The Echo-State Network (ESN) is a robust recurrent neural network and a generalized form of classical neural networks in time-series model designs. ESN inherits a simple approach for training and demonstrates the high computational capability to solve non-linear problems. However, input weights and the reservoir's internal weights are pre-defined when optimizing with only the output weight matrix. This paper proposes a Hybrid Gravitational Search Algorithm (HGSA) to compute ESN output weights. In Gravitational Search Algorithm (GSA), Square Quadratic Programming (SQP) is united as a local search strategy to raise the standard GSA algorithm's efficiency. Later, an HGSA-SQP and the validation data set to establish the relation configuration of the ESN output weights. Experimental results indicate that the proposed configuration of HGSA-SQP- ESN is more efficient than the other conventional models of ESN with the minimum generalization error.

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