Multi-Objective Gray Wolf Cooperative Optimization of VMD-LSTM Parameters for Load Forecasting and Its Application

Li, Xin; Shi, Yong; Li, Jiawei; Zhang, Tengya; Du, Chao

doi:10.3390/en19010145

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Open AccessArticle

Multi-Objective Gray Wolf Cooperative Optimization of VMD-LSTM Parameters for Load Forecasting and Its Application

by

Xin Li

,

Yong Shi

^*

,

Jiawei Li

,

Tengya Zhang

and

Chao Du

School of Electrical and Control Engineering, Shaanxi University of Science & Technology, Xi’an 710021, China

^*

Author to whom correspondence should be addressed.

Energies 2026, 19(1), 145; https://doi.org/10.3390/en19010145 (registering DOI)

Submission received: 24 November 2025 / Revised: 24 December 2025 / Accepted: 25 December 2025 / Published: 26 December 2025

(This article belongs to the Special Issue Advanced Modeling, Control, and System Design for Next-Generation Electrical Drives)

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Abstract

To address the issue of inaccurate load forecasting affecting the effectiveness of minimum demand scheduling in railway traction stations, this study introduces a multi-objective grey wolf optimizer (MOGWO) to jointly optimize the parameters of variational mode decomposition (VMD) and long short-term memory network (LSTM) within the forecasting framework. The proposed MOGWO-VMD-LSTM model enhances the data decomposition capability of VMD and improves LSTM training, prediction accuracy, and inverse normalization reconstruction. Using a 10-day load dataset from a traction station, the model’s performance is compared against LSTM and VMD-LSTM baselines. Simulation results demonstrate superior performance in terms of mean absolute error (MAE), root mean squared error (RMSE), and mean absolute percentage error (MAPE) metrics. Application of the forecasting results to traction station scheduling reduces the single-peak power purchase from 22.279 MW to 20.052 MW, achieving a 9.995% reduction, indicating strong practical potential.

Keywords: traction station; minimum demand scheduling; load forecasting; multi-objective grey wolf optimizer (MOGWO); peak shaving; microgrid

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MDPI and ACS Style

Li, X.; Shi, Y.; Li, J.; Zhang, T.; Du, C. Multi-Objective Gray Wolf Cooperative Optimization of VMD-LSTM Parameters for Load Forecasting and Its Application. Energies 2026, 19, 145. https://doi.org/10.3390/en19010145

AMA Style

Li X, Shi Y, Li J, Zhang T, Du C. Multi-Objective Gray Wolf Cooperative Optimization of VMD-LSTM Parameters for Load Forecasting and Its Application. Energies. 2026; 19(1):145. https://doi.org/10.3390/en19010145

Chicago/Turabian Style

Li, Xin, Yong Shi, Jiawei Li, Tengya Zhang, and Chao Du. 2026. "Multi-Objective Gray Wolf Cooperative Optimization of VMD-LSTM Parameters for Load Forecasting and Its Application" Energies 19, no. 1: 145. https://doi.org/10.3390/en19010145

APA Style

Li, X., Shi, Y., Li, J., Zhang, T., & Du, C. (2026). Multi-Objective Gray Wolf Cooperative Optimization of VMD-LSTM Parameters for Load Forecasting and Its Application. Energies, 19(1), 145. https://doi.org/10.3390/en19010145

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Multi-Objective Gray Wolf Cooperative Optimization of VMD-LSTM Parameters for Load Forecasting and Its Application

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