优化的GM(1,1)幂模型及其应用

针对GM(1,1)幂模型的幂指数和背景值的优化问题, 首先归纳出GM(1,1)幂模型的建模步骤和传统方法的不足, 然后以平均相对误差最小化为目标、参数之间的关系为约束条件, 构建了两个非线性优化模型, 实现对GM(1,1)幂模型的幂指数和背景值插值系数的优化. 结果表明, 优化的GM(1,1)幂模型使得平均相对误差绝对值在理论上达到最小优化, 解决了传统建模方法与模型检验的脱节问题, 其模拟和预测精度都高于传统模型. 最后, 以我国高中升学率的数据为例验证了本文优化方法的优越性和有效性.

Optimized GM(1,1)power model and its application

As to the optimization of the power exponent and background value in the GM(1,1) power model,this paper summarizes the modeling steps and disadvantages of the traditional method.Two non-linear optimization models are constructed with the objective of minimum average relative error, the constraints of relationships between parameters in order to optimize the power exponent and the background value.The results show that the optimized models make the absolute value of the average relative error smallest in theory.The new method has solved the problem of the inconsistency in grey model testing.Finally,we illustrated the superiority and effectiveness of the new methods with the example of simulating and forecasting the promotion rates from senior secondary schools to higher education in China.