Predicting the drill penetration rate is a fundamental requirement in mining operations, profoundly impacting both the cost-effectiveness of mining activities and strategic mine planning. Given the intricate web of factors influencing rotary drilling performance, the necessity for advanced modeling techniques becomes evident. To this end, the hybrid extreme gradient boosting (XGBoost) was utilized to gauge the penetration rate of rotary drilling machines, utilizing random search, grid search, Harris Hawk optimization (HHO), and the dragonfly algorithm (DA) as metaheuristic algorithms. Our research draws from extensive data collected in copper mine case studies, encompassing both field and investigational data. This dataset incorporates critical material properties, such as tensile strength (TS), uniaxial compressive strength (UCS), as well as vital rock-mass characteristics including joint direction (JD), joint spacing (JS), and bit diameter (D). Our investigation evaluates the reliability of these prediction methods using various performance indicators, including mean absolute error (MAE), root mean square error (RMSE), average absolute relative error (AARE), and coefficient of determination (R2). The multivariate analysis reveals that the HHO-XGB model stands out, demonstrating superior prediction accuracy (MAE: 0.457; RMSE: 2.19; AARE: 2.29; R2: 0.993) compared to alternative models. Furthermore, our sensitivity analysis emphasizes the substantial impact of uniaxial compressive strength and tensile strength on the drill penetration rate. This underlines the importance of considering these material properties in mining operations. In conclusion, our research offers robust models for forecasting the penetration rate of similar rock formations, providing invaluable insights that can significantly enhance mining operations and planning processes.