# Mutational Chemotaxis Motion Driven MdpI for Engineering Applications
## 4 Discussion of Experimental Results
### Parameters Sensitivity Analyses
#### 4.1.2 Determination of Chemotaxis Motion Step Size

Table 2: _Cont._  
\begin{table}
\begin{tabular}{l 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 HMCMMFOstep1 & \(8.66303\times 10^{3}\) & \(7.84705\times 10^{3}\) & \(2.04834\times 10^{2}\) & \(1.33106\times 10^{1}\) & \(3.00878\times 10^{2}\) & \(4.65364\times 10^{0}\) \\ HMCMMFOstep2 & \(7.97589\times 10^{3}\) & \(8.53624\times 10^{3}\) & \(2.00760\times 10^{2}\) & \(3.74399\times 10^{0}\) & \(3.00002\times 10^{2}\) & \(4.76692\times 10^{-3}\) \\ HMCMMFO\(\delta\)4 & \(9.35529\times 10^{3}\) & \(8.74887\times 10^{3}\) & \(2.00604\times 10^{2}\) & \(3.30324\times 10^{0}\) & \(3.00002\times 10^{2}\) & \(7.33390\times 10^{-3}\) \\ HMCMMFO\(\delta\)4 & \(8.96686\times 10^{3}\) & \(7.10186\times 10^{3}\) & \(2.01220\times 10^{2}\) & \(4.63905\times 10^{0}\) & \(3.00006\times 10^{2}\) & \(1.51866\times 10^{-2}\) \\ HMCMMFO\(\delta\)5 & \(8.37666\times 10^{3}\) & \(8.18901\times 10^{3}\) & \(2.02887\times 10^{2}\) & \(1.06536\times 10^{1}\) & \(3.00002\times 10^{2}\) & \(6.01558\times 10^{-3}\) \\ HMCMMFO\(\delta\)6 & \(6.84418\times 10^{3}\) & \(7.32319\times 10^{3}\) & \(2.01161\times 10^{2}\) & \(4.46624\times 10^{0}\) & \(3.00002\times 10^{2}\) & \(5.42726\times 10^{-3}\) \\ HMCMMFO  
\begin{table}
\begin{tabular}{l c c c c c c} \hline HMCMMFOstep5 & 4.79878 \(\times\) 10\({}^{2}\) & 2.11073 \(\times\) 10\({}^{1}\) & 5.68237 \(\times\) 10\({}^{2}\) & 1.16246 \(\times\) 10\({}^{1}\) & 6.03160 \(\times\) 10\({}^{2}\) & 1.36591 \(\times\) 10\({}^{0}\) \\ HMCMMFOstep6 & 4.78631 \(\times\) 10\({}^{2}\) & 2.90738 \(\times\) 10\({}^{1}\) & 5.65631 \(\times\) 10\({}^{2}\) & 1.70457 \(\times\) 10\({}^{1}\) & 6.03028 \(\times\) 10\({}^{2}\) & 1.40687 \(\times\) 10\({}^{0}\) \\ HMCMMFOstep7 & 4.80517 \(\times\) 10\({}^{2}\) & 2.68455 \(\times\) 10\({}^{1}\) & 5.63865 \(\times\) 10\({}^{2}\) & 2.00864 \(\times\) 10\({}^{1}\) & 6.03027 \(\times\) 10\({}^{2}\) & 1.71435 \(\times\) 10\({}^{0}\) \\ \hline  & **F7** & \multicolumn{2}{c}{**F8**} & \multicolumn{2}{c}{**F9**} \\ \hline HMCMMFOstep1 & 8.09803 \(\times\) 10\({}^{2}\) & 2.23524 \(\times\) 10\({}^{1}\) & 8.71397 \(\times\) 10\({}^{2}\) & 1.85329 \(\times\) 10\({}^{1}\) & 1.00859 \(\times\) 10\({}^{3}\) & 8.06705 \(\times\) 10\({}^{1}\) \\ HMCMMFOstep2 & 8.10786 \(\times\) 10\({}^{2}\) & 2.87670 \(\times\) 10\({}^{1}\) & 8.65882 \(\times\) 10\({}^{2}\) & 1.36839 \(\times\) 10\({}^{1}\) & 1.00787 \(\times\) 10\({}^{3}\) & 7.71723 \(\times\) 10\({}^{1}\) \\ HMCMMFOstep3 & 8.02920 \(\times\) 10\({}^{2}\) & 2.05684 \(\times\) 10\({}^{1}\) & 8.65062 \(\times\) 10\({}^{2}\) & 1.55406 \(\times\) 10\({}^{1}\) & 1.11090 \(\times\) 10\({}^{3}\) & 2.45938 \(\times\) 10\({}^{2}\) \\ HMCMMFOstep4 & 8.09671 \(\times\) 10\({}^{2}\) & 2.81699 \(\times\) 