Cooperative co-evolution deep echo state network for time series prediction

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Abstract The deep echo state network demonstrates strong predictive performance in time series tasks, but inter-layer weight optimization and reservoir structure design are still challenging tasks. To address this, we propose the cooperative co-evolution deep echo state network (CCEDESN). Firstly, inspired by the hierarchical structure of the brain, we introduce a modular hierarchical design. Each layer of the reservoir contains multiple sub-reservoirs, with central neurons in each sub-reservoir interacting with those in other sub-reservoirs to enhance information processing. Secondly, an advanced cooperative co-evolution algorithm is proposed to simultaneously optimize the layer connection weights and (hyper)parameters of the deep echo state network. We evaluate the CCEDESN model on the Mackey-Glass system, Sunspot data, and Apple stock opening prices. The experimental results show that the CCEDESN model achieves superior prediction accuracy compared to other models.