# A Compact Cat Swarm Optimization Algorithm Based on Small Sample Probability Model
## 4 Experimental Results and Analysis
### Comparison against Swarm-Based Version Algorithms Based on Iterations and Solution
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Remark** & **DE** & **PSO** & **W** & **CSO** & **W** & **SSPCCSO** \\ \hline fu38 & \(-1.056\times 10^{3}\pm\) & \(-1.283\times 10^{3}\pm\) & \(-\) & \(\mathbf{10^{3}\pm 3.91}\times\) & \(-\) & \(0.000\times 10^{0}\) \\ fu39 & \(1.09\times 10^{1}\) & \(2.18\times 10^{2}\) & \(-\) & \(\mathbf{10^{3}\pm 3.91}\times\) & \(-\) & \(0.00\times 10^{0}\) \\  & \(1.09\times 10^{1}\) & \(2.18\times 10^{2}\) & \(-\) & \(\mathbf{10^{1}}\) & \(-\) & \(0.000\times 10^{0}\) \\ fu40 & \(8.338\times 10^{3}\pm\) & \(1.201\times 10^{3}\pm\) & \(-\) & \(\mathbf{0.001\times 10^{0}\pm}\) & \(-\) & \(8.704\times 10^{-3}\pm\) \\ fu39 & \(1.12\times 10^{3}\) & \(2.18\times 10^{2}\) & \(-\) & \(\mathbf{0.01\times 10^{0}\pm}\) & \(-\) & \(2.16\times 10^{-4}\) \\ fu40 & \(8.969\times 10^{4}\pm\) & \(1.701\times 10^{4}\pm\) & \(-\) & \(\mathbf{0.001\times 10^{0}\pm}\) & \(-\) & \(1.463\times 10^{-1}\pm\) \\  & \(7.75\times 10^{3}\) & \(-\) & \(-\) & \(\mathbf{0.01\times 10^{0}}\) & \(-\) & \(2.02\times 10^{-1}\) \\ fu41 & \(2.142\times 10^{9}\pm\) & \(-\) & \(\mathbf{1.784\times 10^{7}\pm}\) & \(-\) & \(4.898\times 10^{1}\pm\) & \(-\) & \(\mathbf{1.397\times 10^{0}\pm}\) \\  & \(5.71\times 10^{8}\) & \(-\) & \(-\) & \(1.38\times 10^{-2}\) & \(-\) & \(\mathbf{5.03\times 10^{0}}\) \\ fu42 & \(1.364\times 10^{1}\pm\) & \(-\) & \(\mathbf{6.878\times 10^{0}\pm}\) & \(-\) & \(\mathbf{0.001\times 10^{0}\pm}\) & \(-\) & \(7.812\times 10^{-2}\pm\) \\  & \(4.46\times 10^{-1}\) & \(-\) & \(\mathbf{4.73\times 10^{-1}}\) & \(-\) & \(\mathbf{0.01\times 10^{0}}\) & \(-\) & \(3.72\times 10^{-2}\) \\ fu43 & \(3.711\times 10^{-2}\pm\) & \(-\) & \(\mathbf{0.001\times 10^{0}\pm}\) & \(-\) & \(2.039\times 10^{-2}\pm\) \\  & \(3.27\times 10^{4}\) & \(-\) & \(\mathbf{0.01\times 10^{0}}\) & \(-\) & \(3.72\times 10^{-2}\) \\ fu44 & \(4.684\times 10^{2}\pm\) & \(-\) & \(\mathbf{0.001\times 10^{0}\pm}\) & \(-\) & \(\mathbf{0.001\times 10^{0}\pm}\) \\  & \(1.35\times 10^{1}\) & \(\mathbf{0.01\times 10^{0}}\) & \(-\) & \(\mathbf{0.01\times 10^{0}}\) & \(-\) & \(\mathbf{0.01\times 10^{0}}\) \\ fu45 & \(2.539\times 10^{6}\pm\) & \(-\) & \(\mathbf{0.001\times 10^{0}\pm}\) & \(-\) & \(1.433\times 10^{1}\pm\) \\  & \(2.09\times 10^{5}\) & \(-\) & \(2.17\times 10^{3}\) & \(-\) & \(\mathbf{0.01\times 10^{0}}\) & \(-\) & \(1.92\times 10^{1}\) \\ fu46 & \(3.152\times 10^{4}\pm\) & \(-\) & \(\mathbf{0.001\times 10^{0}\pm}\) & \(-\) & \(3.577\times 10^{3}\pm\) \\  & \(1.18\times 10^{3}\) & \(-\) & \(\mathbf{0.01\times 10^{0}}\) & \(-\) & \(8.68\times 10^{3}\) \\ fu47 & \(4.675\times 10^{6}\pm\) & \(\mathbf{2.183\times 10^{6}\pm}\) & \(-\) & \(1.694\times 10^{7}\pm\) & \(-\) & \(3.749\times 10^{6}\pm\) \\  & \(2.19\times 10^{5}\) & \(\mathbf{4.01\times 10^{5}}\) & \(-\) & \(4.31\times 10^{6}\) & \(+\) & \(2.47\times 10^{6}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: _Cont._ \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Iterations** & **PSO** & **CSO** & **cPSO** & **SSPCCSO** \\ \hline I 100 & 8202.6317 & 0.00000 & 55.695 & 5.809 \\ \hline I 200 & 3754.9483 & 0.000000 & 19.852 & 4.277 \\ \hline I 1000 & 1417.4688 & 0.000000 & 0.61648 & 0.03692 \\ \hline I 2000 & 1414.2868 & 0.000000 & 0.36894 & 0.000032 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The convergence results on test function 1 based on the same iterations. Because of too many local cycles in the seeking mode, there is not any advantage shown in the computing costs. However, the gradient descent method introduced can make up for this shortcoming. It can end unnecessary calculations in advance, so the algorithm achieves a better performance in less running time.