## 4 Methodology
### Mutation Strategies
```
1k=index(n-i+1);
2x=Position(k,:);
3A=randperm(nPop/2);
4A(A==index(1))=[];
5a=index(1);
6b=index(A(2));
7c=index(A(3));
8d=index(A(4));
9e=index(A(5));
10y=Position(a,:)+beta.*(Position(b,:)-Position(c,:))+beta. *(Position(d,:)-Position(e,:));
11 forj=1:dimdo
12 ify(j)>rand\(\
ot\sim rand>0.75\)then
13y(j)=Position(a,j);
14
15
16
17
18
19 else
20 Execute the roulette strategy to determine the value of y(j) from b, c, d or e ;
21
22
23 end if
24
25 end if
26z=zeros(1,dim);
27j0=randi([1 numbel(x)]);
28 forj=1:numel(x)do
29 ifj==j0\(\mid\mid\)rand\(<=pCR\)then
21z(j)=y(j);
22
23 end if
24
25 else
26z(j)=x(j);
27
28
29 end if
30
31 end if
```

**Algorithm 3**The mutation method of poor individuals

### Jumping Method

It can be seen from MDE that elite individuals influence the search of the population. When a solution is too excellent, they will quickly converge to this position. If the solution is a local optimum, they may fall into a trap, leading the population to lose diversity. Elite individuals are forced to leave their positions and search for other space if the global optimal solution is not updated after ten iterations, as shown in Equation (4). \[X_{i}^{j}=\left\{ \begin{array}{ll}1-X_{i}^{j}&if(rand<=2*i/nPop)\\ X_{i}^{j}&else\end{array} \right. \tag{4}\]

where \(nPop\) is the population size, \(j\) is the dimension, and \(i\) represents the \(i\)-th elite individual according to the sorting order. This method allows most individuals to have the opportunity to escape local traps, and also allows several individuals to continue searching around their positions. ## 5 Experimental Results and Analysis

### Approaches Used for Comparisons

To validate the superiority of the proposed MDE, the classification performance is compared with two previous works, DE [28] and BBO_PSO [21], and a metaheuristic algorithm SCA [30]. BBO_PSO is a new hybrid PSO-assisted biogeography-based optimization for emotion recognition, and SCA is a sine cosine algorithm for feature selection. Table 1 provides additional information concerning the algorithms. _beta_min_ and _beta_max_ represent the lower and upper bounds of the scaling factor, and the most popular strategy set _beta_ in DE by using a Gaussian distribution with a mean of 0.5 and a standard deviation of 0.3. These values are consistent with the settings of SaDE [31], and they are beneficial to producing small and large search step sizes. \(pCR\) means the crossover probability, \(KeepRate\) is rate of kept habitats, \(pMutation\) is the mutation probability, \(w\) is the inertia weight, and \(c1\) and \(c2\) are learning factors. _thres_ is a threshold value. The algorithms adopt Equation (3) as their objective function. The maximum objective functions of the algorithms are set to 2000, and this process is repeated 20 times with a population size of 20. We apply the Wilcoxon rank-sum and Friedman tests to determine if there are significant differences in the experimental results in which a significance level of 0.05 is chosen. ### Experimental Analysis

KNN and RF are adopted as classifiers, where \(K\) is 5, and the Euclidean distance is selected as the computational method for data points. The number of decision trees is set to 100, and the splitting criterion of decision trees is the Gini index (\(gdi\)), which reflects the influence of a certain feature on the classification results. All data serve as samples, and the data are randomly divided into 10 parts through 10-fold cross validation. One of them is used for testing, while the other parts are used for training. We obtain the final average recognition error after repeating ten times, and the bold font indicates that a algorithm has obtained the optimal solution. #### 5.2.1 Simulation Results on the K-Nearest Neighbor Classifier

Figure 5 displays the experimental results using the KNN classifier, and it shows the average, maximum, and minimum errors obtained from each independent run.