CM（1,1）模型一般以模型还原值与实际值平均相对误差检验模型的模拟精度。本文以模型还原值与实际值平均相对误差最小化为目标函数将CM（1,1）模型转化成一个不用进行灰微分方程参数辨识的优化模型，称之为改进的GM（1,1）模型，简称IGM（1,1）。IGM（1,1）避开了灰微分方程参数辨识时传统的优化无法求解，本文针对IGM（1,1）模型的直接建模。由于IGM（1,1）目标函数非连续，不可导，用传统的优化无法求解，本文针对IGM（1,1）模型的模拟特性设计了求解该优化模型的遗传算法并进行了算例验证，秋解结果表明了IGM（1,1）模型IGM（1,1）模型。

Generally GM (1,1) model takes the average relative error between restored value of the model and real value as the criterion to evaluate the simulation precision. In this paper, GM (1,1) model was converted to an optimization model, which doesn't need to identify the parameters of grey differential equation, using the average relative error between restored value of the model and real value as objective function. The model was called Improve GM (1,1) model, IGM (1,1) for short. IGM (1,1) avoids the problem how to rationally select background values in parameter identification of grey differ-'ential equation and realize the direct modeling of GM (1,1). The object function of IGM(1,1) is unable to be gained by classical optimization approaches due to its discontinuousness arid non-differentiability. We design a genetic algorithm for IGM (1,1) based on its characteristics and test the algorithm with an example. The result acquired shows that the simulation precision of IGM (1,1) model is much higher than that of GM(1,1) mode.