The paper introduces a Gradient Search-based Binary Runge Kutta Optimizer (GBRUN) for feature selection (FS) in high-dimensional datasets. The GBRUN algorithm converts the continuous Runge Kutta optimizer (RUN) into a binary version using S-, V-, and U-shaped transfer functions. It enhances the exploration capability of the algorithm through an improved Gradient Search method (GSR). The performance of GBRUN is evaluated on five standard datasets and compared with other advanced algorithms. The results show that GBRUN outperforms other algorithms in terms of classification accuracy and the number of selected features. Additionally, the GBRUN algorithm is combined with EfficientNet for COVID-19 CT image classification, achieving better results in terms of accuracy, recall, precision, F1-score, AUC, and ROC. The paper concludes by highlighting the effectiveness of GBRUN in FS and its potential for real-world applications.The paper introduces a Gradient Search-based Binary Runge Kutta Optimizer (GBRUN) for feature selection (FS) in high-dimensional datasets. The GBRUN algorithm converts the continuous Runge Kutta optimizer (RUN) into a binary version using S-, V-, and U-shaped transfer functions. It enhances the exploration capability of the algorithm through an improved Gradient Search method (GSR). The performance of GBRUN is evaluated on five standard datasets and compared with other advanced algorithms. The results show that GBRUN outperforms other algorithms in terms of classification accuracy and the number of selected features. Additionally, the GBRUN algorithm is combined with EfficientNet for COVID-19 CT image classification, achieving better results in terms of accuracy, recall, precision, F1-score, AUC, and ROC. The paper concludes by highlighting the effectiveness of GBRUN in FS and its potential for real-world applications.