# Mutational Chemotaxis Motion Driven MdpI for Engineering Applications
## 4 Discussion of Experimental Results
### Comparison with Advanced Algorithms
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **F1** & \multicolumn{2}{c}{**F2**} & \multicolumn{2}{c}{**F3**} \\ \cline{2-6}  & **AVG** & **STD** & **AVG** & **STD** & **AVG** & **STD** \\ \hline HMCMMFO & 9.04208 \(\times\) 10\({}^{3}\) & 8.03368 \(\times\) 10\({}^{3}\) & 2.05737 \(\times\) 10\({}^{2}\) & 1.27916 \(\times\) 10\({}^{1}\) & 3.00005 \(\times\) 10\({}^{2}\) & 9.47002 \(\times\) 10\({}^{-3}\) \\ FSTPSO & 2.24935 \(\times\) 10\({}^{10}\) & 7.20644 \(\times\) 10\({}^{9}\) & 3.38172 \(\times\) 10\({}^{3}\) & 1.01762 \(\times\) 10\({}^{3}\) & 8.76469 \(\times\) 10\({}^{4}\) & 2.03541 \(\times\) 10\({}^{4}\) \\ ALCPSO & 5.69193 \(\times\) 10\({}^{3}\) & 6.76754 \(\times\) 10\({}^{3}\) & 2.41025 \(\times\) 10\({}^{17}\) & 8.32693 \(\times\) 10\({}^{17}\) & 2.67799 \(\times\) 10\({}^{4}\) & 3.63044 \(\times\) 10\({}^{3}\) \\ CDLOBA & 5.01333 \(\times\) 10\({}^{3}\) & 5.42594 \(\times\) 10\({}^{3}\) & 1.13044 \(\times\) 10\({}^{12}\) & 3.71628 \(\times\) 10\({}^{12}\) & 1.26087 \(\times\) 10\({}^{3}\) & 1.59138 \(\times\) 10\({}^{3}\) \\ BSSFOA & 6.94886 \(\times\) 10\({}^{10}\) & 4.63503 \(\times\) 10\({}^{9}\) & 4.96079 \(\times\) 10\({}^{39}\) & 1.90717 \(\times\) 10\({}^{60}\) & 1.05247 \(\times\) 10\({}^{7}\) & 2.29879 \(\times\) 10\({}^{7}\) \\ SCADE & 1.91644 \(\times\) 10\({}^{10}\) & 2.82685 \(\times\) 10\({}^{9}\) & 2.85732 \(\times\) 10\({}^{37}\) & 1.02110 \(\times\) 10\({}^{38}\) & 6.18223 \(\times\) 10\({}^{4}\) & 7.12746 \(\times\) 10\({}^{3}\) \\ CGPSO & 1.41430 \(\times\) 10\({}^{8}\) & 1.56060 \(\times\) 10\({}^{7}\) & 1.02685 \(\times\) 10\({}^{14}\) & 7.37472 \(\times\) 10\({}^{3}\) & 7.74256 \(\times\) 10\({}^{2}\) & 7.70923 \(\times\) 10\({}^{1}\) \\ OBLGWO & 1.41222 \(\times\) 10\({}^{7}\) & 6.42248 \(\times\) 10\({}^{6}\) & 5.38329 \(\times\) 10\({}^{16}\) & 9.80940 \(\times\) 10\({}^{16}\) & 1.79685 \(\times\) 10\({}^{4}\) & 5.24282 \(\times\) 10\({}^{3}\) \\ \hline  & **F4** & **F5** & \multicolumn{2}{c}{**F6**} & \multicolumn{2}{c}{**F**} \\ \cline{2-6}  & **AVG** & **STD** & **AVG** & **STD** & **AVG** & **STD** \\ \hline HMCMMFO & 4.78053 \(\times\) 10\({}^{2}\) & 1.94693 \(\times\) 10\({}^{1}\) & 5.65518 \(\times\) 10\({}^{2}\) & 1.09386 \(\times\) 10\({}^{1}\) & 6.05534 \(\times\) 10\({}^{2}\) & 2.09891 \(\times\) 10\({}^{6}\) \\ FSTPSO & 4.25834 \(\times\) 10\({}^{3}\) & 1.34899 \(\times\) 10\({}^{3}\) & 8.09741 \(\times\) 10\({}^{2}\) & 4.36397 \(\times\) 10\({}^{1}\) & 6.67701 \(\times\) 10\({}^{2}\) & 8.86637 \(\times\) 10\({}^{6}\) \\ ALCPSO & 5.03845 \(\times\) 10\({}^{2}\) & 3.76435 \(\times\) 10\({}^{1}\) & 6.08908 \(\times\) 10\({}^{2}\) & 2.48248 \(\times\) 10\({}^{1}\) & 6.04422 \(\times\) 10\({}^{2}\) & 