Variogram modelling optimisation using genetic algorithm and machine learning linear regression: application for Sequential Gaussian Simulations mapping

The objective of this study is to develop an advanced approach to variogram modelling by integrating genetic algorithms (GA) with machine learning-based linear regression, aiming to improve the accuracy and efficiency of geostatistical analysis, particularly in mineral exploration. The study combines GA and machine learning to optimise variogram parameters, including range, sill, and nugget, by minimising the root mean square error (RMSE) and maximising the coefficient of determination (R 2 ). The experimental variograms were computed and modelled using theoretical models, followed by optimisation via evolutionary algorithms. The method was applied to gravity data from the Ngoura-Batouri-Kette mining district in Eastern Cameroon, covering 141 data points. Sequential Gaussian Simulations (SGS) were employed for predictive mapping to validate simulated results against true values. Key findings show variograms with ranges between 24.71 km and 49.77 km, optimised RMSE and R 2 values of 11.21 mGal 2 and 0.969, respectively, after 42 generations of GA optimisation. Predictive mapping using SGS demonstrated that simulated values closely matched true values, with the simulated mean at 21.75 mGal compared to the true mean of 25.16 mGal, and variances of 465.70 mGal 2 and 555.28 mGal 2 , respectively. The results confirmed spatial variability and anisotropies in the N170-N210 directions, consistent with prior studies. This work presents a novel integration of GA and machine learning for variogram modelling, offering an automated, efficient approach to parameter estimation. The methodology significantly enhances predictive geostatistical models, contributing to the advancement of mineral exploration and improving the precision and speed of decision-making in the petroleum and mining industries. • Scientific Contribution Clarified: The novelty of integrating Genetic Algorithms with Linear Regression for variogram optimization is now clearly stated in the abstract and introduction, and its advantage over existing methods is discussed in the results and conclusion. • Geostatistical Conventions and Technical Precision Improved: All notations have been corrected following standard practice (e.g., using 'h' for lag distance), and azimuthal references were revised to use the geological standard (0° = North, clockwise). • Algorithm and Implementation Details Added: Binary tournament selection, survival probability for suboptimal individuals, and the method of hyperparameter search are now explicitly described to enhance reproducibility. • Language and Style Enhanced: The manuscript now uses consistent British English, eliminates personal pronouns, and applies a more formal academic tone throughout. • All Line-by-Line Technical Corrections Addressed: Each of the reviewer's line-specific suggestions—spanning from terminology to figures and equations—was implemented, ensuring clarity, accuracy, and consistency across the manuscript.