基于遗传算法的GM(1,1,λ)模型

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

用差分格式将灰色模型 GM(1,1)模型推广为 GM(1,1,λ)模型 ,λ=0 .5即为 GM(1,1)模型 ;由于参数λ与误差之间存在明显的非线形特性 ,而且某些目标函数不可微 ,使得传统的优化方法无能为力 ,文中应用遗传算法求解最优的 λ值 ,然后进行预测 .由 λ的取值知 ,GM(1,1,λ)模型的预测精度一定比 GM(1,1)高 ,数值计算的结果也证实了这一点 .

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.