# Mutational Chemotaxis Motion Driven MdpI for Engineering Applications
## 4 Discussion of Experimental Results
### Impact of Optimization Strategies on MFO
\begin{table}
\begin{tabular}{c c c c c c c} \hline  & \multicolumn{1}{c}{**F7**} & \multicolumn{2}{c}{**F8**} & \multicolumn{2}{c}{**F9**} \\ \cline{2-7}  & **AVG** & **STD** & **AVG** & **STD** & **AVG** & **STD** \\ \hline HMCMMFO & \(8.17605\times 10^{2}\) & \(2.09013\times 10^{1}\) & \(8.64528\times 10^{2}\) & \(1.59203\times 10^{1}\) & \(1.11123\times 10^{3}\) & \(1.21983\times 10^{2}\) \\ CLSGMFO & \(9.00751\times 10^{2}\) & \(5.15106\times 10^{1}\) & \(9.30074\times 10^{2}\) & \(2.79516\times 10^{1}\) & \(3.50079\times 10^{3}\) & \(9.51979\times 10^{2}\) \\ LGCMFO & \(8.68081\times 10^{2}\) & \(4.90456\times 10^{1}\) & \(9.17209\times 10^{2}\) & \(2.64516\times 10^{1}\) & \(2.92376\times 10^{3}\) & \(7.90733\times 10^{2}\) \\ NMSOLMFO & \(8.64867\times 10^{2}\) & \(5.83245\times 10^{1}\) & \(9.03175\times 10^{2}\) & \(3.27945\times 10^{1}\) & \(1.59150\times 10^{3}\) & \(4.59537\times 10^{2}\) \\ QSMFO & \(5.52241\times 10^{2}\) & \(3.40663\times 10^{1}\) & \(9.92969\times 10^{2}\) & \(2.09746\times 10^{1}\) & \(1.11144\times 10^{3}\) & \(7.76071\times 10^{3}\) \\ CMFO & \(1.25439\times 10^{3}\) & \(1.41749\times 10^{2}\) & \(9.59348\times 10^{2}\) & \(4.02805\times 10^{1}\) & \(4.80020\times 10^{3}\) & \(1.23739\times 10^{3}\) \\ WEMFO & \(9.37825\times 10^{2}\) & \(6.98497\times 10^{1}\) & \(9.86209\times 10^{2}\) & \(4.71145\times 10^{1}\) & \(5.29982\times 10^{3}\) & \(2.17483\times 10^{3}\) \\ \hline  & **F10** & **F11** & & **F12** & \\ \cline{2-7}  & **AVG** & **STD** & **AVG** & **STD** & **AVG** & **STD** \\ \hline HMCMMFO & \(4.14337\times 10^{3}\) & \(6.76492\times 10^{2}\) & \(1.20406\times 10^{3}\) & \(4.01105\times 10^{1}\) & \(2.99045\times 10^{5}\) & \(2.13295\times 10^{5}\) \\ CLSGMFO & \(5.14610\times 10^{3}\) & \(5.92095\times 10^{2}\) & \(1.25692\times 10^{3}\) & \(7.26976\times 10^{1}\) & \(1.36113\times 10^{6}\) & \(3.12632\times 10^{6}\) \\ LGCMFO & \(4.66928\times 10^{3}\) & \(5.95099\times 10^{2}\) & \(1.22641\times 10^{3}\) & \(5.99199\times 10^{1}\) & \(1.69558\times 10^{6}\) & \(3.16562\times 10^{6}\) \\ NMSOLMFO & \(5.56026\times 10^{3}\) & \(6.27896\times 10^{2}\) & \(1.27211\times 10^{3}\) & \(7.16933\times 10^{1}\) & \(1.69407\times 10^{4}\) & \(1.44619\times 10^{4}\) \\ QSMFO & \(4.47754\times 10^{3}\) & \(4.15647\times 10^{2}\) & \(1.20220\times 10^{3}\) & \(3.21058\times 10^{1}\) & \(3.22319\times 10^{6}\) & \(1.99893\times 10^{6}\) \\ CMFO & \(7.23579\times 10^{3}\) & \(1.24780\times 10^{3}\) & \(4.85080\times 10^{3}\) & \(4.35495\times 10^{3}\) & \(2.94481\times 10^{7}\) & \(6.15277\times 10^{7}\) \\ WEMFO & \(5.20927\times 10^{3}\) & \(8.17462\times 10^{2}\) & \(1.37952\times 10^{3}\) & \(8.94922\times 10^{1}\) & \(1.97070\times 10^{6}\) & \(2.08794\times 10^{6}\) \\ \hline  & **F13** & **F14** & & **F15** & \\ \cline{2-7}  & **AVG** & **STD** & **AVG** & **STD** & **AVG** & **STD** \\ \hline HMCMMFO & \(3.42289\times 10^{4}\) & \(2.60128\times 10^{4}\) & \(2.93673\times 10^{4}\) & \(1.73593\times 10^{4}\) & \(1.32157\times 10^{4}\) & \(1.54584\times 10^{4}\) \\ CLSGMFO & \(2.10077\times 10^{5}\) & \(8.04303\times 10^{5}\) & \(3.64888\times 10^{4}\) & \(3.63694\times 10^{4}\) & \(9.03043\times 10^{3}\) & \(1.24897\times 10^{4}\) \\ LGCMFO & \(1.88965\times 10^{5}\) & \(8.04602\times 10^{5}\) & \(4.91007\times 10^{4}\) & \(4.31686\times 10^{4}\) & \(8.63513\times 10^{3}\) & \(8.92177\times 10^{3}\) \\ NMSOLMFO & \(1.65278\times 10^{4}\) & \(1.75963\times 10^{4}\) & \(2.90354\times 10^{3}\) & \(3.16045\times 10^{3}\) & \(8.66224\times 10^{3}\) & \(8.92571\times 10^{3}\) \\ QSMFO & \(1.53350\times 10^{4}\) & \(1.18018\times 10^{4}\) & \(5.43527\times 10^{3}\) & \(2.95458\times 10^{3}\) & \(3.46751\times 10^{3}\) & \(1.60762\times 10^{3}\) \\ CMFO & \(5.99018\times 10^{7}\) & \(3.27735\times 10^{8}\) & \(2.39223\times 10^{5}\) & \(3.66707\times 10^{5}\) & \(6.80532\times 10^{4}\) & \(1.00702\times 10^{5}\) \\ WEMFO & \(1.28597\times 10^{5}\) & \(1.50446\times 10^{5}\) & \(7.13607\times 10^{4}\) & \(5.30010\times 10^{4}\) & \(5.56216\times 10^{4}\) & \(3.97499\times 10^{4}\) \\ \hline  & **F16** & **F17** & & **F18** & \\ \cline{2-7}  & **AVG** & **STD** & **AVG** & **STD** & **AVG** & **STD** \\ \hline HMCMMFO & \(2.25628\times 10^{3}\) & \(2.45440\times 10^{2}\) & \(2.03304\times 10^{3}\) & \(1.98205\times 10^{2}\) & \(2.96542\times 10^{5}\) & \(2.37436\times 10^{5}\) \\ CLSGMFO & \(2.79035\times 10^{3}\) &In order to further verify the difference between the optimization performance of HMCMMFO and other MFO variants, the experiment in this section uses the nonparametric Wilcoxon signed-rank test with a 5% significance level to compare the differences between these variant algorithms.