 17.34 \\ \hline \multirow{4}{*}{\(f_{11}\)} & Mean & \(5.56\times 10^{-184}\) & \(7.83\times 10^{-32}\) & \(1.19\times 10^{-190}\) & \(\mathbf{1.00\times 10^{-192}}\) & \(1.39\times 10^{-192}\) & \(1.99\times 10^{-190}\) & \(9.06\times 10^{-181}\) \\ \cline{2-8}  & Std. & \(\mathbf{0.00}\) & \(2.73\times 10^{-33}\) & **0.00** & \(2.97\times 10^{-161}\) & \(6.97\times 10^{-199}\) & \(3.57\times 10^{-159}\) & \(6.64\times 10^{-144}\) \\ \cline{2-8}  & CPUtime & 24.69 & 15.67 & 14.39 & **11.71** & 14.04 & 13.52 & 15.43 \\ \hline \multirow{4}{*}{\(f_{12}\)} & Mean & \(4.32\times 10^{-5}\) & \(3.05\times 10^{-5}\) & **0.00** & **0.00** & **0.00** & 0.00** & 0.00 \\ \cline{2-8}  & Std. & \(2.98\times 10^{-6}\) & \(3.63\times 10^{-7}\) & **0.00** & **0.00** & **0.00** & **0.00** & **0.00** \\ \cline{2-8}  & CPUtime & 23.53 & 13.24 & 12.88 & **7.54** & 12.67 & 13.85 & 27.48 \\ \hline \multirow{4}{*}{\(f_{13}\)} & Mean & \(1.94\times 10^{-228}\) & \(2.61\times 10^{-8}\) & \(8.74\times 10^{-286}\) & \(\mathbf{1.65\times 10^{-294}}\) & \(8.24\times 10^{-286}\) & \(1.44\times 10^{-288}\) & \(5.74\times 10^{-286}\) \\ \cline{2-8}  & Std.