Gray model (GM(1,1,λ)) based on genetic algorithm

The Gray Model (GM(1,1)) has been improved with the difference scheme and a new Gray Model GM(1,1,λ) has been constructed in this paper. If λ=0.5 the model GM(1,1,λ) is the model GM(1,1).Because of the nonlinear traits between parameter λ and the errors of forecasting and nondifferentiability of object functions, the traditional optimal methods can not solve it. So the Genetic Algorithm has been applied to solving the value of λ and the prime data are forecasted according to λ. In fact, from the value of λ, a conclusion can be drawn that the accuracy of GM(1,1,λ) is much higher than that of the GM(1,1). Some practical examples show the effect of the method is remarkable.