The paper introduces GBRUN, a Gradient Search-based Binary Runge-Kutta Optimizer for Feature Selection. GBRUN converts the continuous Runge-Kutta optimizer (RUN) into a binary version using S-, V-, and U-shaped transfer functions. It also incorporates a gradient search method to enhance the algorithm's exploration capability. The GBRUN algorithm is validated on five high-dimensional datasets and a real-world optimization problem from Arizona State University. Experimental results show that GBRUN outperforms other advanced algorithms in classification accuracy and the number of selected features. Additionally, GBRUN is combined with EfficientNet to select features extracted by EfficientNet for the classification of COVID-19 CT images. The V-shaped (GBRUN-V) and U-shaped (GBRUN-U) algorithms demonstrate better performance than other algorithms. The main contributions of this study include converting the RUN algorithm to a binary version, improving the performance of the BRUN algorithm using an enhanced gradient search method, validating the performance of GBRUN on high-dimensional datasets, and combining GBRUN with EfficientNet for COVID-19 CT image classification. The GBRUN algorithm is designed to solve high-dimensional feature selection problems by balancing exploration and exploitation capabilities to avoid local optima. The algorithm uses a gradient search method and Newton's method to improve exploration capability in the solution space. The GBRUN algorithm is tested on five standard datasets and shows better performance in classification accuracy and feature selection. The algorithm is also applied to the classification of COVID-19 CT images, achieving better results in accuracy, recall, precision, F1-score, and AUC compared to other algorithms. The study concludes that GBRUN is effective for feature selection in high-dimensional data and has potential for real-world applications.The paper introduces GBRUN, a Gradient Search-based Binary Runge-Kutta Optimizer for Feature Selection. GBRUN converts the continuous Runge-Kutta optimizer (RUN) into a binary version using S-, V-, and U-shaped transfer functions. It also incorporates a gradient search method to enhance the algorithm's exploration capability. The GBRUN algorithm is validated on five high-dimensional datasets and a real-world optimization problem from Arizona State University. Experimental results show that GBRUN outperforms other advanced algorithms in classification accuracy and the number of selected features. Additionally, GBRUN is combined with EfficientNet to select features extracted by EfficientNet for the classification of COVID-19 CT images. The V-shaped (GBRUN-V) and U-shaped (GBRUN-U) algorithms demonstrate better performance than other algorithms. The main contributions of this study include converting the RUN algorithm to a binary version, improving the performance of the BRUN algorithm using an enhanced gradient search method, validating the performance of GBRUN on high-dimensional datasets, and combining GBRUN with EfficientNet for COVID-19 CT image classification. The GBRUN algorithm is designed to solve high-dimensional feature selection problems by balancing exploration and exploitation capabilities to avoid local optima. The algorithm uses a gradient search method and Newton's method to improve exploration capability in the solution space. The GBRUN algorithm is tested on five standard datasets and shows better performance in classification accuracy and feature selection. The algorithm is also applied to the classification of COVID-19 CT images, achieving better results in accuracy, recall, precision, F1-score, and AUC compared to other algorithms. The study concludes that GBRUN is effective for feature selection in high-dimensional data and has potential for real-world applications.