Load forecasting impacts directly financial returns and information in electrical systems planning. A promising approach to load forecasting is the Echo State Network (ESN), a recurrent neural network for the processing of temporal dependencies. The low computational cost and powerful performance of ESN make it widely used in a range of applications including forecasting tasks and nonlinear modeling. This paper presents a Bayesian optimization algorithm (BOA) of ESN hyperparameters in load forecasting with its main contributions including helping the selection of optimization algorithms for tuning ESN to solve real-world forecasting problems, as well as the evaluation of the performance of Bayesian optimization with different acquisition function settings. For this purpose, the ESN hyperparameters were set as variables to be optimized. Then, the adopted BOA employs a probabilist model using Gaussian process to find the best set of ESN hyperparameters using three different options of acquisition function and a surrogate utility function. Finally, the optimized hyperparameters are used by the ESN for predictions. Two datasets have been used to test the effectiveness of the proposed forecasting ESN model using BOA approaches, one from Poland and another from Brazil. The results of optimization statistics, convergence curves, execution time profile, and the hyperparameters’ best solution frequencies indicate that each problem requires a different setting for the BOA. Simulation results are promising in terms of short-term load forecasting quality and low error predictions may be achieved, given the correct options settings are used. Furthermore, since there is not an optimal global optimization solution known for real-world problems, correlations among certain values of hyperparameters are useful to guide the selection of such a solution.
Epidemiological time series forecasting plays an important role in health public system, since it allows managers to develop strategic planning to avoid possible epidemics. In this aspect, a hybrid approach is developed to forecast confirmed cases of megingitis in the Para, Parana and Santa Catarina states, Brazil. In this case, ensemble empirical mode decomposition (EEMD) is applied to decompose the original signal, quantile random forests (QRF) is adopted to forecast each component obtained in decomposition stage and multi-objective optimization (MOO) is used to reconstruct the final forecasting. To assess the performance of adopted methodology, comparisons are conducted with approach that considers to reconstruct the signal by simple sum (EEMD-QRF) and QRF without decomposition. In this context criteria such as mean squared error, symmetric mean absolute percentage error and coefficient of determination as well as statistical tests are adopted. As results, EEMD-QRF-MOO reached lower errors and better coefficient of determination in most of the cases. Indeed, the EEMD-QRF-MOO and EEMD-QRF squared errors are statistical equals, and lower than QRF squared errors. With these results it is conclude that using decomposition technique combined with machine learning models and optimization approach can be adopted to enhance the model performance, whose results may be used to perform accurate forecasting.
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