# A Knowledge-Guided Competitive Co-Evolutionary Algorithm for Feature Selection
## 3 Knowledge-Guided Evolutionary Algorithm
### Feature Grouping Based on Correlation
The treatment for special cases is as shown in Table 1.

Figure 4: Resource allocation mechanism based on success rate. An additional simple method is to adopt a nonlinear approach for resource allocation instead of directly distributing resources based on performance proportions. For instance, a sigmoid function based on success rates can be used for resource allocation, ensuring that, even with significant performance differences, resource distribution does not become too extreme. The general form of the function used is as follows:

\[\text{sigmoid}(x)=\frac{1}{1+e^{-\beta(x-\alpha)}} \tag{4}\]

Here, \(\alpha\) and \(\beta\) are adjustable parameters controlling the center point and the slope of the function, respectively. We set \(\alpha\) to 0.5 (assuming an ideal state where both populations equally share resources), and \(\beta\) can be adjusted based on actual needs to control the smoothness of resource distribution. A higher \(\beta\) value makes the resource allocation more sensitive to performance differences, while a lower value results in more even distribution. ## 5 Experimental Setup

### Classification Datasets

This study utilizes five diverse datasets for classification tasks, all sourced from online website like the UCI Machine Learning Repository [36]. Each dataset is meticulously selected to encapsulate a wide spectrum of challenges commonly encountered in the machine learning domain. These challenges range from managing datasets with low to high dimensionality to addressing problems with varying numbers of classes, from simple binary classifications to more complex multi-class scenarios. This variety is crucial for testing the robustness and adaptability of proposed algorithms under varied conditions. Moreover, the datasets are not only diverse in their characteristics but also relevant to real-world applications. They include data from health, chemistry, voice recognition, and consumer preferences, which are critical areas where machine learning models are extensively applied. Table 2 provides a concise overview of these datasets, detailing the number of instances, features, and classes for each. This diverse collection not only tests the adaptability and efficiency of the algorithms but also enhances the robustness of our experimental findings by covering a broad spectrum of data characteristics. ### Performance Metrics

This article utilizes two principal performance indicators to assess the quality of solutions obtained by multi-objective evolutionary algorithms (MOEAs): Hypervolume \begin{table}
\begin{tabular}{c c} \hline
**Special Cases** & **Allocation\_Rate** \\ \hline allocation\_rate \(>\) 0.9 & 0.9 \\ allocation\_rate \(<\) 0.1 & 0.1 \\ success\_rate1 = 0 AND success\_rate2 \(\
eq\) 0 & 0.1 \\ success\_rate1 \(\
eq\) 0 AND success\_rate2 = 0 & 0.9 \\ success\_rate1 = 0 AND success\_rate2 = 0 & 0.5 \\ \hline \end{tabular}
\end{table} 
Table 1: Special case handling. \begin{table}
\begin{tabular}{c c c c c} \hline
**No.** & **Dataset Name** & **Instance** & **Feature** & **Class** \\ \hline
1 & Wine & 178 & 13 & 3 \\
2 & MUSK1 & 476 & 166 & 2 \\
3 & LSVT\_Voice & 126 & 310 & 2 \\
4 & ISOLET5 & 1559 & 617 & 26 \\
5 & Toxic & 171 & 1203 & 2 \\ \hline \end{tabular}
\end{table} 
Table 2: Classification datasets. (HV) [37] and Inverted Generational Distance (IGD) [38]. These indicators are critical for evaluating an algorithm's efficacy in terms of both convergence to the Pareto front and distribution of the solutions across it. For HV, normalization of all objective values obtained by each algorithm is performed initially against the ideal and nadir points, scaling them to the [0, 1] range in each objective direction. The ideal and nadir points are set at (0, 0) and (1.1, 1.1), respectively, with the HV's reference point subsequently established at (1, 1) [32]. This process ensures a standardized basis for comparing the extent of the objective space covered by the solutions from different algorithms.