## 3 Background
### Binary Harris Hawks Optimizer (BHHO)
Selection probabilities, calculated using Equation (13), prioritize these individuals. The offspring of the two parents is created through crossovers described in Equation (14), whereas mutation described in Equation (15) brings new diversity in the genes. These mechanisms lead the population to optimal solutions. \[S_{i}=\frac{f_{i}}{\sum_{j=1}^{P}f_{i}} \tag{13}\]

\[C^{\prime}=crossover(C_{1},C_{2})\, \tag{14}\]

\[C^{\prime}=\left\{ \begin{aligned} C\ with\ probability\ 1-M\\ mutate(C)\ with\ probability\ M\end{aligned} \right. \tag{15}\]

Here, C represents the original chromosome, and C\({}^{\prime}\) is the resulting chromosome after mutation. The algorithm begins with a randomly initialized population, where each individual represents a subset of features encoded as a binary vector. Fitness evaluation guides the selection process, using techniques such as roulette wheel or tournament selection to prioritize individuals with higher scores. Offspring are generated through crossover operations that exchange feature subsets between parents, while mutation introduces random changes, preserving genetic diversity and preventing premature convergence. Crossover and mutation operations are controlled by predefined probabilities, ensuring a balance between exploration and exploitation. This iterative process tracks the best-performing individual across generations and repeats until a termination condition, such as reaching the maximum iterations, is met. The final output is the optimal feature subset that represents the best solution identified. Algorithm 4 illustrates the GA workflow. ```
1. Initialize population P with random feature subsets as binary vectors
2. Evaluate the fit-ness of each individual in P using the fitness function
3. while stopping condition is not met do
4. Select parents from P based on fitness, using selection mechanisms such as roulette wheel or tournament selection, where individuals with higher fitness have a greater chance of being chosen
5. Apply crossover operation to selected parent pairs with a predefined crossover probabil-ity, generating offspring by exchanging genetic information (feature subsets)
6. Apply mutation to the offspring with a predefined mutation probability, introducing ran-dom changes to maintain diversity and prevent premature convergence
7. Evaluate the fitness of the new individuals to determine their quality as potential solu-tions
8. Replace old population with the newly generated population, selecting the best individu-als to guide the evolutionary process
9. Return the best individual as the optimal feature subset with the highest fitness
```

**Algorithm 4** Genetic Algorithm (GA) for Feature Selection

Due to the GAs ability to avoid local optima and the fact that they are efficient in high-dimensional search space, GAs are suitable for FS in bioinformatics and other domains such as image processing. However, careful parameter tuning is required to strike a balance between computational cost and convergence speed. ## 4 Methodology

This section presents the detailed methodology employed in this study to develop a non-invasive BGL estimation model using PPG signals and HRV features. The methodology comprises three primary stages: data preparation and feature extraction, FS using metaheuristic algorithms, and regression-based model evaluation. The general workflow is depicted in Figure 3, highlighting the contribution of this research in optimizing FS using metaheuristic algorithms. ### Data Preparation

#### 4.1.1 Dataset Description

The public dataset [6] utilized in this research comprises PPG signals collected from 52 subjects, including both male and female participants aged between 17 and 61 years, with a male-to-female ratio of 75:25. Each PPG signal was recorded for one minute with a sampling rate of 30 Hz, along with a reference BGL measurement using a commercially available glucometer (Accu-Check). The BGL measurements range from 68 to 211 mg/dL, which is adequate to evaluate the model's performance effectively.