# A Knowledge-Guided Competitive Co-Evolutionary Algorithm for Feature Selection
## 1 Introduction  
In today's machine learning landscape, the widespread presence of high-dimensional data in real-world scenarios presents substantial challenges [1; 2]. As datasets burgeon with features, from image characteristics in computer vision to genetic markers in bioinformatics, the demand for robust feature selection has become more pressing than ever [3; 4]. These complex datasets frequently include irrelevant, noisy, or redundant features that not only hinder the learning process but also impair the effectiveness of algorithms [5; 6]. Effective feature selection techniques boost model accuracy by isolating and preserving only the most impactful features for predictive modeling [7]. Additionally, by reducing the number of features, these techniques cut down on storage needs and computational expenses, thus enhancing the interpretability and efficiency of models [8]. Feature selection is inherently a challenging combinatorial optimization problem aimed at reducing the feature space while simultaneously enhancing the classifier's performance [9]. These objectives typically conflict; a minimal set of features might omit critical information, adversely impacting the model's performance. This problem's complexity escalates with the exponential growth in the number of potential feature subsets as the initial feature count increases, making a robust search strategy essential for effective feature selection [10]. In response to these challenges, the past few decades have seen the emergence of many effective algorithms, including filter-based methods, embedded methods, and wrapper methods. Filter-based methods, such as chi-square tests [11] and mutual information, evaluate the relevance of features independent of any learning algorithm. Embedded methods, like LASSO regression [12], perform feature selection during the model training process. Wrapper methods, such as Recursive Feature Elimination (RFE) [13], use a predictive model to evaluate feature subsets. Among all methods, metaheuristic algorithms stand out, particularly multi-objective evolutionary algorithms (MOEAs) [14; 15], which excel in balancing conflicting objectives without requiring gradient information. These algorithms, such as the NSGA-II [16], utilize principles of natural evolution--such as selection, crossover, and mutation--to explore and exploit the search space effectively. By mimicking natural selection processes, MOEAs can efficiently navigate the large and complex search spaces found in high-dimensional feature selection tasks. Despite their advantages, the computational complexity of MOEAs scales significantly with the increase in the number of features [17]. This complexity can be attributed to the need to evaluate a vast number of potential solutions, each representing a different subset of features. The performance of these algorithms often deteriorates as the dimensionality of the data increases, necessitating innovative approaches to reduce computational overhead and enhance the search process's efficiency [18]. The evolving landscape of feature selection has prompted the development of more sophisticated approaches. Using a single algorithm to balance convergence and diversity in multi-objective optimization problems (MOPs) [19] is challenging. Thus, the current trend is to combine multiple algorithms [20; 21]. This approach can be categorized into two main types: multi-algorithm methods (using various algorithms within the same population) [22; 23] and multi-population methods (using multiple populations, each targeting a specific objective) [24; 25]. In multi-algorithm methods, by integrating various algorithmic strategies, it is possible to effectively balance the exploration speed and the diversity of population development. It can synergize different evolutionary strategies to optimize performance across various feature selection scenarios. This method not only leverages the strengths of individual algorithms but also fosters a more dynamic and adaptive search process.