A Hybrid Model Integrating Variational Mode Decomposition and Intelligent Optimization for Vegetable Price Prediction

In recent years, China’s vegetable market has faced frequent and drastic price fluctuations due to factors such as supply–demand relationships and climate change, which significantly affect government bodies, farmers, consumers, and other participants in the vegetable industry and supply chain. Traditional forecasting methods demonstrate evident limitations in capturing the nonlinear characteristics and complex volatility patterns of price series, underscoring the necessity of developing high-precision prediction models. This study proposes a hybrid forecasting model integrating variational mode decomposition (VMD), the Fruit Fly Optimization Algorithm (FOA), and a gated recurrent unit (GRU). The model employs VMD for multi-scale decomposition of original price series and utilizes the FOA for adaptive optimization of the GRU’s critical parameters, effectively addressing the challenges of high volatility and nonlinearity in agricultural price forecasting. Empirical analysis conducted on daily price data of six major vegetables, specifically, Chinese cabbage, cucumber, beans, tomato, chili, and radish, from 2014 to 2024 reveals that the proposed model significantly outperforms traditional methods, single deep learning models, and other hybrid models in predictive performance. Experimental results indicate substantial improvements in key metrics including the Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and Coefficient of Determination (R 2 ), with R 2 values consistently exceeding 99.4% and achieving over 5% enhancement compared to the baseline GRU model. This research establishes a novel methodological framework for analyzing agricultural price forecasting while providing reliable technical support for market monitoring and policy regulation.