Optimization of GM (1,1) Model Based on Bilevel Programming

Abstract

GM (1, 1) is a biased grey exponential model, whose accuracy depends on the structure of background values and the selection of original conditions. Current literatures optimized GM (1, 1) models just by optimizing background values or original conditions separately, or by combining them jointly. However, these methods all ignored the accumulative errors between the optimization of background value and the optimization of original condition. Besides, they can not reflect the dynamic characteristics of the data sequence. Considering the accumulation and spread of the error between the optimization of background value and that of original condition, a new optimized model of GM (1, 1) Based on bilevel programming is put forward. The bilevel programming model is set up on the basis of two objective functions which minimize the square sum of relative errors. Various weights are optimized for individual data sequence. Furthermore, a validity analysis method Based on the grey relational degree between simulation data sequence and the original one is introduced. The simulation results show that the proposed model has extremely high fitting accuracy regardless of the scale of development coefficient. Both of approachability and similarity of the simulation data sequence to the original one reach the best.