基于离散灰色模型的优化方法研究

为了改进离散灰色模型的预测精度,对离散灰色模型进行了修正,建立了离散灰色优化模型。离散灰色优化模型的核心在于对1阶累加生成序列(first order-accumulating generator operator(1-AGO)sequence)的平移变换。其中,最佳平移值可以通过最优化方法得到。算例的对比结果显示,DGOM(1,1)模型的模拟精度高于DGM(1,1)模型的模拟精度。进一步的研究表明,将DGOM(1,1)模型与其他优化模型相结合,可以使模型的模拟精度更高。文中讨论了DGOM(1,1)模型的特征,包括平移变换提升模拟精度的机理、DGOM(1,1)模型与其他优化模型之间的关系等。工作丰富了灰色预测理论,并且提出了一些新的灰色预测模型。

Study of Optimization Method Based on Discrete Grey Model

In order to improve the forecasting precision of discrete grey model (DGM), a new modified DGM(1,1) model called discrete grey optimization model (DGOM) is created. The key of this model is a parallel transformation which is applied to the first order-accumulating generator operator (1-AGO) sequence. And the optimal parallel value c can be obtained based on the optimization method. The contrasted result of a numerical example shows that DGOM(1,1) yields a more accurate prediction capability than DGM(1,1) does. Integrating with other improved models such as optimized starting-point fixed discrete grey model and residual modified model, DGOM(1,1) can be characterized by even more accurate prediction for the grey modeling. Moreover, the mechanism of the parallel transformation to improve the forecasting precision and the relationship between DGOM(1,1) and another optimization of DGM are also discussed to demonstrate the characteristics of DGOM(1,1) more clearly. This work contributes significantly to improve grey forecasting theory and proposes more novel grey forecasting models.