Particle Swarm optimization based Neural Network Model for Chaotic Time Series Forecasting

Abstract

Training model weight is a challenging research topics in the field of chaotic time series modeling and analysis, and intelligent optimization algorithm provides an effective solution to this kind of problem. Aiming at the nonlinear characteristics of dynamic systems, this paper proposes an improved particle swarm optimization (IPSO) based neural network to forecast the chaotic time series. The novel particle swarm optimization (PSO) algorithm is used to optimize the output weight matrix of a neural network, and the hybrid model is available for the chaotic time series modeling process. To enhance the generalization ability and prevent over-fitting, the objective function of this paper is the weighted sum of the L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> norm of the loss function and the L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> norm of the output weights. Our work improves the original PSO algorithm by improving the initialization strategy of the population. Furthermore, some new strategies are proposed to disturb the population, which can increase population diversity and enhance search performance. To verify the efficiency, we evaluate the IPSO based forecasting model with some other intelligent optimization algorithm based models. And simulations show the IPSO based model achieves the highest forecasting accuracy on both Lorenz data and Beijing air quality index data, which testifies the validity of the proposed model in chaotic time series forecasting.