基于粒子群算法求解GM(1,1)模型参数的研究

Research about Solving GM(1,1) Model Parameters Based on Particle Swarm Algorithm

探讨用粒子群优化算法求解GM(1,1)模型参数a,b,将用该参数建立的GM(1,1)模型与最小二乘法建立的GM(1,1)预测模型进行了效果比较.实例验证结果表明:对于较平缓变化数据序列,2种方法建立的GM(1,1)模型拟合还原精度相差不大,粒子群算法稍优;对于非平缓变化数据序列,经粒子群算法优化参数后,模型精度显著高于最小二乘法;灰色关联度分析表明,粒子群算法优化参数建立的GM(1,1)模型拟合序列几何形状上更接近原始序列.

A new method which is used to solve the parameters of grey GM （1 , 1 ） model parameters a,b based on Particle Swarm Optimization is discussed and the result of the traditional Least Square Method compares with the result of the new GM（ 1,1 ） model with the solved parameters. The test testify result shows that there is little difference of the precisions of model to solving parameters between PSO and LSM for stable data sequence, but the precision of fitting of model to solving parameters based on PSO is much higher than that of LSM for unstable data sequence. In addition, the result of grey correlation analysis also shows that the precision of fitting of model based on PSO is improved.