GM(1,1)模型初始条件和初始点的优化

在对GM(1,1)模型的初始条件进行优化时,由于优化的目标函数为误差平方和最小,而模型的检验标准为平均相对误差最小,两个准则的不一致性导致优化效果不理想.本文以相对误差平方和最小为目标优化GM(1,1)模型,分别对初始条件和初始点进行优化,给出优化的计算公式,并证明在原始序列相对误差平方和最小的准则下,初始条件优化和初始点优化是统一的.实例表明运用优化公式与数值最优解计算得到的模型平均相对误差非常接近,且运用优化公式比数值解求解更方便.

Optimizing the initial condition and the initial point of GM(1,1)

In view of the problem of optimizing the initial value in GM(1,1) model, as criterion of the objective function with the minimum of the square sum of the error and the model test with the minimum of average relative error is inconsistency, leads to the optimization effect is not very good. In this paper, optimizing the GM(1,1) model with the minimum of the square sum of the relative error as the target, respectively optimizing the initial condition and the initial point, the algorithm of optimize formula is given. It proved that under the criterion of minimum the square sum of the relative error in original sequence, the initial conditions optimization and the initial point optimization are unified. Examples show that the results of average relative error calculated by optimizing formula is in close proximity to the numerical solutions. Using the optimization formula to calculating is more convenient than the numerical solution.