The present study first of all concerns the first and second law analyzes of an electrically conducting fluid past a rotating disk in the presence of a uniform vertical magnetic field, analytically via Homotopy Analysis Method (HAM), and then applies Artificial Neural Network (ANN) and Particle Swarm Optimization (PSO) algorithm in order to minimize the entropy generation. In the first part of this study, entropy generation equation is derived as a function of velocity and temperature gradients and non-dimensionalized using geometrical and physical flow field-dependent parameters. A very good agreement can be seen between some of the obtained results of the current study and the results of the previously published data. The effects of physical flow parameters such as magnetic interaction parameter, unsteadiness parameter, disk stretching parameter, Prandtl number, Reynolds number and Brinkman number on all fluid velocity components, temperature distribution and the averaged entropy generation number are checked and analyzed. For minimizing the entropy generation value a procedure based on ANN and PSO is proposed. This procedure comprises three steps. The first step is to find entropy generation for values of some different affecting factors. In the second step, some distinct multi-layer perceptron ANNs based on the data obtained from step one are trained. In step three, PSO is used to minimize the entropy generation in the considered stretchable rotating disk. (C) 2013 Elsevier Ltd. All rights reserved.