The optimization technique is widely used in various fields of study, including computer science, engineering [11], health [12], agriculture, and feature selection [13]. The primary aim of optimization is to choose the optimal solution to a given problem among the available solutions that match the problem description. Additionally, optimization algorithms have a goal that must be reduced or maximized under the addressed problem [14–16].

Recently, numerous studies have used optimization to resolve given problems, such as the Whale Optimization Algorithm (WOA). WOA was used to locate the optimal weights for training the neural community and developed a multi-objective model of WOA, which was then applied to the problem of forecasting wind speed. Additionally, WOA was widely employed to determine the final location and length of capacitors used inside the radial system [17]. Additionally, they used WOA to circumvent the difficulty of determining the final length used by a distributed generator [18], and they benefited from the use of WOA for image segmentation [19,20].

The nature of EEG alerts may be very complicated since they are no longer linked, however random. The EEG dimension is determined by various factors, most notably the individual's age, gender, psychological state, and intellectual state of the issue [21]. Thus, comprehending the behavior and movement of brain cells involves various linear and nonlinear signal-processing methods that result in the physiological state and circumstances of the issue. Numerous ways are advocated for capturing the dynamic capabilities and sudden changes that may occur. The first step is preprocessing, which includes recording warnings, removing artifacts, signal averaging, output thresholding, and signal enhancement. The second stage is the function extraction technique within the procedure, which determines a feature vector from an ordinary vector [22].

Optimizer of Genetic Algorithm (GA) is inspired by biology (survival of the fittest). Initialization is a critical GA process. Alternatively, other genetic operators, such as elitism, may be used [23]. The advantages of this optimizer are its simplicity and ability to deal with noisy fitness functions. Due to delayed convergence, premature convergence, and parameter change, complexity is not scalable. This technique is utilized in the construction of image processing filters as well as antennas.

Particle Swarm Optimization (PSO) is another optimization technique that simulates the motions and interactions of individuals in a flock of birds or a school of fish [24]. Every particle is guided by its best-known location and the swarm's optimal position. It is stable, simple to implement, and a suitable model of collaboration, but starting settings are elusive. It has a long convergence time and a high computational cost. Gene clustering, antenna design, vehicle routing, control design, and dimension reduction are only a few examples of uses.

The Grey Wolf Optimizer (GWO) is an algorithm that mimics grey wolf leadership, social structure, and hunting behavior. Encircling and assaulting the victim are the first two phases. This optimizer possesses Exploration and exploitation must be conducted in a balanced manner. While high search accuracy is simple to implement, it results in premature convergence due to the fluctuating positions of the three leaders. The greater the number of variables, the lower performance is achieved. It is utilized in feature selection, parameter adjustment of PID controllers, clustering, robotics, and route finding [25].

The foraging behaviors of humpback whales inspired the Whale Optimization Algorithm (WOA). They catch fish with bubbles as they swirl around a school of fish. It is a simple method for exploring a vast search space that is sluggish to convergence, prone to local optima stagnation, and computationally costly. WOA is applied in route planning, voltage offset reduction, and precision control of laser sensor systems [26].

Two publicly accessible datasets for electroencephalogram (EEG) signal processing are utilized in this work to test our suggested method. Tab. 2 shows the description of the dataset. The Statistics of the EEG Dataset is discussed in Tab. 3 and Fig. 5 shows the correlation matrix of EEG dataset. The BCI Competition IV dataset is the first. The fourth BCI competition was held in 2008 at Austria's Graz University of Technology. For the sake of this research, we will analyze dataset 2a from the competition mentioned above. This dataset is freely accessible through [28]. The dataset contains the EEG data of nine healthy individuals. The subjects were healthy and ordinary people. They were instructed to complete the motor imagery activities while seated in a comfy armchair in front of an LCD display. To finish all charges, subjects used four distinct kinds of motor imagery. These activities required the use of one's imagination to move the left or right hand, foot, or tongue. To initiate the experimental paradigm, a brief auditory beep was played. Then, after two seconds, a fixation cross appeared on the LCD and was replaced by an arrow pointing up, down, right, or left. The participants completed one of the imaging tasks involving the mouth, feet, and left or right-hand motions, depending on the orientation of the needle. The performance subject retained the chosen item's imagination for about three seconds until the fixation cross vanished and the LCD became completely dark. Then, after a brief pause of about two seconds, the next job was resumed. This procedure was repeated 72 times for each of the four activities, totaling 288 instances of motor imagery per participant.

Each dataset is subdivided into three equal-sized segments at random: training, validation, and test. During the learning phase, training is utilized to fine-tune the KNN classifier. Validation is a technique for testing. When determining the fitness function of a particular solution. Normalize data to ensure that all features are contained within the same limits and are handled equally by the machine learning model. One of the simplest methods for scaling data is to use the min-max scaler, which scales and bounds data features between 0 and 1.

The evaluation metrics of the suggested method and compared algorithms are shown in Tab. 4. The used variables in Tab. 4 are the number of optimizer's runs, M, the best solution at the run number j, gj∗. In addition, gj∗ vector size, size(gj∗). A number of tested points, N. Classifier label of the output for a point i, Ci, and label of the class for a point i, Li. Finally, the total number of features, D, and Match, is used to calculate the matching between two inputs.

Results of the experimental for the two tested datasets, D1 and D2, based on the suggested and compared methods are shown in Tab. 5. The results are compared to GWO, GA, WOA, and PSO algorithms. The average error of (0.161956522) for D1 and of (0.027467811) is much better based on the suggested method. The average select error of (0.385714286) and (0.61875) for D1 and D2, respectively, show the performance of the SFS-Guided WOA algorithm. Average, best, worst fitness and standard deviation show the quality of the suggested method compared to other optimization techniques.

ANOVA and Wilcoxon Signed Rank tests are performed to confirm the suggested method compared to other algorithms. Tabs. 6 and 7 show the ANOVA test results of the tested algorithms based on the first dataset (D1) and the second dataset (D2), respectively. The results indicated that the p-value is less than 0.05. Wilcoxon Signed-Rank test results based on ten runs for the first dataset (D1) and the second dataset (D2) using the suggested and compared algorithms are shown in Tabs. 8 and 9, respectively. The statistical tests results confirm the performance of the SFS-Guided WOA algorithm for the EEG datasets.

The average error of the suggested (bSFS-Guided WOA) and compared algorithms (bPSO, bWOA, bGA and bGWO) over the two tested datasets (D1 and D2) is shown in Fig. 6. The figure indicates the performance of the suggested method over the tested datasets. Residual, Homoscedasticity, QQ plots and heat map of the suggested and compared algorithms over the first tested dataset (D1) and the second dataset (D2) are shown in Figs. 7 and 8, respectively.