## 4 Methodology
### Modified Evaluation Function  
The aforementioned fitness function in the previous section is a multi-objective function that depends on the accuracy and the number of selected features. \(f(X)\) tends to maximize the \(Acc(X)\) and maximize the minimization process of the selected number of features \((1-\frac{L_{f}}{L_{f}})\). Note that the lower the number of selected features, \(L_{f}\), the higher the term \((1-\frac{L_{f}}{L_{f}})\). In other words, \(f(X)\) is strictly increased by increasing \(Acc(X)\) and strictly increased by decreasing \(L_{f}\). One issue we should demonstrate in the current fitness function is that it does not consider an important measurement called the correlation [119]. According to \(f(\cdot)\), there is no such term (or terms) in \(f(X)\) that considers the correlation among the features in the candidate solution or between each feature and the corresponding class label either. Therefore, this function has this limitation with respect to our earlier claim in Section 1. This is because it does not concern the relationship among the variables in the selected subset [120]. Furthermore, random-based search has no prior information about the correlation, and it can be improved by improving the decision-making in random-based algorithms.  
**Motivational Example:** Let us assume that we have a dataset with 100 features and two subsets of features, \(S_{1}\) and \(S_{2}\), which contain 40 and 36 features, respectively. Let the accuracy of \(S_{1}\) be 0.94 and the accuracy of \(S_{2}\) be 0.92. According to Equation (9), with \(wf=1\), the fitness score of \(S_{1}\) is 1.54, and the fitness score of \(S_{2}\) is 1.56, which means that \(S_{2}\) is better than \(S_{1}\). However, the accuracy of \(S_{1}\) is better than the accuracy of \(S_{2}\). Thus, not capturing the correlation between features in the fitness function may lead to a higher number of features or decreased accuracy.  
We tackled this complication by introducing new two terms to the fitness function in Equation (9). These two terms represent the different correlation aspects, as explained below. Thus, \(S_{1}\) will be selected instead of \(S_{2}\) if and only if the correlation among its features is lower than the correlation among the features in \(S_{2}\) and the correlation among each feature and the corresponding label in \(S_{1}\) is higher than the correlation among each feature and the corresponding label in \(S_{2}\). In this work, note that the label with different categories is tackled using hot encoding [121]. According to our claim, the fitness function \(f(\cdot)\) is modified and reformulated as follows:  
\[f(X)=max(Acc(X)+w_{f}*\bigg{(}(1-\frac{L_{f}}{L_{f}})-Correlation(X)+Correlation (X,I)\bigg{)} \tag{11}\]where \(Correlation(X)\) is the correlation among the features in \(X\), and \(Correlation(X,I)\) is the correlation between each feature and the label \(l\). According to the same example above with two candidate solutions, \(X_{1}\) and \(X_{2}\), and under the same assumptions, consider that, based on some correlation function, the term \(Correlation(X_{1})\) is 0.01, and \(Correlation(X_{1},I)\) is 0.2, and \(Correlation(X_{2})\) is 0.04, and \(Correlation(X_{2},I)\) is 0.1. Then, the fitness score of \(X_{1}\) is 1.55, and the fitness score of \(X_{2}\) is 1.53 which means that \(X_{1}\) is better than \(X_{2}\).