4.76403 \(\times\) 10\({}^{6}\) \\ CDLOBA & 4.82331 \(\times\) 10\({}^{2}\) & 2.76442 \(\times\) 10\({}^{1}\) & 8.82001 \(\times\) 10\({}^{2}\) & 6.77780 \(\times\) 10\({}^{1}\) & 6.71516 \(\times\) 10\({}^{2}\) & 9.42381 \(\times\) 10\({}^{6}\) \\ BSSFOA & 3.17512 \(\times\) 10\({}^{4}\) & 2.92592 \(\times\) 10\({}^{3}\) & 1.06410 \(\times\) 10\({}^{3}\) & 3.68237 \(\times\) 10\({}^{1}\) & 7.34761 \(\times\) 10\({}^{2}\) & 5.65161 \(\times\) 10\({}^{6}\) \\ SCADE & 3.45962 \(\times\) 10\({}^{3}\) & 7.10815 \(\times\) 10\({}^{2}\) & 8.27990 \(\times\) 10\({}^{2}\) & 2.15557 \(\times\) 10\({}^{1}\) & 6.60604 \(\times\) 10\({}^{2}\) & 5.97788 \(\times\) 10\({}^{6}\) \\ CGPSO & 4.84497 \(\times\) 10\({}^{2}\) & 2.08597 \(\times\) 10\({}^{1}\) & 7.84836 \(\times\) 10\({}^{2}\) & 3.48166 \(\times\) 10\({}^{1}\) & 6.61193 \(\times\) 10\({}^{2}\) & 1.45069 \(\times\) 10\({}^{1}\) \\ OBLGWO & 5.28375 \(\times\) 10\({}^{2}\) & 3.03182 \(\times\) 10\({}^{1}\) & 6.58444 \(\times\) 10\({}^{2}\) & 3.92032 \(\times\) 10\({}^{1}\) & 6.19614 \(\times\) 10\({}^{2}\) & 1.60747 \(\times\) 10\({}^{1}\) \\ \hline  & **F7** & \multicolumn{2}{c}{**F8**} & \multicolumn{2}{c}{**F9**} \\ \cline{2-6}  & **AVG** & **STD** & **AVG** & **STD**  
\begin{table}
\begin{tabular}{c c c c c c c} \hline BSSFOA & 1.06223 \(\times\) 10\({}^{4}\) & 3.52578 \(\times\) 10\({}^{2}\) & 1.52698 \(\times\) 10\({}^{8}\) & 1.94191 \(\times\) 10\({}^{8}\) & 2.64859 \(\times\) 10\({}^{10}\) & 2.12389 \(\times\) 10\({}^{9}\) \\ SCADE & 8.15302 \(\times\) 10\({}^{3}\) & 2.60426 \(\times\) 10\({}^{2}\) & 3.32858 \(\times\) 10\({}^{3}\) & 4.38924 \(\times\) 10\({}^{2}\) & 1.92116 \(\times\) 10\({}^{9}\) & 5.52975 \(\times\) 10\({}^{8}\) \\ CGPSO & 6.28405 \(\times\) 10\({}^{3}\) & 5.89596 \(\times\) 10\({}^{2}\) & 1.27621 \(\times\) 10\({}^{3}\) & 3.59016 \(\times\) 10\({}^{1}\) & 3.01121 \(\times\) 10\({}^{7}\) & 1.49000 \(\times\) 10\({}^{7}\) \\ OBLGWO & 5.31016 \(\times\) 10\({}^{3}\) & 7.39178 \(\times\) 10\({}^{2}\) & 1.30783 \(\times\) 10\({}^{3}\) & 5.14082 \(\times\) 10\({}^{1}\) & 1.50043 \(\times\) 10\({}^{7}\) & 1.45532 \(\times\) 10\({}^{7}\) \\ \hline \multicolumn{5}{c}{**F13**} & \multicolumn{5}{c}{**F14**} & \multicolumn{5}{c}{**F15**} \\ \cline{2-6}  & **AVG** & **STD** & **AVG** & **STD** & **AVG** & **STD** \\ \hline HMCMMFO & 3.05695 \(\times\) 10\({}^{8}\) & 4.06431 \(\times\) 10\({}^{8}\) & 2.78181 \(\times\) 10\({}^{4}\) & 2.06399 \(\times\) 10\({}^{4}\) & 1.26334 \(\times\) 10\({}^{4}\) & 1.47346 \(\times\) 10\({}^{4}\) \\ FSTPSO & 2.26316 \(\times\) 10\({}^{4}\) & 2.09263 \(\times\) 10\({}^{4}\) & 1.53374 \(\times\) 10\({}^{5}\) & 3.13636 \(\times\) 10\({}^{5}\) & 4.29129 \(\times\) 10\({}^{4}\) & 2.96810 \(\times\) 10\({}^{4}\) \\ ALCPSO & 1.91228 \(\times\) 10\({}^{5}\) & 1.33831 \(\times\) 10\({}^{5}\) & 2.66550 \(\times\) 