The present work studied the fundamental of polynomial modeling and artificial neural network (ANN) techniques applied to the bioflotation of apatite, calcite and dolomite using the Rhodococcus opacus biosurfactant. Both techniques were used to model the bioflotation process and optimize some bioflotation parameters (pH and biosurfactant concentration). A full quadratic model optimized with genetic algorithm (GA) and a three-layer feedforward neural network were used to describe the mineral recovery. Different training algorithms and activation functions were tested to gather to an ANN with the best generalization capacity. Although the variation of the sigmoid activation function did not lead to a considerable change in the robustness of the ANN, the use of standard numerical training algorithms produced ANN models with better accuracy. ANN models demonstrated higher adequacy to describe and predict the mineral recovery than polynomial models. For all mineral studied, mineral recovery increased for a more acidic medium and for a higher biosurfactant concentration (BC). BC exhibited a higher effect on mineral recovery than pH, showing pH an increasing effect on mineral recovery as the optimal BC values were approached. Rhodococcus opacus biosurfactant demonstrated to be a promising solution for the separation of carbonate gangue minerals from phosphate ores.