Research And Application Of Numerical Optimization Algorithm For GM(1,1) Model

The grey system theory takes the “small sample” and “poor information” uncertain systems with “partial information known and partial information unknown” as the main points of inquiry.Compared with other methods for solving uncertain problems such as probability statistics and fuzzy mathematics,it is a new historical leap.As the most widely used component of grey system theory,the grey prediction theory predicts the future behavior trend of the system by mining the inherent evolution law of the system.The grey GM(1,1)model is the core of the grey prediction model and the basis of many grey prediction models.Although a large number of successful examples show the superiority of the grey GM(1,1)model in prediction,the model also has defects and causes some cases where the prediction error is too large.Therefore,it is very important to optimize the GM(1,1)model.First of all,based on the cause of the error in the background value construction formula,the third and fourth order Newton-Cotes quadrature formulas in numerical integration are used to reconstruct the background value in combination with the grey dynamic sequence model,and two improved models,namely NC-3-GM(1,1)and NC-4-GM(1,1)models,are established.Then,the applicable scopes of the two models are analyzed in line with the different values of the development coefficient.Secondly,the improved model,namely S-R-GM(1,1)model,in which parameter identification of GM(1,1)model is optimized by the Simpson formula based fourth order Runge-Kutta method,is proposed,and is analyzed and compared with the GM(1,1)model optimized by improved eulerian method in applicable scope.On this basis,the parameter solving method of GM(1,1)model is improved by using the explicit and implicit formulas of the third order,fifth order and sixth order Adams,and the differences of the application scopes of the six optimization methods are discussed and analyzed.In addition,this paper selects five sets of real data from the National Database,and uses the above nine optimization methods for data prediction and error analysis,which verifies the feasibility,universality,accuracy and efficiency of the optimization method.