Multi-objective evolutionary optimization of prediction intervals for solar energy forecasting with neural networks

Abstract

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 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.

Improving Prediction Intervals Using Measured Solar Power with a Multi-Objective Approach

“…The following section describes the multi-objective particle swarm optimization algorithm (MOPSO) applied to PI, originally reported in [21]. This application was inspired by LUBE [16], which used an artificial neural network (ANN) with a single hidden layer to make an estimation of the lower and upper bounds of the PIs.…”

“…LUBE can also be addressed as an actual multi-objective approach that does not require goal weighting. This was the approach proposed by the authors in a previous work [21], where a multi-objective particle swarm optimization evolutionary algorithm (MOPSO) showed very good performance in a solar energy production forecasting problem on Oklahoma solar sites [22], where only meteorological forecasts were used as input. An important advantage of using a multi-objective algorithm is that in a single run the method is able to return a whole set of solutions (Pareto front), which represent the best trade-offs between coverage and width, out of which the user can select a solution for some particular coverage.…”

“…Thus, the main contributions of this article are to study both the degree of improvement of PIs when using measured information and the dependency of that improvement on the prediction horizon. We used the LUBE approach optimized with MOPSO [21]. The MOPSO approach has already been used for estimating PIs for the aggregated daily energy production forecast for next day [21].…”

“…We used the LUBE approach optimized with MOPSO [21]. The MOPSO approach has already been used for estimating PIs for the aggregated daily energy production forecast for next day [21]. However, in the context of solar forecasting, it is also important to provide uncertainty forecasts for intra-day horizons, which is what we do in the current work.…”

HDI-Forest: Highest Density Interval Regression Forest

“…This motivates the development of quality-based PI elicitation principle, which seeks the shortest PI that contains the required amount of probability [Pearce et al, 2018]. So far, quality-based PI estimation has been applied to solve many practical problems, such as the predictions of electronic price [Shrivastava et al, 2015], wind speed [Lian et al, 2016], and solar energy [Galván et al, 2017], etc.…”