Study of the generalized discrete grey polynomial model based on the quantum genetic algorithm

Abstract

The discrete grey model is increasingly used in various real-world forecasting problems, however, in the modeling procedure, neglecting the effect of the time power and requiring the integer-order accumulation impair the prediction performance to some extent. Considering this fact, this paper implements the fractional accumulating generation operator and time power term in the discrete grey polynomial model, and as a consequence, a generalized discrete grey polynomial model, namely GDGMP(1,1,N,α), is proposed. To further improve the prediction accuracy, a metaheuristic algorithm, namely the quantum genetic algorithm (QGA), is applied to determine the emerging coefficients. In the presence of alternate emerging coefficients, the GDGMP(1,1,N,α) model is compatible with other existing grey models. To demonstrate the effectiveness of the newly proposed model, this model is employed to forecast three real cases (i.e., natural gas consumption, electricity consumption, and elderly population) by comparing it with other benchmark models. The experimental results show that among these competitive models, the proposed model achieves the best prediction performance, and its MAPE (often referred to as the core indicator) for natural gas consumption, electricity consumption, and the elderly population achieves values of 6.05%, 3.22%, and 0.66%, respectively, which are all lower than those of the other models, indicating that the proposed model outperforms other benchmarks.