Estimation of energy demand has important implications for economic and social stability leading to a more secure energy future. One-year-ahead energy demand estimation for Turkey has been proposed in this paper, using the metaheuristics method with GDP, the total population, and the quantities of imports and exports, as inputs variables. The records obtained from historical data were bifurcated into training and test datasets, where the training dataset is used by the algorithm in the process of generating models, while the test dataset was used to evaluate the performance of the algorithm. Here, two particular approaches have been proposed: Grammatical Evolution alone, and an ensemble of Grammatical Evolution with Differential Evolution. Under these four different forms are developed, viz, Grammatical Evolution with a recursive grammar (M1), an ensemble of Grammatical evolution executed on a linear grammar and Differential Evolution (M2), an ensemble of Grammatical evolution executed on a quadratic grammar and Differential Evolution (M3), and, Grammatical Evolution with a recursive grammar and Differential Evolution (M4). Moreover, the present approaches were also compared for estimation accuracy against the previously published DE models. It was substantiated that the M4 proposal exhibited the best performance towards estimation. It is therefore established that the current approach exhibits a better estimation capability (with RMSE of 2.2002), compared to the models previously available in the literature. M4 approach is then employed to predict the future energy demand using the same set of socio-economic inputs and the results demonstrated high prediction accuracy with an RMSE of 2.2278.