基于灰色关联度的组合优化模型研究
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摘要
灰色系统理论在处理"小样本、贫信息"不确定性系统方面取得了广泛应用。为进一步提高GM(1,1)模型的预测精度,文章基于数据维度、初始值及原始数据三个影响因素角度构建了等维信息GM(1,1)模型、初始改进GM(1,1)模型和拟合模型,运用灰色关联分析对三个模型的权重进行设置,在此基础上形成基于灰色关联度分析的组合预测模型,最后将该模型应用到江西省GDP预测研究中。结果表明,灰色关联度分析的赋权方法是科学有效的,在不同时期组合优化使用不同的模型有助于整体上的预测精度提高。
Grey system theory has been widely used in dealing with uncertainty system with small samples and poor information. In order to further improve the prediction accuracy of GM(1,1) model, this paper constructs the GM(1,1) model with equal dimensional information, the initial modified GM(1,1) model and the fitting model based on the three influencing factors of data dimension, initial value and original data. Then the paper uses grey relational analysis method to set the weight of the three models,on the basis of which to form a combined prediction model based on grey relational analysis. Finally the newly formed model is applied to the GDP forecast of Jiangxi Province. The results show that the weighting method of grey relational degree analysis is scientific and effective, and that using different models in different periods of combinatorial optimization helps to improve the overall prediction accuracy.
Grey system theory has been widely used in dealing with uncertainty system with small samples and poor information. In order to further improve the prediction accuracy of GM(1,1) model, this paper constructs the GM(1,1) model with equal dimensional information, the initial modified GM(1,1) model and the fitting model based on the three influencing factors of data dimension, initial value and original data. Then the paper uses grey relational analysis method to set the weight of the three models,on the basis of which to form a combined prediction model based on grey relational analysis. Finally the newly formed model is applied to the GDP forecast of Jiangxi Province. The results show that the weighting method of grey relational degree analysis is scientific and effective, and that using different models in different periods of combinatorial optimization helps to improve the overall prediction accuracy.
引文
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[2]邓聚龙,灰色预测与决策[M].武汉:华中理工大学出版社,1988.
[3]刘思峰,曾波,刘解放等.GM(1,1)模型的几种基本形式及其适用范围研究[J].系统工程与电子技术,2014,36(3).
[4]王晓佳,杨善林.基于组合插值的GM(1,1)模型预测方法的改进与应用[J].中国管理科学,2012,20(2).
[5]张怡,魏勇,熊常伟.灰色模型GM(1,1)的一种新优化方法[J].系统工程理论与实践,2007,(4).
[6]罗党,刘思峰,党耀国.灰色模型GM(1,1)优化[J].中国工程科学,2003,(8).
[7]党耀国,刘思峰,刘斌.以x(1)(n)为初始条件的GM模型[J].中国管理科学,2005,13(1).
[8]姚天祥,顾红,高红.新型变权弱化缓冲算子的构造及其应用[J].统计与决策,2013,(22).
[9]吴利丰,刘思峰,刘健.灰色GM(1,1)分数阶累积模型及其稳定性[J].控制与决策,2014,29(5).
[10]郭学军,盖晓华.第三产业发展预测的等维新息模型[J].统计与决策,2004,(8).
[11]李伟,袁亚南,牛东晓.基于缓冲算子和时间响应函数优化灰色模型的中长期负荷预测[J].电力系统保护与控制,2011,39(10).
[12]张彬,西桂权.基于背景值和边值修正的GM(1,1)模型优化[J].系统工程理论与实践,2013,33(3).
[13]周秀文.灰色关联度的研究与应用[D].长春:吉林大学学位论文,2007.
[14]Zeng B,Li C.Forecasting the Natural Gas Demand in China Using aSelf-adapting Intelligent Grey Model[J].Energy,2016,112(1).
[15]Zeng B, Luo C M, Liu S F, et al.A Novel Multi-variable Grey Forecasting Model and Its Application in Forecasting the Amount of Motor Vehicles in Beijing[J].Computers&Industrial Engineering,2016,101(6).
[16]Zeng B.Forecasting the Relation of Supply and Demand of Natural Gas in China During 2015-2020 Using a Novel Grey Model[J].Energy,2017,32(1).
[17]李培培.曲线造型中关于拟合、参数化及形状优化问题的研究[D].济南:山东大学学位论文,2012.
[18]Wang Q, Li C, Cui J J, et al.Application Research of the Polynomial Fitting Model in Transformation of Plane Rectangular Coordinate[J].Applied Mechanics and Materials,2014,57(1572).
[19]孙玉刚.灰色关联分析及其应用的研究[D].南京:南京航空航天大学学位论文,2007.
[20]Wang T,Tang Z.Course Evaluation Model and Its Application Based on Grey Correlation Analysis Method[J].Advanced Engineering Forum,2012,2078(6).
[21]Liu L L.Grey Correlation Analysis on Collaboration Client Evaluation in Supply Network[J].Applied Mechanics and Materials, 2014,3066(539).
[22]陈启明,赵明华.基于灰色关联度的优性组合预测模型存在性及赋权方法[J].统计与决策,2011,(24).
[23]杜红伟,郑笑平,陈兵.基于等维新息GM(1,1)的郑州市需水量预测[J].人民黄河,2009,31(1).
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