# Improving Monarch Butterfly Optimization Algorithm with Self-Adaptive Population
## 6 Conclusions
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multicolumn{6}{c}{**Best**} & \multicolumn{3}{c}{**Mean**} & \multicolumn{3}{c}{**Worst**} & \multicolumn{3}{c}{**SD**} \\ \hline  & **PSO** & **SPMBO** & **PSO** & **SPMBO** & **PSO** & **SPMBO** & **PSO** & **SPMBO** \\ \hline F01 & 74.61 & **0.45** & 85.45 & **53.63** & **92.23** & 135.90 & **4.27** & 43.22 \\ F02 & \(1.97\times 10^{3}\) & **0.81** & \(\textbf{4.91}\times\textbf{10^{5}}\) & \(6.48\times 10^{8}\) & \(\textbf{4.92}\times\textbf{10^{6}}\) & \(1.78\times 10^{10}\) & \(\textbf{1.06}\times\textbf{10^{6}}\) & \(3.11\times 10^{9}\) \\ F03 & \(5.23\times 10^{8}\) & \(\textbf{2.46}\times\textbf{10^{4}}\) & \(4.00\times 10^{9}\) & \(\textbf{1.63}\times\textbf{10^{9}}\) & \(8.91\times 10^{9}\) & \(\textbf{6.08}\times\textbf{10^{9}}\) & \(3.04\times 10^{9}\) & \(\textbf{1.87}\times\textbf{10^{9}}\) \\ F04 & \(8.48\times 10^{6}\) & \(\textbf{3.95}\times\textbf{10^{6}}\) & \(1.07\times 10^{7}\) & \(\textbf{6.09}\times\textbf{10^{6}}\) & \(1.33\times 10^{7}\) & \(\textbf{8.45}\times\textbf{10^{6}}\) & \(1.18\times 10^{6}\) & \(\textbf{1.00}\times\textbf{10^{6}}\) \\ F05 & \(2.03\times 10^{5}\) & **18.17** & \(1.49\times 10^{6}\) & \(\textbf{1.00}\times\textbf{10^{6}}\) & \(3.78\times 10^{6}\) & \(\textbf{3.07}\times\textbf{10^{6}}\) & \(1.26\times 10^{6}\) & \(\textbf{9.74}\times\textbf{10^{5}}\) \\ F06 & \(185.80\) & **0.07** & 237.00 & **131.20** & **303.80** & 522.10 & **31.63** & 163.90 \\ F07 & \(1.03\times 10^{8}\) & \(\textbf{9.80}\times\textbf{10^{-4}}\) & \(\textbf{1.95}\times\textbf{10^{8}}\) & \(2.58\times 10^{8}\) & \(\textbf{3.17}\times\textbf{10^{6}}\) & \(1.41\times 10^{9}\) & \(\textbf{5.91}\times\textbf{10^{7}}\) & \(4.68\times 10^{8}\) \\ F08 & \(2.01\times 10^{8}\) & **0.77** & \(\textbf{4.29}\times\textbf{10^{5}}\) & \(5.82\times 10^{8}\) & \(\textbf{7.92}\times\textbf{10^{8}}\) & \(2.94\times\textbf{10^{9}}\) & \(\textbf{1.30}\times\textbf{10^{8}}\) & \(9.43\times 10^{8}\) \\ F09 & \(0.04\) & 0.50 & **19.92** & \(3.57\times 10^{62}\) & \(\textbf{115.80}\) & \(1.01\times 10^{64}\) & \(\textbf{27.03}\) & \(1.97\times 10^{63}\) \\ F10 & \(\textbf{6.80}\times\textbf{10^{3}}\) & **3.44** & \(1.31\times 10^{4}\) & \(\textbf{5.51}\times\textbf{10^{3}}\) & \(\textbf{1.80}\times\textbf{10^{4}}\) & \(3.65\times 10^{4}\) & \(\textbf{3.10}\times\textbf{10^{3}}\) & \(8.30\times 10^{3}\) \\ F11 & 352.00 & **37.45** & 467.70 & **290.60** & 522.90 & **513.00** & **40.55** & 159.70 \\ F12 & 228.00 & **18.07** & 261.80 & **115.30** & 288.00 & **251.80** & **11.26** & 73.14 \\ F13 & 914.10 & **12.95** & \(1.82\times 10^{9}\) & \(\textbf{2.28}\times\textbf{10^{4}}\) & \(4.37\times 10^{10}\) & \(\textbf{4.88}\times\textbf{10^{5}}\) & \(7.97\times 10^{9}\) & \(\textbf{9.05}\times\textbf{10^{4}}\) \\ \hline Total & 1 & 12 & 4 & 9 & 7 & 6 & 9 & 4 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Best, mean, worst function values and SD values obtained by the PSO and SPMBO algorithms with dimension \(D=60\). **Author Contributions:** [PERSON], [PERSON], and [PERSON] implemented the algorithms and designed the experiments; [PERSON], [PERSON], and [PERSON] performed the experiments; [PERSON], [PERSON], and [PERSON] collected and analyzed the data; [PERSON], [PERSON], and [PERSON] wrote the paper. **Acknowledgments:** This work was supported by the National Natural Science Foundation of China (No. 61772225), the Foundation for Distinguished Young Talents in Higher Education of Guangdong (No. 2015 KQNCX153), Science and Technology Program of Huizhou (No. 2015B010002002, No. 2016X0431046, No. 2016X0434049, No. 2016X0432047, No. 2017c0406022, No. 2017c0407023, No. 2017c0414030). **Conflicts of Interest:** The authors declare no conflict of interest.