# Mutational Chemotaxis Motion Driven MdpI for Engineering Applications
## 4 Discussion of Experimental Results
### Parameters Sensitivity Analyses  
#### 4.1.1 Determination of the Parameter \(\delta\)  
In order to discuss the influence of \(\delta\) in hybrid-Cauchy-and-Gaussian mutation on the algorithm's accuracy, the parameter-sensitivity experiment of \(\delta\) is carried out in this paper. If the value of \(\delta\) is too large, the updated individual will exceed the space boundary. Therefore, this experiment adopts boundary control for the updated agent and reinitializes the individuals beyond the spatial range. Meanwhile, to ensure the experiment's fairness, as per other AI work [63, 64, 65], this experiment adopts the single-variable principle to only assign different values to \(\delta\), specifically \(\delta i=[0.1,\ 0.2,\ \ldots,\ 0.9]\). In addition, other experimental environments are described above. In the 30 test functions, the average value of the optimal solution is obtained in each function by HMCMMFO with different \(\delta\), and the most suitable \(\delta\) is determined according to the average-ranking value of each algorithm. As shown in Table 2 below, ARV is the average ranking of the algorithm in the 30 functions, and Rank is the final ranking of the algorithm obtained according to ARV. From the data in the table, it can be seen that \(\delta\) in the range from 0.1 to 0.5 has better results in solving the optimal values among the \begin{table}
\begin{tabular}{c c c c} \hline
**No.** & **Functions** & **Bound** & **F (min)** \\ \hline F1 & Shifted and Rotated Bent Cigar Function & \([-100,100]\) & 100 \\ F2 & Shifted and Rotated Sum of Different Power Function & \([-100,100]\) & 200 \\ F3 & Shifted and Rotated Zakharov Function & \([-100,100]\) & 300 \\ F4 & Shifted and Rotated Rosenbrock’s Function & \([-100,100]\) & 400 \\ F5 & Shifted and Rotated Rastrigin’s Function & \([-100,100]\) & 500 \\ F6 & Shifted and Rotated Expanded Scaffer’s F6 Function & \([-100,100]\) & 600 \\ F7 & Shifted and Rotated Lunack Bi\_Rastrigin Function & \([-100,100]\) & 700 \\ F8 & Shifted and Rotated Non-Continuous Rastrigin’s Function & \([-100,100]\) & 800 \\ F9 & Shifted and Rotated Levy Function & \([-100,100]\) & 900 \\ F10 & Shifted and Rotated Schwefel’s Function & \([-100,100]\) & 1000 \\ F11 & Hybrid Function1 (\(N=3\)) & \([-100,100]\) & 1100 \\ F12 & Hybrid Function2 (\(N=3\)) & \([-100,100]\) & 1200 \\ F13 & Hybrid Function3 (\(N=3\)) & \([-100,100]\) & 1300 \\ F14 & Hybrid Functional4 (\(N=4\)) & \([-100,100]\) & 1400 \\ F15 & Hybrid Function5 (\(N=4\)) & \([-100,100]\) & 1500 \\ F16 & Hybrid Function6 (\(N=4\)) & \([-100,100]\) & 1600 \\ F17 & Hybrid Function6 (\(N=5\)) & \([-100,100]\) & 1700 \\ F18 & Hybrid Function6 (\(N=5\)) & \([-100,100]\) & 1800 \\ F19 & Hybrid Function6 (\(N=5\)) & \([-100,100]\) & 1900 \\ F20 & Hybrid Function6 (\(N=6\)) & \([-100,100]\) & 2000 \\ F21 & Composition function1 (\(N=3\)) & \([-100,100]\) & 2100 \\ F22 & Composition function2 (\(N=3\)) & \([-100,100]\) & 2200 \\ F23 & Composition function3 (\(N=4\)) & \([-100,100]\) & 2300 \\ F24 & Composition function4 (\(N=4\)) & \([-100,100]\) & 2400 \\ F25 & Composition function5 (\(N=5\)) & \([-100,100]\) & 2500 \\ F26 & Composition function6 (\(N=5\)) & \([-100,100]\) & 2600 \\ F27 & Composition function7 (\(N=6\)) & \([-100,100]\) & 2700 \\ F28 & Composition function8 (\(N=6\)) & \([-100,100]\) & 2800 \\ F29 & Composition function9 (\(N=3\)) & \([-100,100]\) & 2900 \\ F30 & Composition function10 (\(N=3\)) & \([-100,100]\) & 3000 \\ \hline \end{tabular}
\end{table} 
Table 1: Description of the CEC2017 functions. 30 functions, and their ARV and Rank are stronger than those of other \(\delta\). This is because larger \(\delta\) will cause the population individual to cross the boundary, and out-of-bounds processing needs to be conducted; in this case, the hybrid-Cauchy-and-Gaussian-mutation strategy will become meaningless. Therefore, it can be concluded from the data that this strategy can play best role when the value of \(\delta\) is 0.3.