This work performs a comparative analysis between three global optimization methods—Luus-Jaakola, Differential Evolution, and Firefly—applied to four benchmark functions with different levels of complexity and multimodality: a unimodal polynomial function, Rastrigin, Six-Hump Camelback, and Goldstein-Price. Computational routines were developed in Python to implement each algorithm, evaluating their performance in terms of accuracy, robustness, and computational efficiency. The results indicate that the Luus-Jaakola method showed rapid convergence and high accuracy in all tested cases, standing out for its simplicity of implementation........

Keywords: Optimization, Luus-Jaakola, Differencial Evolution, Firefly.

Accurate prediction of drilling Rate of Penetration (ROP), there are opportunities of optimizing drilling performance, reducing non-productive time (NPT), and maintaining operational safety during hydrocarbon exploration. Traditional empirical correlations and mechanistic models, including Bourgoyne-Young and specific energy-based methodologies, offer interpretive ROP estimation solutions though may not easily generalize in heterogeneous formations, dynamic downhole conditions and nonlinear interactions between the drilling parameters........

Keywords: Drilling, Rate of Penetratandion (ROP), Physics-Informed Neural Networks, Machine Learning, Drilling Mechanics, Multivariate Time Series.