Chaotic Time Series Prediction using Three-Dimensional FOA and Echo State Network

Chaotic time series prediction is critical in the fields of artificial intelligence. Recently, the Echo State Network (ESN) with nonlinear computing capability has been widely used to perform time series prediction tasks. However, the parameters of ESN are needed to vary to application scenarios and are usually set by human experience, which affects the performance of ESN. In this work, the Three-Dimensional Fruit Fly Optimization Algorithm is proposed to optimize the parameters of ESN (TDFOA-ESN) by adding swarm collaboration and random perturbation. The effectiveness of the proposed algorithm is verified by using benchmark datasets (NARMA and Mackey-Glass) and real-world time series (Beijing PM2.5 Data). In addition, the root mean squared error, normal root mean squared error and determination coefficient are used to evaluate the performance of TDFOA-ESN model. The experiment shows that the normal root mean squared error is reduced by 80.85% compared with other approaches. Therefore, the proposed TDFOA-ESN model provides a beneficial alternative for the time series prediction tasks.