# Mutational Chemotaxis Motion Driven MdpI for Engineering Applications
## 6 Conclusions and Future Work  
The HMCMMFO proposed in this paper substantially improves optimization performance over the traditional MFO. By introducing a hybrid-mutation strategy, the diversity of the algorithm is increased, and its ability to jump out of the local optimal space is enhanced. A chemotaxis-motion strategy is adopted to guide individuals to move toward the optimal solution and improve the optimization accuracy of the algorithm. In the test functions of CEC2017, the most suitable parameter settings in the optimization strategy are determined through parameter-sensitivity analysis. MFO variants using different mechanisms are compared to prove the effectiveness of the improved strategy. Comparing HMCMMFO with MFO variants, original metaheuristics, and advanced algorithms proves that HMCMMFO has more superior optimization performance. Moreover, five typical engineering design examples are verified in this paper to discuss the application value of HMCMMFO in solving practical problems in the real world. The results show that HMCMMFO has significant advantages in solving constraint problems. Due to the time-consuming nature of HMCMMFO in dealing with large-scale and complex problems, the next piece of research is planned to combine HMCMMFO with distributed platforms to deal with such problems in a parallel way. In addition, balancing the global-exploration and local-exploitation capabilities of HMCMMFO is crucial to improving the overall optimization performance of the algorithm. Therefore, the next piece of work will also investigate the flame-number formula of HMCMMFO and adopt a dynamic-adaptive mechanism based on the number of evaluations to balance the algorithm's exploration and exploitation. At the same time, relying on the powerful optimization ability of HMCMMFO, its applications in image segmentation [21] and \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline \multirow{2}{*}{**Algorithm**} & \multicolumn{6}{c}{**Optimal Values for Variables**} & \multirow{2}{*}{**Optimum Cost**} \\ \cline{2-2} \cline{4-7}  & \(b\) & \(m\) & \(p\) & \(I_{1}\) & \(I_{2}\) & \(d_{1}\) & \(d_{2}\) \\ \hline HMCMMFO & 3.5 & 0.7 & 17 & 7.3 & 7.71532 & 3.350215 & 5.286654 & 2994.4711 \\ AGOA [89] & 3.5 & 0.7 & 17 & 7.310097 & 7.737602 & 3.350234 & 5.287056 & 2995.3092 \\ IDARSOA [82] & 3.50608 & 0.7 & 17 & 7.3 & 7.71926 & 3.353154 & 5.288364 & 2998.7797 \\ GWO [73] & 3.50669 & 0.7 & 17 & 7.380933 & 7.815726 & 3.357847 & 5.286768 & 3001.2880 \\ PSO [100] & 3.50001 & 0.7 & 17 & 8.3 & 7.8 & 3.352412 & 5.286715 & 3005.7630 \\ SCA [69] & 3.50875 & 0.7 & 17 & 7.3 & 7.8 & 3.461020 & 5.289213 & 3030.5630 \\ GSA [86] & 3.6 & 0.7 & 17 & 8.3 & 7.8 & 3.369658 & 5.289224 & 3051.1200 \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Comparison results of speed-reducer-design problem. dynamic-landscape processing are also worthy research directions. In addition, future research can also be extended to a multi-objective optimization algorithm to solve more complex issues in real industrial environments. The following supporting information can be downloaded at: [[https://www.mdpi.com/article/10.3390/app122312179/s1](https://www.mdpi.com/article/10.3390/app122312179/s1)]([https://www.mdpi.com/article/10.3390/app122312179/s1](https://www.mdpi.com/article/10.3390/app122312179/s1)), Table S1: The relevant parameters involved in experiments; Table S2: Parameter settings of MFO variants; Table S3: Wilcoxon sign rank test comparison results of MFO variants; Table S4: Parameter settings of original algorithms; Table S5: Comparison results of Wilcoxon sign rank test for original algorithms; Table S6: Parameter settings of advanced algorithms; Table S7: Comparison results of Wilcoxon sign rank test for advanced algorithms. Conceptualization, methodology, software, validation, formal analysis, investigation, data curation, resources, writing, writing--review and editing, visualization, H.Y., S.Q., A.A.H., L.S. and H.C.; supervision, L.S. and H.C.; funding acquisition, project administration, L.S.