Optimization Research And Application Of Grey System Theory Dynamic Model GM(1,1)

The gray system theory is proposed on the uncertainty problem with noexperience and less data. Gray model GM （1,1） is the most widely used dynamicmodel of the gray system theory and can be used for the prediction of the dominantfactor in the complex things, Currently scholars mainly concentrated in the initialseries of processing, the background value of the improvements, as well as graycountdown.This paper researches Optimization and Application of GM （1,1） and gives twoeffective optimization method. One way is to Optimize the gray theory dynamic modelby designing rational gray action and another way is to design new algorithms-thehybrid genetic algorithm, and estimate parameter of gray model GM （1,1）.Firstly, Optimize the gray theory dynamic model by replacing the gray actionb withb₁+kb₂and demonstrate the reasonable of a new method by solving thealbino equation of GM （1,1） model. Gives Reasonable proof of the processing of theraw data and Provides an effective method for the data processing of the belowexamples.Secondly，In allusion to that the basic genetic algorithm can easily fall into localoptimal solution and its late local poor shortcomings, but the hybrid genetic algorithmcan overcome this. This paper presents a hybrid genetic algorithm with a local searchtechnique, a local search technology into the genetic algorithm. The basic geneticalgorithm and with hybrid genetic algorithm to the numerical results shows that thealgorithm has high efficiency. Estimation parameter of gray model GM （1,1） byhybrid genetic algorithm. After taking example, it shows the proposed hybridalgorithm has a good performance.Finally, In order to improve the prediction accuracy, this paper presents thecombined model. On the basis of the ARIMA model, exponential smoothing modeland GM（1,1） model, we can give each single model different weight coefficient byusing the method of taking the variance of the reciprocal to create a combinationmodel, and verified the its superiority through numerical example.