# Echo State Network Optimization using Hybrid- Structure Based Gravitational Search Algorithm with Square Quadratic Programming for Time Series Prediction

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.

[1] Ahmad Z., Memon M., Memon A, Munshi P., and Memon M., “A New Hybrid Approach of Gravitational Search Algorithm with Spiral- Shaped Mechanism-Based RBF Neural Network,” in Proceeding of the 22nd International Arab Conference on Information Technology, Jordan, pp. 1-6, 2021.

[2] Bedekar P. and Bhide S., “Optimum Coordination of Directional Overcurrent Relays Using the Hybrid GA-NLP approach,” IEEE Transactions on Power Delivery, vol. 26, no. 1, pp. 109-119, 2010.

[3] Fu T., “A Review on Time Series Data Mining,” Engineering Applications of Artificial Intelligence, vol. 24, no. 1, pp. 164-181, 2011.

[4] Hornik K., Stinchcombe M., and White H., “Multilayer Feedforward Networks Are Universal Approximators,”Neural Networks, vol. 2, no. 5, pp. 359-366, 1989.

[5] Jaeger H. and Haas H., “Harnessing Nonlinearity: Predicting Chaotic Systems and Saving Energy in Wireless Communication,” Science, vol. 403, no. 5667, pp. 78-80, 2004.

[6] Kobialka H. and Kayani U., “Echo State Networks With Sparse Output Connections,” in Proceeding of the International Conference on Artificial Neural Networks, Berlin, pp. 356-361, 2010.

[7] Kumar Y., Verma S., and Sharma S., “Multi-Pose Facial Expression Recognition Using Hybrid Deep Learning Model With Improved Variant of Gravitational Search Algorithm,” The (23) ( x y)dxadi dybx y xzdi dzxy czdi Echo State Network Optimization using Hybrid-Structure Based Gravitational Search ... 535 International Arab Journal of Information Technology, vol. 19, no. 2, pp. 281-287, 2022.

[8] Liu J., Sun T., Luo Y., Fu Q., Cao Y., Zhai J, and Ding X., “Financial Data Forecasting Using Optimized Echo State Network,” in Proceeding of the International Conference on Neural Information Processing, Bangkok, pp. 138-149, 2018.

[9] Lorenz E., “Deterministic Nonperiodic Flow,” Journal of Atmospheric Sciences, vol. 20, no. 2, pp. 130-141, 1963.

[10] Lv S., Peng L, and Wang L., “Stacked Autoencoder With Echo-State Regression for Tourism Demand Forecasting Using Search Query Data,” Applied Soft Computing, vol. 73, pp. 119-133, 2018.

[11] Memon M., He J, Lu Y., Zhu N., and Memon A., “An Improvised Sub-Document Based Framework for Efficient Document Clustering,” Journal of Internet Technology, vol. 20, no. 4, pp. 1191-1203, 2019.

[12] Memon M., Qu S., Lu Y., Memon A., and Memon A., “An Ensemble Classification Approach Using Improvised Attribute Selection,” in Proceeding of the 22nd International Arab Conference on Information Technology, Jordan, pp. 1-5, 2021.

[13] Memon M., Lu Y., Chen P., Memon A., Pathan M., and Zardari Z., “An Ensemble Clustering Approach for Topic Discovery Using Implicit Text Segmentation,” Journal of Information Science, vol. 47, no. 4, pp. 431-457, 2021.

[14] Peng H., Wu S., Wei C., and Lee S., “Time Series Forecasting With A Neuro-Fuzzy Modeling Scheme,” Applied Soft Computing, vol. 32, pp. 481-493, 2015.

[15] Wang L., Hu H., Liu R., and Zhou X., “An Improved Differential Harmony Search Algorithm for Function Optimization Problems." Soft Computing, vol. 23, no. 13, pp. 4827-4852, 2019.

[16] Wang L., Lv S., and Zeng Y., “Effective Sparse Adaboost Method With ESN and FOA for Industrial Electricity Consumption Forecasting in China,” Energy, vol. 155, pp. 1013-1031, 2018.

[17] Zhou H. and Qiao J., “Soft Sensing of Effluent Ammonia Nitrogen Using Rule Automatic Formation-Based Adaptive Fuzzy Neural Network,” Desalination and Water Treatment, vol. 140, pp. 132-142, 2019.