Fractional-Order Boosted Jellyfish Search Optimizer with Gaussian Mutation for Income Forecast of Rural Resident

The disposable income of residents can reflect the living standard of people in the area. For government departments, it is necessary to master the trend of rural resident income to formulate corresponding policies benefiting farmers. Thus, this paper proposes a grey model with an improved jellyfish search optimizer to predict the rural resident income in Shaanxi Province. Firstly, by applying fractional-order modified strategy and Gaussian mutation mechanism to the original algorithm, the proposed algorithm shows better performance in solving accuracy, stability, and convergence acceleration when compared with different classical methods on cec2017 and cec2019 test functions. Then, based on the fractional time-delayed grey model, a discrete fractional time-delayed grey model with triangular residual correction (TDFTDGM) is proposed by replacing the derivative with a first-order difference and introducing the triangular residual correction functions. Finally, the improved jellyfish search optimizer is used to explore the optimal order of the TDFTDGM model. The all-around performance of the forecast model is incomparable to additional grey models compared on four measure criteria, which means it is a practical approach for long-term prediction with small samples. Moreover, the forecast data of rural resident income in Shaanxi Province from 2021 to 2025 are given for reference.