# Mutational Chemotaxis Motion Driven MdpI for Engineering Applications
## 4 Discussion of Experimental Results
### Impact of Optimization Strategies on MFO
#### 4.2.2 Balance and Diversity Analysis of HMCMMFO and MFO  
To further analyze the changes produced by the strategies proposed in this paper on the optimization performance of MFO, this section analyzes the diversity and balance of HMCMMFO and MFO. As shown in Figure 3 below, this section selects three functions from the 30 test functions for discussion, namely F1, F11, and F25. In the figure, the first column is the balance plots of HMCMMFO, the second column is the balance plots of MFO, and the third column is the diversity plots, including HMCMMFO and MFO.  
Figure 2: MFO convergence curves with different strategies.  
There are three curves in the equilibrium graph's first and second columns: exploration, exploitation, and incremental-decremental. Among them, the exploration curve represents the proportion of the global search process of the algorithm, the exploitation curve represents the proportion of the local-exploitation process of the algorithm, and the incremental-decremental curve is a dynamic curve that changes with the changes in the exploration and exploitation curves. When the global-exploration ability of the algorithm is greater than its local-exploitation ability, the incremental-decremental curve increases, and vice versa. The curve reaches the vertex position when the algorithm's global-exploration ability and local-exploitation ability are equal. In the F1, F11, and F25 balance plots shown below, the global-exploration ability of traditional MFO is weak, but the local-exploitation ability is strong. Although the stronger local-exploitation ability helps the MFO algorithm to search for the solution space finely, global exploration that is too short will affect the population's optimal solution and reduce its optimization accuracy. Moreover, the HMCMMPO proposed in this paper effectively improves the global-exploration ability of the algorithm. For example, the global-exploration stage of MFO in F1 only accounts for 5.7944%, while HMCMMPO accounts for 19.5147%, and still has a large proportion of the exploitation process. When HMCMMPO does not reach half of the maximum evaluation times, its exploration curve decreases slowly compared with MFO's, and oscillation is large. When it exceeds half of the maximum evaluation times, the exploitation curve increases rapidly, and then the slope of the curve slowly approaches 0. The reason for this phenomenon is that the algorithm adopts hybrid mutation on the individual in the first half of the evaluation, which increases the exploration performance of the algorithm. The chemotaxis motion is adopted in the second half to guide the individual to approach the optimal solution, increasing the algorithm's local-exploitation ability.  
Figure 3: Balance-and-diversity-analysis plots.  
In the diversity plots, the horizontal coordinate indicates the number of iterations, and the vertical coordinate represents the diversity metric. The algorithm population is affected by random initialization, which leads to good population diversity at the beginning of the algorithm and gradually decreases as it keeps approaching the optimal solution. In F1, F11, and F25, the diversity curve of MFO decreases rapidly and approaches 0 in the middle of the iteration. A too-fast decline in diversity will lead the algorithm to local optimum, while too-fast convergence is not conducive to finding higher-quality optimal solutions. In the early stage of the iteration, HMCMMFO has a slow decline in diversity curve, rich diversity, and large fluctuation, which means that the hybrid mutation adopted in the early stage is helpful for the algorithm to explore the solution space comprehensively. HMCMMFO diversity drops fast when the algorithm just enters the second half of the iteration, which indicates that the chemotaxis-motion strategy can help an individual to approach the optimal solution effectively.