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In the context of forecasting for renewable energy, it is common to produce point forecasts but it is also important to have information about the uncertainty of the forecast. To this extent, instead of providing a single measure for the prediction, lower and upper bound for the expected value for the solar radiation are used (prediction interval). This estimation of optimal prediction intervals requires the simultaneous optimization of two objective measures: on one hand, it is important that the coverage probability of the interval is as close as possible to a given target value. On the other, in order to bound uncertainty, intervals must be narrow; this means that there is a trade-off between both objectives, as narrow intervals reduce the coverage probability for those solutions, as the actual value of solar radiation is more likely to fall outside the predicted margins. In this work we propose a multi-objective evolutionary approach that is able to optimize both goals simultaneously. The proposal uses neural networks to create complex non-linear models whose outputs are the upper and lower limits of the prediction intervals. Results have been compared with a single-objective optimization of similar neural network architectures and a baseline algorithm (quantile estimation with gradient boosting). Results show that the neural network is able to provide accurate results. Also, the multi-objective approach is able to obtain the best results and has also the advantage that a single run is able to obtain prediction intervals for any target coverage probability. (C) 2017 Elsevier Inc. All rights reserved.
estimation of prediction intervals; neural networks; multi-objective particle swarm optimization; solar energy forecasting