# 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 = 200** & **F\({}_{1}\)** & **F\({}_{2}\)** & **F\({}_{3}\)** & **F\({}_{4}\)** & **F\({}_{5}\)** & **F\({}_{6}\)** & **F\({}_{7}\)** & **F\({}_{8}\)** \\ \hline CGWO DS: DGWO & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 1.1045E\(-\)05 \\ CGWO DS: GWO & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 4.0936E\(-\)01 & 1.4149E\(-\)05 & 6.7956E\(-\)08 & 7.8980E\(-\)08 & 9.8921E\(-\)01 \\ CGWO DS: GGSA & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 7.8980E\(-\)08 & 2.9598E\(-\)07 & 6.7956E\(-\)08 \\ CGWO DS: ABC & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 5.8736E\(-\)06 \\ \hline
**Dim = 200** & **F\({}_{9}\)** & **F\({}_{10}\)** & **F\({}_{11}\)** & **F\({}_{12}\)** & **F\({}_{13}\)** & **F\({}_{14}\)** & **F\({}_{15}\)** & **F\({}_{16}\)** \\ CGWO DS: DGWO & 6.6532E\(-\)08 & 6.7956E\(-\)08 & 1.9544E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 \\ CGWO DS: GWO & 1.3953E\(-\)05 & 6.7956E\(-\)08 & 2.7851E\(-\)07 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 3.9874E\(-\)06 & 6.7956E\(-\)08 \\ CGWO DS: GGSA & 1.0292E\(-\)06 & 6.7956E\(-\)08 & 1.9544E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.6737E\(-\)06 & 5.1153E\(-\)03 & 7.8980E\(-\)08 \\ CGWO DS: ABC & 6.6532E\(-\)08 & 6.7956E\(-\)08 & 1.9544E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 \\ \hline \end{tabular}
\end{table} 
Table 10. \(p\)-values produced by Wilcoxon rank-sum test comparing CGWO DS. DGWO, GWO, GGSA, and ABC at Dim = 200 (\(p\geq 0.05\) have been underlined). \begin{table}
\begin{tabular}{c c c c c c c c c} \hline
**Dim = 300** & **F\({}_{1}\)** & **F\({}_{2}\)** & **F\({}_{3}\)** & **F\({}_{4}\)** & **F\({}_{5}\)** & **F\({}_{6}\)** & **F\({}_{7}\)** & **F\({}_{8}\)** \\ \hline CGWO DS: DGWO & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 1.1045E\(-\)05 \\ CGWO DS: GWO & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 4.0936E\(-\)01 & 1.4149E\(-\)05 & 6.7956E\(-\)08 & 7.8980E\(-\)08 & 9.8921E\(-\)01 \\ CGWO DS: GGSA & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 7.8980E\(-\)08 & 2.9598E\(-\)07 & 6.7956E\(-\)08 \\ CGWO DS: ABC & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 5.8736E\(-\)06 \\ \hline
**Dim = 200** & **F\({}_{9}\)** & **F\({}_{10}\)** & **F\({}_{11}\)** & **F\({}_{12}\)** & **F\({}_{13}\)** & **F\({}_{14}\)** & **F\({}_{15}\)** & **F\({}_{16}\)** \\ CGWO DS: DGWO & 6.6532E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 \\ CGWO DS: GWO & 6.6532E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 & 6.7956E\(-\)08 \\ \hline \end{tabular}
\end{table} 
Table 11. \(p\)-values produced by Wilcoxon rank-sum test comparing CGWO DS. DGWO, GWO, GGSA, and ABC at Dim = 300 (\(p\geq 0.05\) have been underlined).