These models account for the spatial effects resulting from the proximity of events. A compromise exists in the mathematical accuracy of model parameters when spatial correlations are present in the data of the phenomenon. Data reliant on spatial correlations are crucial in statistical modelling, especially in environmental science, economics, epidemiology, and various other disciplines.

This study employs and compares three artificial intelligence approaches—the genetic algorithm (GA), the TABU search algorithm (TSA), and the binary firefly algorithm (Binary FFA)—to determine which is the most efficient for estimating the parametric regression function for spatially dependent data.

The Mean Absolute Percentage Error numbers derived from the simulation demonstrated that the Binary FFA method yielded the most accurate estimations. This illustrates the superiority of the algorithm compared to conventional methods, as well as Genetic Algorithms (GA) and Tabu Search Algorithms (TSA), in environmental assessments (particularly, water pollution in the Euphrates River) and the estimation of regression models for geographically dependent data.

The regression parameter analysis for spatially dependent environmental data about Euphrates River pollution indicates that the temperature variablity exerted little influence on total dissolved salts. Conversely, the variables calcium (Ca), magnesium (Mg), and potassium (K) exhibited a significant and advantageous influence on total dissolved salts. In contrast, the variable sodium (Na) displayed a distinctly detrimental effect simultaneously.