基于微粒群算法的GM(2,1,λ,ρ)优化模型  

GM(2,1,λ,ρ) based on particle swarm optimization

作　　者：刘虹[1] 张岐山[1] 

机构地区：[1]福州大学机械工程与自动化学院,福州350002

出　　处：《系统工程理论与实践》2008年第10期96-101,共6页Systems Engineering-Theory & Practice

基　　金：国家自然科学基金(70571015);福建省自然科学基金(A0620001)

摘　　要：为了提高灰色GM(2,1)模型的预测精度,本文首先对灰色GM(2,1)模型的向前、向后差分进行线性组合出灰色GM(2,1,λ)模型,利用参数λ修正背景值;然后引入参数ρ对原始数列进行数乘变换,进一步将模型拓展为灰色GM(2,1,λ,ρ)模型.由于参数λ,ρ与误差之间为明显的非线性关系,难以解析,本文基于微粒群算法(PSO),给出PSO-GM(2,1,λ,ρ)优化方法.在该方法中,用λ,ρ构成一个二维的微粒群,以绝对的平均相对误差作适应度函数,以其最小为目标,求解最优的λ,ρ值.实例计算表明,该方法收敛速度快,预测精度高于普通模型,而且可满足实际需要.In order to improve the prediction accuracy, firstly GM （2, 1 ） has been improved with the linear combination of the forward and backward differenee scheme, where the parameter λ has been used to correct the background value; secondly the parameter ρ was used for a multiple transformation on the initial data, a new GM（2, 1,λ, ρ） has been constructed in this paper, Because of the nonlinear traits between λ, ρ and the prediction errors, they are difficult to be solved, then GM（2, 1,λ, ρ ） based on Particle Swarm Optimization（ PSO-GM （2, 1, λ, ρ） ） has been proposed, where ）, and ρ have been constituted a two-dimensional particle swarm, absolute of mean relative error has been as fitness function, its minimization has been as objective function, then the best λ, ρ have been solved. The practical examples show that the speed of convergence in PSO-GM （2,1,λ, ρ） is rapid, the prediction accuracy is much higher than that of the GM（2,1 ）, and it can meet practical need.

关 键 词：灰色GM(2 1)模型 背景值 数乘变换 微粒群算法 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]