An evolutionary features-based neural grey system model and its application

Effectively addressing nonlinear small-sample data has been a critical focus in time-series research. Due to their “black-box” nature and strong reliance on data scale, traditional machine learning models often struggle with such datasets, prompting many studies to adopt neural grey models. However, existing neural grey models frequently suffer from overfitting and limited predictive accuracy. To address these issues, this study integrates the random vector functional link network into grey models for the first time and proposes five evolutionary feature-based training algorithms for the hybrid framework. Through evaluations on five real-world cases using four accuracy metrics, the proposed model which is based on moth-flame optimization algorithm demonstrates superior performance, achieving mean absolute percentage error improvements ranging from 6.5181% to 96.7559% compared to 21 grey models and 15 machine learning models. Additionally, the study reveals that increasing neuron counts and iteration steps enhances model complexity and training time, underscoring the importance of optimizing these parameters for improved performance. This research bridges the gap in random vector functional link network applications for small-sample data and partially alleviates the limitations of neural grey models in terms of overfitting and predictive accuracy.