Study On The Optimization Of GM(1,1) Model

GM(1,1) model is one of the important contents in the grey system theory. Because itrequires small sample capacity, and it’s easy to calculate, it is widely used in society,economy, ecological, agriculture and many other prediction and decision making systems.Especially, under the condition of small sample, less information unstable system and datainadequate, it also can get successful results. Thus, it has an important position in theprediction and decision making field.Based on GM(1,1) model, the paper proposed several kinds of extension of the greyprediction model: GOM(1,1) model, grey Verhulst model and GM(1,1)power model andoptimization processing, getting better simulation effect and prediction accuracy improvegreatly, which gives the theoretical support for more extensive application and efficiencyimprovement.Firstly, based on the definition of the GM(1,1) model background value, it launchesthe background value formula generated by the original data, making the simulation andprediction accuracy of the optimized model improve significantly.Secondly, on the analysis of the problems existing in current GOM(1,1) model, thepaper improves the initial condition and the background value and gives the parametersformula with original data, so we can construct a new optimization GOM(1,1) model.Through stimulation data we can know that the simulation and prediction precision ishigher and more stable.Thirdly, through analyzing the problems existing in grey Verhulst model, the papergenerates a new sequence by accumulating the original data sequence. By minimizing theresults that the minus between the accumulating sequence and the simulation sequence, itestablishes an unconstrained optimization model, getting a solution of correction of initialvalue parameter, making the optimized model has higher simulation and predictionaccuracy.Finally, as for the optimization of GM(1,1) power model on initial condition, thispaper puts forward a solution that is based on the linear combination between the first data and the last data of the original sequence and constructs combination the optimizationmodel with the initial condition combination weighting, then gives the method of solvingthe optimal combination weighting, making the application of the GM(1,1) power modelget further promotion.