Designing dilation-erosion perceptrons with differential evolutionary learning for air pressure forecasting

The dilation-erosion perceptron (DEP) is a class of hybrid artificial neurons based on framework of mathematical morphology (MM) with algebraic foundations in the complete lattice theory (CLT). A drawback arises from the gradient estimation of dilation and erosion operators into classical gradient-based learning process of the DEP model, since they are not differentiable of usual way. In this sense, we present a differential evolutionary learning process, called DEP(MDE), using a modified differential evolution (MDE) to design the DEP model for air pressure forecasting. Also, we have included an additional step into learning process, called automatic phase fix procedure (APFP), to eliminate time phase distortions observed in some forecasting problems. Furthermore, an experimental analysis is presented using two complex time series, where five well-known performance metrics and an evaluation function are used to assess forecasting performance.