# Improving Monarch Butterfly Optimization Algorithm with Self-Adaptive Population
## 5 Simulation Results
### PSO vs. SPMBO
#### 5.2.2 \(D=60\)  
In this subsection, the dimension of the thirteen benchmark problems is set to 60. As before, the maximum generation (\(t_{m}\)), i.e., function evaluations (FEs), is considered as the stop condition and is set to 50. After thirty implementations, the best, mean, and worst function values and SD values were obtained for PSO and SPMBO and are recorded in Table 5. \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline  & **Best** & \multicolumn{2}{c}{**Mean**} & \multicolumn{2}{c}{**Worst**} & \multicolumn{2}{c}{**SD**} \\ \hline  & **PSO** & **SPMBO** & **PSO** & **SPMBO** & **PSO** & **SPMBO** & **PSO** & **SPMBO** \\ \hline F01 & 29.95 & **0.04** & 36.00 & **5.28** & 43.13 & **24.37** & **3.06** & 6.45 \\ F02 & 96.30 & **0.10** & 357.50 & **96.33** & 1.37 \(\times\)\(10^{3}\) & **1.32 \(\times\)\(10^{3}\)** & **251.00** & 274.20 \\ F03 & \(2.22\times 10^{7}\) & \(\textbf{6.96}\times\textbf{10}^{3}\) & \(2.93\times 10^{8}\) & \(\textbf{2.83}\times\textbf{10}^{8}\) & \(1.28\times 10^{9}\) & \(\textbf{8.86}\times\textbf{10}^{8}\) & \(4.31\times 10^{8}\) & \(\textbf{3.06}\times\textbf{10}^{8}\) \\ F04 & \(9.63\times 10^{5}\) & \(\textbf{4.07}\times\textbf{10}^{5}\) & \(1.71\times 10^{6}\) & \(\textbf{8.43}\times\textbf{10}^{5}\) & \(2.87\times 10^{6}\) & \(\textbf{1.49}\times\textbf{10}^{6}\) & \(3.49\times 10^{5}\) & \(\textbf{2.56}\times\textbf{10}^{5}\) \\ F05 & \(2.39\times 10^{4}\) & \(\textbf{7.19}\times\textbf{10}^{-3}\) & \(\textbf{4.62}\times\textbf{10}^{4}\) & \(7.49\times 10^{4}\) & \(\textbf{2.09}\times\textbf{10}^{5}\) & \(3.52\times 10^{5}\) & \(\textbf{3.24}\times\textbf{10}^{4}\) & \(1.13\times 10^{5}\) \\ F06 & \(38.02\) & \(\textbf{5.18}\times\textbf{10}^{-3}\) & \(80.32\) & \(\textbf{36.60}\) & **115.00** & 189.20 & **16.08** & 58.80 \\ F07 & \(4.03\times 10^{6}\) & \(\textbf{2.28}\times\textbf{10}^{-4}\) & \(\textbf{2.66}\times\textbf{10}^{7}\) & \(7.46\times\textbf{10}^{7}\) & \(\textbf{6.70}\times\textbf{10}^{7}\) & \(\textbf{5.75}\times\textbf{10}^{8}\) & \(\textbf{1.62}\times\textbf{10}^{7}\) & \(1.60\times\textbf{10}^{8}\) \\ F08 & \(3.39\times 10^{7}\) & **0.02** & \(\textbf{9.37}\times\textbf{10}^{7}\) & \(1.92\times 10^{8}\) & \(\textbf{1.96}\times\textbf{10}^{8}\) & \(8.58\times\textbf{10}^{8}\) & \(\textbf{3.99}\times\textbf{10}^{7}\) & \(2.75\times 10^{8}\) \\ F09 & \(\textbf{5.53}\times\textbf{10}^{-3}\) & 6.68 & **3.14** & \(2.29\times 10^{22}\) & **27.13** & \(6.77\times 10^{23}\) & **6.10** & \(1.22\times 10^{23}\) \\ F10 & \(1.73\times 10^{3}\) & **3.27** & \(3.16\times 10^{3}\) & \(\textbf{3.10}\times\textbf{10}^{3}\) & \(\textbf{5.21}\times\textbf{10}^{3}\) & \(9.37\times 10^{3}\) & **976.60** & \(2.94\times 10^{3}\) \\ F11 & 180.00 & **1.20** & 204.80 & **89.07** & 240.00 & **221.30** & **18.34** & 60.96 \\ F12 & 107.00 & **0.86** & 120.40 & **36.15** & 138.00 & **103.90** & **6.47** & 35.62 \\ F13 & 231.80 & **20.83** & 569.30 & **459.80** & \(2.39\times 10^{3}\) & **751.00** & 372.00 & **220.90** \\ \hline Total & 1 & 12 & 4 & 9 & 6 & 7 & 10 & 3 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Best, mean, worst function values and SD values obtained by the PSO and SPMBO algorithms with dimension \(D=30\).