10\({}^{4}\) & 4.10110 \(\times\) 10\({}^{4}\) & 1.19935 \(\times\) 10\({}^{4}\) & 9.61744 \(\times\) 10\({}^{3}\) \\ CDLOBA & 3.93413 \(\times\) 10\({}^{10}\) & 5.20883 \(\times\) 10\({}^{9}\) & 4.28871 \(\times\) 10\({}^{3}\) & 3.32841 \(\times\) 10\({}^{3}\) & 9.85047 \(\times\) 10\({}^{4}\) & 6.35953 \(\times\) 10\({}^{4}\) \\ BSSFOA & 6.15265 \(\times\) 10\({}^{8}\) & 3.05402 \(\times\) 10\({}^{8}\) & 3.33185 \(\times\) 10\({}^{8}\) & 3.49954 \(\times\) 10\({}^{8}\) & 1.35846 \(\times\) 10\({}^{9}\) & 1.43455 \(\times\) 10\({}^{9}\) \\ SCADE & 5.43284 \(\times\) 10\({}^{6}\) & 1.53440 \(\times\) 10\({}^{6}\) & 3.36376 \(\times\) 10\({}^{5}\) & 2.01937 \(\times\) 10\({}^{5}\) & 1.10667 \(\times\) 10\({}^{7}\) & 1.10265 \(\times\) 10\({}^{7}\) \\ CGPSO & 1.99876 \(\times\) 10\({}^{5}\) & 1.21607 \(\times\) 10\({}^{5}\) & 1.38928 \(\times\) 10\({}^{4}\) & 8.14814 \(\times\) 10\({}^{3}\) & 5.21935 \(\times\) 10\({}^{5}\) & 2.57225 \(\times\) 10\({}^{5}\) \\ OBLGWO & 3.05695 \(\times\) 10\({}^{8}\) & 4.06431 \(\times\) 10\({}^{8}\) & 5.74416 \(\times\) 10\({}^{4}\) & 4.46473 \(\times\) 10\({}^{4}\) & 8.07591 \(\times\) 10\({}^{4}\) & 5.75320 \(\times\) 10\({}^{4}\) \\ \hline \multicolumn{5}{c}{**F16**} & \multicolumn{5}{c}{**F17**} & \multicolumn{5}{c}{**F18**} \\ \cline{2-6}  & **AVG** & **STD** & **AVG** & **STD** & **AVG** & **STD** \\ \hline HMCMMFO & 2.18654 \(\times\) 10\({}^{3}\) & 2.53645 \(\times\) 10\({}^{2}\) & 1.95862 \(\times\) 10\({}^{3}\) & 1.53751 \(\times\) 10\({}^{2}\) & 2.67430 \(\times\) 10\({}^{5}\) & 1.22752 \(\times\) 10\({}^{5}\) \\ FSTPSO & 3.77056 \(\times\) 10\({}^{3}\) & 4.68395 \(\times\) 10\({}^{2}\) & 2.61466 \(\times\) 10\({}^{3}\) & 2.81489 \(\times\) 10\({}^{2}\) & 1.99070 \(\times\) 10\({}^{6}\) & 2.62927 \(\times\) 10\({}^{6}\) \\ ALCPSO & 2.56164 \(\times\) 10\({}^{3}\) & 2.65815 \(\times\) 10\({}^{2}\) & 2.13464 \(\times\) 10\({}^{3}\) & 1.83086 \(\times\) 10\({}^{2}\) & 2.31803 \(\times\) 10\({}^{5}\) & 3.48936 \(\times\) 10\({}^{5}\) \\ CDLOBA & 3.37554 \(\times\) 10\({}^{3}\) & 4.55811 \(\times\) 10\({}^{2}\) & 2.84930 \(\times\) 10\({}^{3}\) & 3.06689 \(\times\) 10\({}^{2}\) & 1.19113 \(\times\) 10\({}^{5}\) & 6.15026 \(\times\) 10\({}^{4}\) \\ BSSFOA & 4.54964 \(\times\) 10\({}^{3}\) & 1.18493 \(\times\) 10\({}^{5}\) & 4.29716 \(\times\) 10\({}^{4}\) & 2.42077 \(\times\) 10\({}^{8}\) & 1.41621 \(\times\) 10\({}^{8}\) \\ SCADE & 3.79560 \(\times\) 10\({}^{3}\) & 2.85942 \(\times\) 10\({}^{2}\) & 2.53314 \(\times\) 10\({}^{3}\) & 1.22389 \(\times\) 10\({}^{2}\) & 5.10740 \(\times\) 10\({}^{6}\) & 2.91497 \(\times\) 10\({}^{6}\) \\ CGPSO & 2.94824 \(\times\)To clearly understand the difference in optimization performance between advanced algorithms and HMCMMFO, the nonparametric Wilcoxon signed-rank test method at a 5% significance level is used for this experiment.