# A Knowledge-Guided Competitive Co-Evolutionary Algorithm for Feature Selection
## 3 Knowledge-Guided Evolutionary Algorithm
### Feature Grouping Based on Correlation
The key differentiator is the use of correlation-based feature grouping in the KGEA, which guides the crossover and mutation processes and significantly narrows the search space. This strategy leads to more informed genetic operations and enhances the efficiency of the algorithm. These comparisons underline the benefits of integrating domain knowledge into the evolutionary process, particularly in scenarios where the relationships among decision variables significantly impact the outcome. It supports the premise that a knowledge-guided approach in evolutionary algorithms can significantly enhance performance, especially in complex problem domains such as feature selection in high-dimensional datasets. \begin{table}
\begin{tabular}{c c c c} \hline \multirow{2}{*}{**Dataset**} & \multicolumn{2}{c}{**KCCEA (Optimal)**} & \multicolumn{2}{c}{**KCCEA (0.5)**} \\ \cline{2-5}  & **Mean** & **Variance** & **Mean** & **Variance** \\ \hline
1 & \(2.55\times 10^{-2}\) & \(2.63\times 10^{-4}\) & \(2.74\times 10^{-2}\) & \(2.91\times 10^{-4}\) \\
2 & \(2.55\times 10^{-2}\) & \(1.11\times 10^{-5}\) & \(2.01\times 10^{-2}\) & \(1.93\times 10^{-5}\) \\
3 & \(2.54\times 10^{-2}\) & \(3.55\times 10^{-5}\) & \(2.23\times 10^{-2}\) & \(1.39\times 10^{-5}\) \\
4 & \(2.10\times 10^{-2}\) & \(4.12\times 10^{-4}\) & \(1.87\times 10^{-2}\) & \(5.13\times 10^{-4}\) \\
5 & \(3.63\times 10^{-2}\) & \(1.05\times 10^{-4}\) & \(3.29\times 10^{-2}\) & \(2.70\times 10^{-4}\) \\ \hline \end{tabular}
\end{table} 
Table 4: Mean IGD performance on test data. The best performance is highlighted in gray. \begin{table}
\begin{tabular}{c c c c} \hline \multirow{2}{*}{**Dataset**} & \multicolumn{2}{c}{**NSSGA-II**} & \multicolumn{2}{c}{**KGEA**} & \multicolumn{2}{c}{**KCCEA**} \\ \cline{2-5}  & **Mean** & **Variance** & **Mean** & **Variance** \\ \hline
1 & \(2.05\times 10^{-2}\) & \(1.43\times 10^{-4}\) & \(2.85\times 10^{-2}\) & \(2.71\times 10^{-4}\) & \(2.55\times 10^{-2}\) & \(2.63\times 10^{-4}\) \\
2 & \(1.66\times 10^{-1}\) & \(1.09\times 10^{-4}\) & \(5.60\times 10^{-2}\)

### Effectiveness of Dynamic Resource Allocation

The dynamic resource allocation mechanism in the KCCEA significantly improves performance over the KGEA by adjusting the allocation ratio based on the success rates of the two algorithms. This adaptive approach enhances the exploration and exploitation balance, leading to better overall results. As shown in Tables 5 and 6, the KCCEA achieves lower IGD values and higher HV values across multiple datasets, particularly in high-dimensional feature spaces. For instance, in the ISOLET5 dataset, the KCCEA achieves an IGD of 0.021 and an HV of 0.544, outperforming the KGEA. This mechanism ensures that computational resources are allocated optimally, leveraging the strengths of both the KGEA and NSGA-II. By maintaining a balance between competition and cooperation, the KCCEA prevents the dominance of a single algorithm, resulting in a more robust and efficient evolutionary process. The dynamic resource allocation effectively adapts the search strategy based on real-time performance, improving the quality of solutions and providing a competitive edge in tackling complex feature selection tasks in high-dimensional datasets. ### Knowledge-Guided Competitive-Cooperative Evolutionary Algorithm against Baseline Algorithm

The Knowledge-Guided Competitive-Cooperative Evolutionary Algorithm (KCCEA) effectively integrates the Knowledge-Guided Evolutionary Algorithm (KGEA) with the traditional NSGA-II, showcasing significant performance enhancements in complex feature selection tasks across high-dimensional datasets. This integration facilitates a robust comparative analysis that highlights the benefits of incorporating domain-specific knowledge into evolutionary strategies. As evidenced by the results presented in Tables 5 and 6, the KCCEA surpasses the NSGA-II in four out of five experiments.