Abstract The determination of the optimal neural network topology is an important aspect when using neural models. Due to the lack of consistent rules, this is a difficult problem, which is solved in this paper using an evolutionary algorithm namely Differential Evolution. An improved, simple, and flexible self-adaptive variant of Differential Evolution algorithm is proposed and tested. The algorithm included two initialization strategies (normal distribution and normal distribution combined with the opposition based principle) and a modified mutation principle. Because the methodology contains new elements, a specific name has been assigned, SADE-NN-1. In order to determine the most influential inputs of the models, a sensitivity analysis was applied. The case study considered in this work refer to the oxygen mass transfer coefficient in stirred bioreactors in the presence of n-dodecane as oxygen vector. The oxygen transfer in the fermentation broths has a significant influence on the growth of cultivated microorganism, the accurate modeling of this process being an important problem that has to be solved in order to optimize the aerobic fermentation process. The neural networks predicted the mass transfer coefficients with high accuracy, which indicates that the proposed methodology had a good performance. The same methodology, with a few modifications, and with the best neural network models, was used for determining the optimal conditions for which the mass transfer coefficient is maximized. A short review of the differential evolution methodology is realized in the first part of this article, presenting the main characteristics and variants, with advantages and disadvantages, and fitting in the modifications proposed within the existing directions of research.