# Mutational Chemotaxis Motion Driven MdpI for Engineering Applications
## 4 Discussion of Experimental Results
### Comparison with Original Algorithms
\begin{table}
\begin{tabular}{c c c c c c} \hline  & **F1** & **F2** & **F3** & \\ \cline{2-6}  & **AVG** & **STD** & **AVG** & **STD** & **AVG** & **STD** \\ \hline HMCMMFO & \(9.80294\times 10^{3}\) & \(8.67716\times 10^{3}\) & \(2.10105\times 10^{2}\) & \(1.95548\times 10^{1}\) & \(3.00025\times 10^{2}\) & \(8.14402\times 10^{-2}\) \\ SCA & \(1.22222\times 10^{10}\) & \(1.96238\times 10^{9}\) & \(2.90172\times 10^{34}\) & \(8.10053\times 10^{34}\) & \(3.77999\times 10^{4}\) & \(5.92640\times 10^{3}\) \\ FA & \(1.44254\times 10^{10}\) & \(1.24469\times 10^{9}\) & \(1.05613\times 10^{34}\) & \(2.35540\times 10^{34}\) & \(6.17194\times 10^{4}\) & \(6.95564\times 10^{3}\) \\ WOA & \(2.62081\times 10^{6}\) & \(1.45296\times 10^{6}\) & \(1.32144\times 10^{24}\) & \(5.24072\times 10^{24}\) & \(1.55853\times 10^{5}\) & \(5.63397\times 10^{4}\) \\ GOA & \(8.70605\times 10^{7}\) & \(3.38904\times 10^{8}\) & \(3.39750\times 10^{29}\) & \(1.86088\times 10^{30}\) & \(1.87791\times 10^{3}\) & \(3.41613\times 10^{3}\) \\ GWO & \(2.08506\times 10^{9}\) & \(1.37458\times 10^{9}\) & \(9.52398\times 10^{30}\) & \(3.68834\times 10^{31}\) & \(3.11186\times 10^{4}\) & \(1.09033\times 10^{4}\) \\ \hline  & **F4** & **F5** & & **F6** & \\ \cline{2-6}  & **AVG** & **STD** & **AVG** & **STD** & **AVG** & **STD** \\ \hline HMCMMFO & \(4.82113\times 10^{2}\) & \(1.68093\times 10^{1}\) & \(5.64407\times 10^{2}\) & \(1.85969\times 10^{1}\) & \(6.04935\times 10^{2}\) & \(1.81119\times 10^{0}\) \\ SCA & \(1.41644\times 10^{3}\) & \(2.88610\times 10^{2}\) & \(7.76337\times 10^{2}\) & \(1.86038\times 10^{1}\) & \(6.50345\times 10^{2}\) & \(5.13636\times 10^{0}\) \\ FA & \(1.36794\times 10^{3}\) & \(1.30754\times 10^{2}\) & \(7.60093\times 10^{2}\) & \(1.23883\times 10^{1}\) & \(6.44207\times 10^{2}\) & \(2.46820\times 10^{0}\) \\ WOA & \(5.37710\times 10^{2}\) & \(4.27357\times 10^{1}\) & \(7.89919\times 10^{2}\) & \(6.08936\times 10^{1}\) & \(6.68318\times 10^{2}\) & \(9.55672\times 10^{0}\) \\ GOA & \(5.02471\times 10^{2}\) & \(1.75301\times 10^{1}\) & \(6.22152\times 10^{2}\) & \(3.71558\times 10^{1}\) & \(6.26699\times 10^{2}\) & \(1.38950\times 10^{1}\) \\ GWO & \(5.99420\times 10^{2}\) & \(7.69352\times 10^{1}\) & \(5.98055\times 10^{2}\) & \(2.97506\times 10^{1}\) & \(6.06722\times 10^{2}\) & \(3.37262\times 10^{0}\) \\ \hline  & **F7** & **F8** & & **F9** & \\ \cline{2-6}  & **AVG** & **STD** & **AVG** & **STD** & **AVG** & **STD** \\ \hline HMCMMFO & \(8.17904\times 10^{2}\) & \(3.04063\times 10^{1}\) & \(8.64352\times 10^{2}\) & \(1.18965\times 10^{1}\) & \(1.14232\times 10^{3}\) & \(1.50046\times 10^{2}\) \\ SCA & \(1.13362\times 10^{3}\) & \(4.30939\times 10^{1}\) & \(1.05252\times 10^{3}\) & \(1.67232\times 10^{1}\) & \(5.72874\times 10^{3}\) & \(1.10108\times 10^{3}\) \\ FA & \(1.37609\times 10^{3}\) & \(3.87283\times 10^{1}\) & \(1.05363\times 10^{3}\) & \(1.06885\times 10^{1}\) & \(5.41486\times 10^{3}\) & \(5.35328\times 10^{2}\) \\ WOA & \(1.23989\times 10^{3}\) & \(8.26385\times 10^{1}\) & \(1.01339\times 10^{3}\) & \(5.49513\times 10^{1}\) & \(8.51073\times 10^{3}\) & \(2.93031\times 10^{3}\) \\ GOA & \(8.31785\times 10^{2}\) & \(2.47063\times 10^{1}\) & \(9.00602\times 10^{2}\) & \(2.54215\times 10^{1}\) & \(3.62090\times 10^{3}\) & \(2.04697\times 10^{3}\) \\ GWO & \(8.55401\times 10^{2}\) & \(3.13429\times 10^{1}\) & \(8.91975\times 10^{2}\) & \(1.81598\times 10^{1}\) & \(1.75641\times 10^{3}\) & \(4.84758\times 10^{2}\) \\ \hline  & **F10** & & **F11** & & **F12** & \\ \cline{2-6}  & **AVG** & **STD** & **AVG** & **STD** & **AVG** & **STD** \\ \hline HMCMMFO & \(3.94563\times 10^{3}\) & \(7.83295\times 10^{2}\) & \(1.20235\times 10^{3}\) & \(4.27168\times 10^{1}\) & \(2.53419\times 10^{5}\) & \(1.95894\times 10^{5}\) \\ SCA & \(8.16479\times 10^{3}\) & \(2.19303\times 10^{2}\) & \(2.146661\times 10^{3}\) & \(3.321220\times 10^{2}\) & \(1.08585\times 10^{9}\) & \(2.83877\times 10^{8}\) \\ FA & \(8.01204\times 10^{3}\) & \(1.91427\times 10^{2}\) & \(3.59287\times 10^{3}\) & \(4.69048\times 10^{2}\) & \(1.57000\times 10^{9}\) & \(2.87851\times 10^{8}\) \\ WOA & \(6.07641\times 10^{3}\) & \(7.56256\times 10^{2}\) & \(1.57520\times 10^{3}\) & \(4.56758\times 10^Table S5 in the Supplementary Material shows the comparison results of using the Wilcoxon signed-rank test to evaluate HMCMMFO with other original metaheuristic algorithms.