广义累加灰色预测控制模型的性质及优化

对广义累加灰色预测控制模型进行了深入研究，发现该模型实际上是GM（1，1）模型、阶段模型、跳跃模型、非等间隔模型等的统一形式；然后研究了初始点的变化对模型参数及预测值的影响，利用矩阵分析推导了它们之间的数量关系；提出了利用广义累加生成矩阵中元素的优化、初始点的优化、初始条件选取的优化对广义累加灰色预测控制模型进行组合优化的方法. 最后利用经典的“电视机销售问题”进行了实例分析，验证了组合优化方法的有效性.

Properties and optimization of generalized accumulation grey model

Through the in-depth study of generalized accumulation grey model, it is found that the model actually is an uniform for GM(1,1) model (grey model), stage model, jump model and non-equidistance model. Then we research the influence of the parameters and the forecasting value on changing the initial point, the quantitative relationship between changed and before is deduced by matrix analysis. What's more, an optimization method for generalized accumulation grey model is proposed by combining the optimization of generalized accumulated generating matrix, the optimization of initial point and the optimization of the initial condition selection. Finally, an empirical study, the classic "TV sales problem", is investigated, it is certified that the combined optimization method is effective.