## 6 Simulations
### Simulation Results
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Policy**} & \multirow{2}{*}{**NSP**} & \multicolumn{6}{c}{**Ring**} & \multicolumn{6}{c}{**Cube/Trigonal Pyramid/Hypercube**} & \multirow{2}{*}{**Ave. Rank**} \\ \cline{3-3} \cline{5-11}  & & & **Mean** & **Min.** & **Max.** & **Std.** & & **Mean** & **Min.** & **Max.** & **Std.** & \\ \hline \multirow{5}{*}{_R-B_} & 2 & 99.96 & 99.83 & 100.05 & 0.06 & 35.46 & - & - & - & - & - \\ \cline{2-11}  & 4 & 99.89 & 99.76 & 99.98 & 0.05 & 28.2 & 99.91 & 99.8 & 100.05 & 0.05 & 30.84 \\ \cline{2-11}  & 8 & 99.82 & 99.72 & 99.92 & 0.05 & 19.16 & 99.81 & 99.69 & 99.9 & 0.04 & 18.88 \\ \cline{2-11}  & 16 & 99.7 & 99.58 & 99.84 & 0.06 & 7.34 & 99.7 & 99.58 & 99.89 & 0.06 & 7.3 \\ \cline{2-11}  & 2 & 99.99 & 99.87 & 100.09 & 0.06 & 38 & - & - & - & - & - \\ \cline{2-11}  & 4 & 99.91 & 99.83 & 100 & 0.04 & 31.04 & 99.9 & 99.75 & 99.96 & 0.04 & 29.84 \\ \cline{2-11}  & 8 & 99.82 & 99.7 & 99.89 & 0.04 & 19.24 & 99.76 & 99.65 & 99.84 & 0.04 & 12.58 \\ \cline{2-11}  & 16 & 99.69 & 99.61 & 99.77 & 0.03 & 6.14 & 99.64 & 99.55 & 99.77 & 0.05 & 3.74 \\ \hline \multirow{5}{*}{R-W} & 2 & \(8.58\times 10^{10}\) & \(9.25\times 10^{8}\) & \(3.48\times 10^{11}\) & \(7.48\times 10^{10}\) & 49.42 & - & - & - & - & - \\ \cline{2-11}  & 4 & \(1.17\times 10^{11}\) & \(8.86\times 10^{10}\) & \(4.16\times 10^{11}\) & \(9.66\times 10^{10}\) & 51.16 & \(1.11\times 10^{11}\) & \(7.72\times 10^{8}\) & \(3.55\times 10^{11}\) & \(8.10\times 10^{10}\) & 51 \\ \cline{2-11}  & 8 & \(1.61\times 10^{11}\) & \(1.62\times 10^{10}\) & \(7.86\times 10^{11}\) & \(1.49\times 10^{11}\) & 52.92 & \(1.42\times 10^{11}\) & \(7.88\times 10^{9}\) & \(5.17\times 10^{11}\) & \(1.13\times 10^{11}\) & 52.6 \\ \cline{2-11}  & 16 & \(3.07\times 10^{11}\) & \(5.37\times 10^{10}\) & \(1.19\times 10^{12}\) & \(2.25\times 10^{11}\) & 58.84 & \(2.85\times 10^{11}\) & \(4.49\times 10^{10}\) & \(1.02\times 10^{12}\) & \(1.85\times 10^{11}\) & 58.78 \\ \hline \multirow{5}{*}{_R-R_} & 2 & 99.93 & 99.85 & 100.05 & 0.04 & 33.42 & - & - & - & - & 26.56 \\ \cline{2-11}  & 4 & 99.87 & 99.79 & 99.99 & 0.04 & 26.54 & 99.94 & 99.85 & 100.07 & 0.04 & 18.48 \\ \cline{1-1} \cline{2-11}  & 8 & 99.81 & 99.74 & 99.89 & 0.03 & 18.32 & 99.81 & 99.66 & 99.93 & 0.05 & 9.4 \\ \cline{1-1} \cline{2-11}  & 16 & 99.7 & 99.62 & 99.84 & 0.05 & 7.56 & 99.71 & 99.6 & 99.87 & 0.06 & 26.56 \\ \hline \multicolumn{2}{c}{_p_-value} & \multicolumn{6}{c}{0} & \multicolumn{6}{c}{19} \\ \hline \hline \end{tabular}  
* All values are calculated when the mean of the objective function value of the proposed method with a single population is set to 100%. NSP stands for number of sub-populations.  
\end{table} 
Table 6: _Cont._Table 7 shows the best values of the mean, the minimum, and the maximum, the standard deviation values, and the average rank of the results calculated using optimal objective function values using only migration model of each migration policy with 640 individuals through 50 trials for Case 1 and a _p_-value by Friedman test. It is studied that the mean, the minimum, and the maximum values, and the average rank using _W-B_ policy are the best among all migration policies **(bold numbers)**. It is also studied that there are significant differences at 0.05 significance level among all parameters in Table 6.  
The best topology, the best number of individuals, and the best number of sub-populations are investigated in Table 8. Table 8 explains the comparison of the mean, the minimum, the maximum the standard deviation values, and average rank of the results calculated using objective function values using only migration model with the _W-B_ policy among various topologies, various numbers of individuals, and various number of sub-populations and a p-value by Friedman test. When the number of individuals is 40 with 4 or 8 sub-population, the results include penalty value because dependent variables are out of allowable ranges.