# Mutational Chemotaxis Motion Driven MdpI for Engineering Applications
## 4 Discussion of Experimental Results
### Impact of Optimization Strategies on MFO
#### 4.2.1 Comparison between Mechanisms
\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 & \(9.88074\times 10^{3}\) & \(8.36593\times 10^{3}\) & \(2.57815\times 10^{2}\) & \(2.58794\times 10^{2}\) & \(3.00026\times 10^{2}\) & \(7.17286\times 10^{-2}\) \\ CMMFO & \(9.01626\times 10^{3}\) & \(8.01713\times 10^{3}\) & \(2.00000\times 10^{2}\) & \(3.33524\times 10^{-4}\) & \(3.00001\times 10^{2}\) & \(3.40189\times 10^{-3}\) \\ HMMMFO & \(4.46256\times 10^{8}\) & \(4.77887\times 10^{8}\) & \(1.48764\times 10^{19}\) & \(7.29118\times 10^{19}\) & \(1.26610\times 10^{4}\) & \(5.07162\times 10^{3}\) \\ MFO & \(1.43280\times 10^{10}\) & \(9.64728\times 10^{9}\) & \(3.08359\times 10^{37}\) & \(1.47328\times 10^{38}\) & \(1.06204\times 10^{5}\) & \(6.27301\times 10^{4}\) \\ \hline  & **F4** & \multicolumn{2}{c}{**F5**} & \multicolumn{2}{c}{**F6**} \\ \cline{2-6}  & **AVG** & **STD** & **AVG** & **STD** & **AVG** & **STD** \\ \hline HMCMMFO & \(4.77557\times 10^{2}\) & \(2.31258\times 10^{1}\) & \(5.65091\times 10^{2}\) & \(1.22131\times 10^{1}\) & \(6.06060\times 10^{2}\) & \(1.53909\times 10^{0}\) \\ CMMFO & \(4.77661\times 10^{2}\) & \(1.94289\times 10^{1}\) & \(6.92106\times 10^{2}\) & \(4.49923\times 10^{1}\) & \(6.37071\times 10^{2}\) & \(1.10670\times 10^{1}\) \\ HMMMFO & \(5.12020\times 10^{2}\) & \(1.47713\times 10^{1}\) & \(6.09776\times 10^{2}\) & \(1.57299\times 10^{1}\) & \(6.08643\times 10^{2}\) & \(1.63674\times 10^{0}\) \\ MFO & \(1.21151\times 10^{3}\) & \(7.57463\times 10^{2}\) & \(7.12338\times 10^{2}\) & \(5.05325\times 10^{1}\) & \(6.37028\times 10^{2}\) & \(1.10430\times 10^{1}\) \\ \hline  & **F7** & \multicolumn{2}{c}{**F8**} & \multicolumn{2}{c}{**F9**} \\ \cline{2-6}  & **AVG** & **STD** & **AVG** & **STD** & **AVG** & **STD** \\ \hline HMCMMFO & \(8.17282\times 10^{2}\) & \(2.25823\times 10^{1}\) & \(8.60641\times 10^{2}\) & \(1.62711\times 10^{1}\) & \(1.09963\times 10^{3}\) & \(1.29386\times 10^{2}\) \\ CMMFO & \(1.10897\times 10^{3}\) & \(1.82774\times 10^{2}\) & \(9.87306\times 10^{2}\) & \(4.24357\times 10^{1}\) & \(7.30599\times 10^{3}\) & \(2.19949\times 10^{3}\) \\ HMMMFO & \(9.13037\times 10^{2}\) & \(1.75738\times 10^{1}\) & \(8.95471\times 10^{2}\) & \(1.26446\times 10^{1}\) & \(1.21187\times 10^{3}\) & \(1.31024\times 10^{2}\) \\ MFO & \(1.16361\times 10^{3}\) & \(2.30837\times 10^{2}\) & \(1.00535\times 10^{3}\) & \(3.71062\times 10^{1}\) & \(7.50263\times 10^{3}\) & \(2.59327\times 10^{3}\) \\ \hline  & **F10** & \multicolumn{2}{c}{**F11**} & \multicolumn{2}{c}{**F12**} \\ \cline{2-6}  & **AVG** & **STD** & **AVG** & **STD** & **AVG** & **STD** \\ \hline HMCMMFO & \(4.07312\times 10^{3}\) & \(5.96620\times 10^{2}\) & \(1.20139\times 10^{3}\) & \(3.81300\times 10^{1}\) & \(2.56822\times 10^{5}\) & \(1.79231\times 10^{5}\) \\ CMMFO & \(5.42916\times 10^{3}\) & \(5.94213\times 10^{2}\) & \(1.39367\times 10^{3}\) & \(1. To visualize the impact of the two optimization mechanisms on the optimization performance of MFO, convergence plots of nine test functions are selected in this experiment, as shown in Figure 2 below. HMMFO with hybrid-mutation strategy has a better optimization accuracy than the traditional MFO on eight functions.