# A Knowledge-Guided Competitive Co-Evolutionary Algorithm for Feature Selection
## 3 Knowledge-Guided Evolutionary Algorithm
### Feature Grouping Based on Correlation
Compared to GD, the IGD can identify uneven distribution of solutions, making the evaluation more objective. Therefore, the IGD is chosen as the final evaluation metric. Figure 5: The calculation method of IGD. ### Parameter Settings

In this study, each algorithm undergoes 30 distinct trials on every dataset to ensure robust statistical analysis. Consistency across these trials is maintained by using a fixed initial random seed for all algorithms. As outlined in [32], we adapt the population size based on the number of features present in each dataset. Specifically, the population size \(N\) is dynamically adjusted to match the number of features up to a maximum of 200. This cap is imposed to strike an optimal balance between algorithmic diversity and computational efficiency. Consequently, even for datasets with more than 200 features, the population size remains limited to 200. For the sigmoid function that equilibrates the resource allocation, \(\alpha\) is set to 0.5 (assuming that, ideally, the two populations distribute the resources equally), and \(\beta\) is set to 2 to control the degree of smoothing of the resource allocation. The algorithms are set to run for 100 generations, providing a deep exploration of the solution space. For the purpose of evaluating classification performance, we partition each dataset into training and testing subsets. The training set comprises roughly 70% of the data, with the remaining 30% allocated to the testing set. This split is consistently applied across all 30 executions of each algorithm on a given dataset, ensuring comparability of results. However, the specific partition varies from one dataset to another, maintaining rigorous evaluation standards across different data contexts. ## 6 Experimental Results and Analysis

### Grouping Threshold Sensitivity Analysis

This work conducted an analysis on the sensitivity to grouping thresholds. We varied the threshold from 0.5 to 0.95 and observed how the number of groups and the balance within the groups (standard deviation of group sizes) changed. As illustrated in Figure 6, we found that, as the threshold increased, the number of groups decreased while the balance improved. By normalizing the number of groups and balance to the same scale, and identifying the threshold where the difference between them was minimal, we determined the optimal grouping threshold, as shown in Table 3. This threshold provides the best compromise between the number of groups and balance during the grouping process. Subsequently, we applied the optimal threshold for each dataset within the KCCEA and compared it with a default threshold of 0.5. The results of these comparative experiments are presented in \[\text{HV}(S) =\lambda\Bigg{(}\bigcup_{x\in S}[f_{1}(x),r_{1}]\times\cdots\times [f_{m}(x),r_{m}]\Bigg{)}\]0

\[\text{HV}(S) =\lambda\Bigg{(}\bigcup_{x\in S}[f_{1}(x),r_{1}]\times\cdots\times [f_{m}(x),r_{m}]\Bigg{)}\]1 Groupingperformance by threshold. As can be seen from the results, the algorithm performs best when using the optimal thresholds we obtained, outperforming other takes on several test problems, especially on problems with high feature dimensions. ### Effectiveness of Knowledge-Guided Evolution

The improved algorithm KGEA is compared with the traditional multi-objective evolutionary algorithm to verify the effectiveness of the knowledge-guided evolution method. The experimental method is the same as above; the NSGA-II is set according to the parameters in the paper [16], the KGEA mutation and crossover probability are both set to 0.5, and the grouping threshold is the optimal threshold calculated in the previous section. The empirical results shown in Tables 5 and 6 indicate that the Knowledge-Guided Evolutionary Algorithm (KGEA) outperforms the traditional NSGA-II in four out of five experiments within a set number of evolutionary generations. The effectiveness of the KGEA is demonstrated through comparison with the baseline NSGA-II, which does not utilize knowledge-based feature grouping.