Enhancing Time Series Forecasting with an Optimized Binary Gravitational Search Algorithm for Echo State Networks

The echo state network (ESN) is a cutting-edge reservoir computing technique designed to handle time-dependent data, making it highly effective for addressing time series prediction tasks. ESN inherits the more precise design of standard neural networks and the relatively simple learning process and has a strong computing capacity for solving nonlinear problems. It can disseminate low-dimensional information cues to high-dimensional areas enabling extracting data. However, this study has proven that not all reservoir output dimensions directly impact model generalization. This study desires to enhance the ESN model's generalization abilities by decreasing the redundant reservoir output feature. A remarkable hybrid model is proposed that optimizes the ESN output association through feature selection. This model is called the binary improved gravitational search algorithm (BIGSA) echo state network (BIGSA-ESN). BIGSA's feature selection approach complements the ESN output connection architecture. In this study, evaluation was performed using root mean square error (RMSE). The experimental findings on the Lorenz and Mackey-Glass benchmark time-series datasets demonstrate that the proposed technique outperforms conventional evolutionary methods. Moreover, empirical findings on predicting a significant water quality parameter from the wastewater treatment process (WWTP) dataset demonstrate that the proposed ensemble of BIGSA models performs very well in real-world scenarios.