灰色Verhulst模型的改进及其应用

Improvement of Grey Verhulst Model and Application

针对灰色Verhulst模型的不足,讨论了灰色Verhulst模型的参数优化问题.首先,利用最小二乘原理给出了一种初值优化的改进模型.其次,在平均相对误差最小准则下,将Verhulst模型的参数优化转化为线性规划问题,然后利用粒子群优化算法估计Verhulst模型中的参数,得到另外一种改进模型.最后,给出了一个仿真实例,结果表明灰色Verhulst模型的改进方法是可行的和有效的,而且具有较高的拟合和预测精度.

Based on deficiency of traditional grey verhulst,the parameter optimum of grey verhulst model are discussed.Firstly,an initial value improvement model is established using the least square criteria.Secondly,under the minimizing the average relative error criterion, the parameter optimum of grey verhulst model can be transformed to linear programming. The particle swarm optimization algorithm is used to solve the linear programming,then another optimization model of grey verhulst model is obtained.Finally,a simulation example is analyzed.Results show two improvement methods are both feasible and effective,and has high fit and prediction accuracy.