Optimizing Neural Network Ensemble for Short-Term Load Forecasting: A Case Study of a Brazilian Electrical Distribution System

This paper proposes a multivariate optimization framework to construct a neural-network ensemble for short-term load forecasting (STLF) at the distribution-substation level. A linear network, multilayer perceptron, and radial basis function network are combined via a {3,5} simplex-lattice mixture design on the probability simplex of ensemble weights. Correlated forecast-error metrics are reduced through factor analysis with principal-component extraction, and the resulting orthogonal factors are jointly optimized using the normal boundary intersection (NBI) method to generate a Pareto frontier of ensemble configurations. To select a single operating point, we adopt an entropy-based decision rule that maximizes the ratio between Shannon entropy of the mixing weights and a global percentage error (GPE) index, thereby balancing forecast accuracy and weight diversification. Tested on hourly load data from four Brazilian distribution substations over 24-, 48-, and 72-step horizons, the proposed ensemble reduces mean absolute percentage error (MAPE) by up to 20% relative to the best individual network, with consistent improvements also observed for RMSE and MAE. These gains are statistically supported by significance tests. The main contributions are: 1) casting ensemble-weight definition as a structured mixture-design problem 2) integrating factor-analysis/PCA with NBI to handle multiple correlated error metrics in a principled way; and 3) introducing an entropy/GPE-based scalarization that yields accurate and robust ensembles suitable for implementation in operational smart-grid STLF workflows.