Direct Modeling Improved GM (1,1) Model IGM (1,1) by Genetic Algorithm
基于遗传算法的改进的GM(1,1)模型IGM(1,1)直接建模

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 differential 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 and 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.