# Initialisation Approaches for Population-Based Metaheuristic Algorithms: A Comprehensive Review
## 5 Experiment, Result, and Discussion
### Results and Discussion
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{3}{*}{**Function**} & \multirow{3}{*}{**Value**} & \multicolumn{8}{c}{**Grey Wolf Optimizer**} \\ \cline{3-10}  & & **Pop = 10** & **Pop = 20** & **Pop = 30** & **Pop = 50** & **Pop = 100** & **Pop = 300** & **Pop = 500** & **Pop = 1000** \\ \cline{3-10}  & & **Iter = 1000** & **Iter = 900** & **Iter = 800** & **Iter = 600** & **Iter = 500** & **Iter = 300** & **Iter = 100** & **Iter = 10** \\ \hline \multirow{3}{*}{Sphere} & Mean & 0 & 0 & 0 & 0 & 0 & 0 & 2.3000E-06 & 50.3358 \\ \cline{2-10}  & Stand.Div & 0 & 0 & 0 & 0 & 0 & 2.7289E-06 & 53.0968 \\ \cline{2-10}  & Best & 0 & 0 & 0 & 0 & 0 & 0 & 5.6828E-07 & 21.0005 \\ \cline{2-10}  & Worst & 0 & 0 & 0 & 0 & 0 & 0 & 5.6884E-06 & 91.1243 \\ \cline{2-10}  & MeanRunTimes & 1.59E+00 & 2.91E+00 & 6.88E+00 & 6.50E+00 & 9.91E+00 & 4.5197E+00 & 3.6921 & 1.4936 \\ \hline \multirow{3}{*}{Rastrigin} & Mean & 0 & 0 & 0 & 0 & 0 & 5.0086E+00 & 14.6950 & 84.8322 \\ \cline{2-10}  & Stand.Div & 0 & 0 & 0 & 0 & 0 & 6.7312E+00 & 15.1616 & 86.5337 \\ \cline{2-10}  & Best & 0 & 0 & 0 & 0 & 0 & 2.6057E-08 & 8.6052 & 53.7818 \\ \cline{2-10}  & Worst & 0 & 0 & 0 & 0 & 0 & 1.4721E+01 & 20.8869 & 115.8360 \\ \cline{2-10}  & MeanRunTimes & 1.73E+00 & 2.87E+00 & 3.88E+00 & 4.31E+00 & 5.75E+00 & 4.6616E+00 & 3.9513 & 1.6358 \\ \hline \multirow{3}{*}{Rosenbrock} & Mean & 2.56E+01 & 2.56E+01 & 2.56E+01 & 2.52E+01 & 2.54E+01 & 2.5108E+01 & 26.5188 & 1.3708E+03 \\ \cline{2-10}  & Stand.Div & 2.56E+01 & 2.56E+01 & 2.52E+01 & 2.524E+01 & 2.5115E+01 & 26.5425 & 1.6446E+03 \\ \cline{2-10}  & Best & 2.41E+01 & 2.42E+01 & 2.41E+01 & 2.40E+01 & 2.42E+01 & 2.4025E+01 & 25.0393 & 429.0925 \\ \cline{2-10}  & Worst & 2.62E+01 & 2.62E+01 & 2.70E+01 & 2.61E+01 & 2.62E+01 & 2.6104E+01 & 28.7730 & 4.0747E+03 \\ \cline{2-10}  & MeanRunTimes & 1.52E+00 & 3.23E+00 & 5.52E+00 & 3.80E+00 & 6.96E+00 & 4.4560E+00 & 3.5834 & 1.4551 \\ \hline \multirow{3}{*}{Griewank} & Mean & 3.76E-04 & 6.21E-04 & 9.90E-04 & 0 & 0 & 6.0142E-03 & 0.0056 & 1.4594 \\ \cline{2-10}  & Stand.Div & 1.68E-03 & 2.78E-03 & 3.13E-03 & 0 & 0 & 1.4804E-02 & 0.0092 & 1.4767 \\ \cline{2-10}  & Best & 0 & 0 & 0 & 0 & 0 & 0 & 1.6031E-06 & 1.1595 \\ \cline{2-10}  & Worst & 7.52E-03 & 1.24E-02 & 9.91E-03 & 0 & 0 & 6.0169E-02 & 0.0211 & 1.9960 \\ \cline{2-10}  & MeanRunTimes & 1.73E+00 & 3.02E+00 & 5.34E+00 & 6.25E+00 & 9.52E+00 & 6.3599E+00 & 3.8414 & 1.7894 \\ \hline \hline \end{tabular}
\end{table} 
Table 14: Result for Grey Wolf Optimizer. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **BA** & **GWO** & **BOA** \\ \hline Pop = 10 & 7.11 & 5.04 & 4.89 \\ Iter = 1000 & 6.30 & 4.07 & 4.22 \\ \hline Pop = 30 & 5.59 & 4.63 & 3.26 \\ \hline Pop = 50 & 5.19 & 3.65 & 3.67 \\ Iter = 500 & 4.30 & 3.91 & 3.35 \\ \hline Pop = 30 & 3.30 & 3.70 & 4.43 \\ Iter = 100 & 2.70 & 5.13 & 5.67 \\ \hline Pop = 100 & 1.52 & 5.87 & 6.52 \\ \hline N & 10 & 10 & 10 \\ \hline Chi-Square & 113.914 & 29.445 & 49.249 \\ \hline df & 7 & 7 & 7 \\ \hline Asymp. Sig. & 0.000 & 0.000 & 0.000 \\ \hline \hline \end{tabular}
\end{table} 
Table 16: Friedman test result.