Time series forecasting (TSF) is an important tool to support decision making (e.g., planning production resources). Artificial neural networks (ANNs) are innate candidates for TSF due to advantages such as nonlinear learning and noise tolerance. However, the search for the best model is a complex task that highly affects the forecasting performance. In this work, we propose two novel evolutionary artificial neural networks (EANNs) approaches for TSF based on an estimation distribution algorithm (EDA) search engine. The first new approach consist of sparsely connected evolutionary ANN (SEANN), which evolves more flexible ANN structures to perform multi-step ahead forecasts. The second one, consists of an automatic Time lag feature selection EANN (TEANN) approach that evolves not only ANN parameters (e.g., input and hidden nodes, training parameters) but also which set of time lags are fed into the forecasting model. Several experiments were held, using a set of six time series, from different real-world domains. Also, two error metrics (i.e., mean squared error and symmetric mean absolute percentage error) were analyzed. The two EANN approaches were compared against a base EANN (with no ANN structure or time lag optimization) and four other methods (autoregressive integrated moving average method, random forest, echo state network and support vector machine). Overall, the proposed SEANN and TEANN methods obtained the best forecasting results. Moreover, they favor simpler neural network models, thus requiring less computational effort when compared with the base EANN. 
Evolutionary optimization of sparsely connected and time-lagged neural networks for time series forecasting