Fuzzy Echo State Neural Network with Differential Evolution Framework for Time Series Forecasting

In this paper, differential evolution (DE) is used to find optimal weights for echo state neural network model and also to optimize the number of rules of the modeled fuzzy system that presents the input to the echo state neural network (ESNN) model. ESNN designed in this work possess a recurrent neuronal infra-structure called as reservoir. This work aims to develop a good reservoir for the ESNN model employing the coherent features and the ability of the differential evolution algorithm and fuzzy rule base system. DE aims to pre-train the fixed weight values of the network with its effective exploration and exploitation capability and fuzzy rule base system (FRBS) formulates a set of rules, which provides inferences for the inputs presented to the echo state network model. The performance of the developed optimized network is evaluated based on the error metrics and the computational time incurred for the training of the model. The test results of ESNN model using DE and FRBS are compared with that of ESNN without optimization and fuzzy rule to prove its validity and also with the related existing techniques. The perceived DE based fuzzy ESNN model is verified for its effectiveness with a set of time series forecasting benchmark problems. The empirical results prove the superiority and the effectiveness of the DE based fuzzy ESNN learning outcomes.