Energy demand prediction is an important problem whose solution is evaluated by policy makers in order to take key decisions affecting the economy of a country. A number of previous approaches to improve the quality of this estimation have been proposed in the last decade, the majority of them applying different machine learning techniques. In this paper, the performance of a robust hybrid approach, composed of a Variable Neighborhood Search algorithm and a new class of neural network called Extreme Learning Machine, is discussed. The Variable Neighborhood Search algorithm is focused on obtaining the most relevant features among the set of initial ones, by including an exponential prediction model. While previous approaches consider that the number of macroeconomic variables used for prediction is a parameter of the algorithm (i.e., it is fixed a priori), the proposed Variable Neighborhood Search method optimizes both: the number of variables and the best ones. After this first step of feature selection, an Extreme Learning Machine network is applied to obtain the final energy demand prediction. Experiments in a real case of energy demand estimation in Spain show the excellent performance of the proposed approach. In particular, the whole method obtains an estimation of the energy demand with an error lower than 2%, even when considering the crisis years, which are a real challenge. (C) 2016 Elsevier Ltd. All rights reserved.