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

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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.

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Abbreviations

GDGMP(1,1,N,α):

Generalized discrete grey polynomial model

GM(1,1):

Traditional grey model

DGM(1,1):

Discrete grey model

FDGM(1,1):

Fractional discrete grey model

NDGM(1,1):

Nonhomogeneous discrete grey model

FNDGM(1,1):

Fractional nonhomogeneous discrete grey model

FDGM(1,1,Tα):

Fractional discrete grey model with time power term

DGMP(1,1):

Discrete grey polynomial model

FAGM(1,1):

Fractional grey model

OBGM(1,1):

Grey model based on optimization of background value

ARGM(1,1):

Combination of GM(1,1) and ARIMA

FNGM(1,1):

Fractional nonhomogeneous grey model

QGA:

Quantum genetic algorithm

r-FAGO:

R-order accumulating generation operator

MAPE:

Mean absolute percentage error

RMSPE:

Root mean square percentage error

MAE:

Mean absolute error

MSE:

Mean square error

IA:

Index of agreement

R/CC:

Correlation coefficient

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Acknowledgements

This work was supported by the Fundamental Research Funds for the Central Universities of China (2019YBZZ062) and the Postgraduate Research & Practice Innovation Program of Jiangsu Province (KYCX20 1144).

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Authors and Affiliations

  1. School of Science, Inner Mongolia Agricultural University, Hohhot, 010018, China

    Chong Liu

  2. School of Economics and Business Administration, Central China Normal University, Wuhan, 430079, China

    Wen-Ze Wu

  3. Institute of EduInfo Science and Engineering, Nanjing Normal University, Nanjing, 210097, China

    Wanli Xie

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  1. Chong Liu
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  2. Wen-Ze Wu
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Correspondence to Wen-Ze Wu.

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Liu, C., Wu, WZ. & Xie, W. Study of the generalized discrete grey polynomial model based on the quantum genetic algorithm. J Supercomput 77, 11288–11309 (2021). https://doi.org/10.1007/s11227-021-03713-8

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