# A Novel Complex-Valued Encoding Grey Wolf Optimization Algorithm
## 3 Complex-Valued Encoding Grey Wolf Optimization Algorithm (CGWO)
### CGWO Algorithm
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline
**Dim = 50** & \(\mathbf{F_{1}}\) & \(\mathbf{F_{2}}\) & \(\mathbf{F_{3}}\) & \(\mathbf{F_{4}}\) & \(\mathbf{F_{5}}\) & \(\mathbf{F_{6}}\) & \(\mathbf{F_{7}}\) & \(\mathbf{F_{8}}\) \\ \hline CGWO \(\approx\) DGWO & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 1.3486E\(-\)03 & 6.7956E\(-\)08 \\ CGWO \(\approx\) GWO & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 3.0566E\(-\)03 & 3.7051E\(-\)05 & 6.7956E\(-\)08 & 7.9479E\(-\)07 & 3.9388E\(-\)07 \\ CGWO \(\approx\) GGSA & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 \\ CGWO \(\approx\) AG0 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 \\ \hline
**Dim = 50** & \(\mathbf{F_{9}}\) & \(\mathbf{F_{10}}\) & \(\mathbf{F_{11}}\) & \(\mathbf{F_{12}}\) & \(\mathbf{F_{13}}\) & \(\mathbf{F_{14}}\) & \(\mathbf{F_{15}}\) & \(\mathbf{F_{16}}\) \\ \hline CGWO \(\approx\) DGWO & 1.1267E\(-\)08 & 5.6999E\(-\)08 & 1.1267E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 \\ CGWO \(\approx\) GWO & 1.1168E\(-\)08 & 5.6775E\(-\)08 & 1.6493E\(-\)01 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.1046E\(-\)07 & 6.7956E\(-\)08 & 1.0646E\(-\)07 \\ CGWO \(\approx\) GGSA & 1.1267E\(-\)08 & 5.6611E\(-\)08 & 1.1267E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 1.6571E\(-\)07 & 5.2269E\(-\)07 \\ CGWO \(\approx\) ARC & 1.1267E\(-\)08 & 5.6939E\(-\)08 & 1.1267E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 \\ \hline \end{tabular}
\end{table} 
Table 8: \(p\)-values produced by Wilcoxon rank-sum test comparing CGWO \(\approx\). DGWO, GWO, GGSA, and ABC at Dim = 50 (\(p\geq\) 0.05 have been underlined). \begin{table}
\begin{tabular}{c c c c c c c c c} \hline
**Dim = 100** & \(\mathbf{F_{1}}\) & \(\mathbf{F_{2}}\) & \(\mathbf{F_{3}}\) & \(\mathbf{F_{4}}\) & \(\mathbf{F_{5}}\) & \(\mathbf{F_{6}}\) & \(\mathbf{F_{7}}\) & \(\mathbf{F_{8}}\) \\ \hline CGWO \(\approx\) DGWO & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 1.3486E\(-\)03 & 6.7956E\(-\)08 \\ CGWO \(\approx\) GWO & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 3.0566E\(-\)03 & 3.7051E\(-\)05 & 6.7956E\(-\)08 & 7.9479E\(-\)07 & 3.9388E\(-\)07 \\ CGWO \(\approx\) GGSA & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 \\ CGWO \(\approx\) AG0 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 \\ CGWO \(\approx\) ARC & 5.6042E\(-\)08 & 6.5014E\(-\)08 & 8.0065E\(-\)09 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 \\ CGWO \(\approx\) ARC & 5.6042E\(-\)08 & 6.5014E\(-\)08 & 8.0065E\(-\)09 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 1.1355E\(-\)01 \\ \hline \end{tabular}
\end{table} 
Table 9: \(p\)-values produced by Wilcoxon rank-sum test comparing CGWO \(\approx\). DGWO, GWO, GGSA, and ABC at Dim = 100 (\(p\geq\) 0.05 have been underlined).