## 3 Background
### Binary Harris Hawks Optimizer (BHHO)
### Feature Selection (FS)

FS is a crucial process in ML that optimizes predictive performance by identifying the most relevant features while reducing computational complexity. By eliminating redundant data, FS enhances model accuracy and efficiency. Figure 7 illustrates its key components, including the original dataset, feature subset selection, subset evaluation, selection criteria, and validation [24]. In this study, FS was framed as a binary combinatorial optimization problem, where features are represented by binary variables: a value of 1 indicates inclusion in the subset, and 0 indicates exclusion. The FS problem was modeled using a binary vector representation. Each vector's length corresponds to the total number of features, and its binary values determine the inclusion of features in the subset. The FS process aimed to optimize the subset of features by balancing model accuracy and computational complexity. The performance of each subset was evaluated using a custom objective function designed to maximize the percentage of predictions within Zone A of the CEG, which represents clinically acceptable accuracy for BGLs. The objective function is expressed mathematically as:

\[\text{Objective Function}=\text{Maximize}\left(\frac{N_{A}}{N_{total}}\times 1 00\right), \tag{18}\]

where \(N_{A}\) is the number of predictions in Zone A, and \(N_{total}\) is the total number of predictions. Given the NP-hard nature of FS [32; 33] and the impracticality of exhaustive search, as previously mentioned, four metaheuristic algorithms, including IDA, BHHO, bGWO, and GA, were employed. These algorithms were selected for their capability to efficiently explore large search spaces while balancing exploration and exploitation [26; 27; 30; 38; 39]. Figure 7: Feature selection process. Each metaheuristic algorithm employed a wrapper approach using three ML models, including RF, ETR, and LightGBM, to evaluate feature subsets iteratively and identify the most relevant feature subsets. The open-source Zoofs library [48] was used to implement these algorithms. Each algorithm iteratively refined feature subsets, optimizing them for the regression task. The ML models were not only used as wrappers but also for comparative evaluation of the selected subsets. The best-performing subsets were identified based on their predictive performance. The parameter configurations for all metaheuristic algorithms were chosen based on thorough experimentation to ensure optimal performance. Details of these configurations and their comparative analysis are discussed in Section 5, \"Results and Discussion\". ### Regression Models

Regression models were applied to predict BGLs using the selected feature subsets. For this study, the three previously mentioned regression models, including RF, ETR, and LightGBM, were chosen for their proven effectiveness in comparable prediction tasks. Moreover, their robust nature and ability to identify complex patterns also contributed to their selection [49; 50; 51]. Below, a description of the regression models is presented. #### 4.3.1 Random Forest (RF)

[PERSON] introduced the RF Regressor in 2001, which is an ensemble learning approach that integrates several decision trees to increase prediction accuracy and stability. Each tree is trained using a bootstrap sample of data, with random feature subsets chosen at each split, and the final predictions are averaged across all trees [49]. This technique decreases variance, captures complicated patterns, and minimizes overfitting, making RF particularly useful for noisy and missing data. However, its ensemble nature might result in increased computing complexity and reduced interpretability when compared to individual decision trees [52; 53]. #### 4.3.2 Extra Trees Regressor (ETR)

The ETR, developed by [PERSON] et al. in 2006, is similar to RF but includes more randomization to improve computing efficiency and decrease overfitting.