Multi-objective ensembles of echo state networks and extreme learning machines for streamflow series forecasting

Streamflow series forecasting composes a fundamental step in planning electric energy production for hydroelectric plants. In Brazil, such plants produce almost 70% of the total energy. Therefore, it is of great importance to improve the quality of streamflow series forecasting by investigating state-of-the-art time series forecasting algorithms. To this end, this work proposes the development of ensembles of unorganized machines, namely Extreme Learning Machines (ELMs) and Echo State Networks (ESNs). Two primary contributions are proposed: (1) a new training logic for ESNs that enables the application of bootstrap aggregation (bagging); and (2) the employment of multi-objective optimization to select and adjust the weights of the ensemble's base models, taking into account the trade-off between bias and variance. Experiments are conducted on streamflow series data from five real-world Brazilian hydroelectric plants, namely those in Sobradinho, Serra da Mesa, Jirau, Furnas and Agua Vermelha. The statistical results for four different prediction horizons (1, 3, 6, and 12 months ahead) indicate that the ensembles of unorganized machines achieve better results than autoregressive (AR) models in terms of the Nash-Sutcliffe model efficiency coefficient (NSE), root mean squared error (RMSE), coefficient of determination (R-2), and RMSE-observations standard deviation ratio (RSR). In such results, the ensembles with ESNs and the multi-objective optimization design procedure achieve the best scores.