10\({}^{1}\) & 8.64766 \(\times\) 10\({}^{2}\) & 1.60089 \(\times\) 10\({}^{1}\) & 1.06668 \(\times\) 10\({}^{3}\) & 1.70977 \(\times\) 10\({}^{2}\) \\ HMCMMFOstep5 & 8.15750 \(\times\) 10\({}^{2}\) & 2.10966 \(\times\) 10\({}^{1}\) & 8.70045 \(\times\) 10\({}^{2}\) & 1.93109 \(\times\) 10\({}^{1}\) & 1.02977 \(\times\) 10\({}^{3}\) & 7.25515 \(\times\) 10\({}^{1}\) \\ HMCMMFOstep6 & 8.14312 \(\times\) 10\({}^{2}\) & 2.88166 \(\times\) 10\({}^{1}\) & 8.60382 \(\times\) 10\({}^{2}\) & 1.23858 \(\times\) 10\({}^{1}\) & 1.06351 \(\times\) 10\({}^{3}\) & 2.09531 \(\times\) 10\({}^{2}\) \\ HMCMMFOstep7 & 8.15832 \(\times\) 10\({}^{2}\) & 2.32068 \(\times\) 10\({}^{1}\) & 8.61928 \(\times\) 10\({}^{2}\) & 1.59051 \(\times\) 10\({}^{1}\) & 1.01560 \(\times\) 10\({}^{3}\) & 8.16708 \(\times\) 10\({}^{1}\) \\ \hline  & **F10** & \multicolumn{2}{c}{**F11**} & \multicolumn{2}{c}{**F12**} \\ \cline{2-7}  & **AVG** & **STD** & **AVG** & **STD** & **AVG** & **STD** \\ \hline HMCMMFOstep1 & 3.48260 \(\times\) 10\({}^{3}\) & 6.58739 \(\times\) 10\({}^{2}\) & 1.19133 \(\times\) 10\({}^{3}\) & 3.43658 \(\times\) 10\({}^{1}\) & 2.05355 \(\times\) 10\({}^{5}\) & 1.81947 \(\times\) 10\({}^{5}\) \\ HMCMMFOstep2 & 3.55392 \(\times\) 10\({}^{3}\) & 4.78136 \(\times\) 10\({}^{2}\) & 1.20569 \(\times\) 10\({}^{3}\) & 4.08568 \(\times\) 10\({}^{1}\) & 1.85451 \(\times\) 10\({}^{5}\) & 1.42475 \(\times\) 10\({}^{5}\) \\ HMCMMFOstep3 & 3.39803 \(\times\) 10\({}^{3}\) & 4.88723 \(\times\) 10\({}^{2}\) & 1.19695 \(\times\) 10\({}^{3}\) & 3.15625 \(\times\) 10\({}^{1}\) & 2.38687 \(\times\) 10\({}^{5}\) & 2.14414 \(\times\) 10\({}^{5}\) \\ HMCMMFOstep4 & 3.54981 \(\times\) 10\({}^{3}\) & 5.82920 \(\times\) 10\({}^{2}\) & 1.20035 \(\times\) 10\({}^{3}\) & 4.25845 \(\times\) 10\({}^{1}\) & 2.53071 \(\times\) 10\({}^{5}\) & 2.20994 \(\times\) 10\({}^{5}\) \\ HMCMMFOstep5 & 3.42152 \(\times\) 10\({}^{3}\) & 4.81097 \(\times\) 10\({}^{2}\) & 1.20382 \(\times\) 10\({}^{3}\) & 3.66358 \(\times\) 10\({}^{1}\) & 2.00713 \(\times\) 10\({}^{5}\) & 1.33010 \(\times\) 10\({}^{5}\) \\ HMCMMFOstep6 & 3.63880 \(\times\) 10\({}^{3}\) & 5.63713 \(\times\) 10\({}^{2}\) & 1.19170 \(\times\) 10\({}^{3}\) & 4.10747 \(\times\) 10\({}^{1}\) & 2.98582 \(\times\) 10\({}^{5}\) & 2.43926 \(\times\) 10\({}^{5}\) \\ HMCMMFOstep7 & 3.58965 \(\times\) 10\({}^{3}\) & 4.99686 \(\times\) 10\({}^{2}\) & 1.18150 \(\times\) 10\({}^{3}\) & 3.10368 \(\times\) 10\({}^{1}\) & 2.03903 \(\times\) 10\({}^{5}\) & 1.58705 \(\times\) 10\({}^{5}\) \\ \hline  & **F13** & \multicolumn{2}{c}{**F14**} & \multicolumn{2}{c}{**F15**} \\ \cline{2-7}  & **AVG** & **STD** & **AVG** & **STD** & **AVG** & **STD** \\ \hline HMCMMFOstep1 & 2.82176 \(\times\) 10\({}^{4}\) & 2.39431 \(\times\) 10\({}^{4}\) & 2.53297 \(\times\) 10\({}^From the above table, it can be seen that HMCMMFO using different step lengths obtained the optimal solution with a similar magnitude in most functions.