基于遗传算法估计灰色模型中的参数

Estimation of grey model parameter based on genetic algorithm

研究表明,GM(1,1)模型中的背景值参数λ和边值对模型的预测精度均有影响,进而分别以平均相对误差达到最小或最大相对误差达到最小为极小化准则,提出了基于遗传算法求解最佳背景值参数λ和最佳边值修正项ε的方法,并且可以确保在相应的模型检验准则下预测的误差达到最小.数值结果表明,采用遗传算法确定最佳的λ、ε可大大地提高模型的预测精度.

Research by this paper indicates that both the background value parameter λ and the boundary condition of GM（1,1 ） model have an effect on model prediction accuracy, then presents a method of achieving an optimal background value parmneterand λ and an optimal boundary improvement condition ε based on genetic algorithm, in order to minimize the average relative error criterion or to minimize the maximum relative error criterion, respectively. This method also ensures the smallest prediction error under corresponding model test criterion. The calculation results show that optimal λ and ε obtained by genetic algorithm can greatly improve the model prediction accuracy.