# K-Means Clustering Algorithm Based on Chaotic Adaptive Artificial Bee Colony
## 4 Numerical Experiments
### CAABC Performance Analysis
& \(\mathbf{0.00}\) & \(2.21\times 10^{-9}\) & **0.00** & **0.00** & **0.00** & **0.00** & **0.00** \\ \cline{2-8}  & CPUtime & 25.65 & 19.56 & 17.55 & **10.59** & 17.66 & 18.95 & 19.05 \\ \hline \multirow{4}{*}{\(f_{14}\)} & Mean & \(1.36\times 10^{-56}\) & \(1.46\) & \(5.95\times 10^{-102}\) & \(\mathbf{3.50\times 10^{-106}}\) & \(5.95\times 10^{-103}\) & \(4.90\times 10^{-105}\) & \(3.93\times 10^{-102}\) \\ \cline{2-8}  & Std. & \(3.00\times 10^{-56}\) & \(1.29\times 10^{-2}\) & \(4.75\times 10^{-102}\) & \(6.99\times 10^{-106}\) & \(\mathbf{6.75\times 10^{-106}}\) & \(7.99\times 10  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**No. ** & **Mean/Std. ** & **ABC** & **IABC** & **AABC** & **CAABC** & **DFSABC\_elite** & **CAABC1** & **CAABC2** \\ \hline \multirow{3}{*}{\(f_{5}\)} & Mean & \(2.52\times 10^{-229}\) & \(2.02\times 10^{-4}\) & \(4.08\times 10^{-227}\) & **0.00** & \(8.15\times 10^{-242}\) & \(4.19\times 10^{-242}\) & \(2.64\times 10^{-220}\) \\ \cline{2-8}  & Std. & **0.00** & \(3.07\times 10^{-5}\) & **0.00** & **0.00** & **0.00** & **0.00** & **0.00** \\ \hline \multirow{3}{*}{\(f_{6}\)} & CPUtime & 79.05 & 59.34 & 60.32 & **37.08** & 40.02 & 43.22 & 69.02 \\ \cline{2-8}  & Mean & \(4.05\times 10^{-195}\) & \(3.05\times 10^{-62}\) & \(6.66\times 10^{-205}\) & \(\textbf{1.47\times 10^{-249}}\) & \(4.56\times 10^{-224}\) & \(2.35\times 10^{-224}\) & \(4.32\times 10^{-205}\) \\ \cline{2-8}  & Std. & **0.00** & \(7.49\times 10^{-63}\) & \(6.02\times 10^{-157}\) & **0.00** & \(3.32\times 10^{-189}\) & \(1.71\times 10^{-189}\) & \(3.90\times 10^{-157}\) \\ \cline{2-8}  & CPUtime & 106.99 & 43.42 & 39.53 & **18.02** & 36.43 & 37.66 & 49.58 \\ \hline \multirow{3}{*}{\(f_{7}\)} & Mean & \(3.70\times 10^{-121}\) & \(4.25\times 10^{-6}\) & \(7.08\times 10^{-120}\) & \(\textbf{1.49\times 10^{-122}}\) & \(1.33\times 10^{-120}\) & \(6.92\times 10^{-121}\) & \(5.45\times 10^{-120}\) \\ \cline{2-8}  & Std. & \(7.66\times 10^{-121}\) & \(2.20\times 10^{-8}\) & \(4.10\times 10^{-119}\) & \(\textbf{3.08\times 10^{-122}}\) & \(2.10\times 10^{-119}\) & \(1.08\times 10^{-119}\) & \(4.02\times 10^{-119}\) \\ \cline{2-8}  & CPUtime & 23.44 & 15.42 & 15.33 & **10.93** & 13.41 & 13.02 & 16.33 \\ \hline \multirow{3}{*}{\(f_{8}\)} & Mean & \(1.08\times 10^{-120}\) & \(3.56\times 10^{-6}\) & \(9.05\times 10^{-119}\) & \(\textbf{2.19\times 10^{-121}}\) & \(5.65\times 10^{-120}\) & \(3.02\times 10^{-120}\) & \(6.23\times 10^{-119}\) \\ \cline{2-8}  & Std. & \(2.23\times 10^{-120}\) & \(6.24\times 10^{-7}\) & \(2.85\times 10^{-118}\) & \(\textbf{4.54\times 10^{-121}}\) & \(1.27\times 10^{-120}\) & \(8.87\times 10^{-121}\) & \(1.85\times 10^{-118}\) \\ \cline{2-8}  & CPUtime & 11.73 & 7.61 & 7.52 & **3.32** & 4.66 & 5.32 & 6.45 \\ \hline \multirow{3}{*}{\(f_{9}\)} & Mean & \(9.34\times 10^{-254}\) & \(1.37\times 10^{-28}\) & \(2.66\times 10^{-258}\) & \(\textbf{2.54\times 10^{-258}}\) & \(9.06\times 10^{-258}\) & \(4.66\times 10^{-258}\) & \(7.59\times 10^{-258}\) \\ \cline{2-8}  & Std. & **0.00** & \(1.24\times 10^{-29}\) & **0.00** & **0.00** & **0.00** & **0.00** & **0.00** \\ \cline{2-8}  & CPUtime & 87.77 & 55.22 & 53.88 & **27.31** & 29.75 & 30.41 & 58.22 \\ \hline \multirow{3}{*}{\(f_{10}\)} & Mean & \(6.63\times 10^{-178}\) & \(5.40\times 10^{-6}\) & \(9.12\times 10^{-123}\) & \(\textbf{1.29\times 10^{-123}}\) & \(9.01\times 10^{-123}\) & \(5.30\times 10^{-123}\) & \(1.17\times 10^{-122}\) \\ \cline{2-8}  & Std. & \(1.65\times 10^{-128}\) & \(1.38\times 10^{-7}\) & \(\textbf{1.84\times 10^{-122}}\) & \(\textbf{2.33\times 10^{-122}}\) & \(9.84\times 10^{-122}\) & \(6.26\times 10^{-123}\) & \(1.83\times 10^{-122}\) \\ \cline{2-8}  & CPUtime & 46.64 & 19.75 & 24.56 & **18.62** & 19.04 & 19.35 & 20.53 \\ \hline \multirow{3}{*}{\(f_{11}\)} & Mean & \(6.63\times 10^{-178}\) & \(8.67\times 10^{-42}\) & \(1.86\times 10^{-204}\) & \(\textbf{4.01\times 10^{-220}}\) & \(9.86\times 10^{-214}\) & \(5.07\times 10^{-214}\) & \(1.21\times 10^{-204}\) \\ \cline{2-8}  & Std.