A New Optimization Approach for Grey Model GM(1,1) - Advanced Research on Computer Education, Simulation and Modeling - page 117

A New Optimization Approach for Grey Model GM(1,1)

Zhanyi Ao 1 , Xiao-qing Ou 2 , and Shaohua Zhu 2

1 Department of Mathematics and Computer Science,
Hebei Normal University of Nationalities,
Chengde. Hebei, 067000,
People's Republic of China
2 Human Resources Department, Jihua 3509 Textile Co., Ltd.,
Hubei Hanchuan 431616, People's Republic of China
{469794021,724479775,108859099}@qq.com

Abstract. A new optimized approach is introduced by the exponential response
of recuperating value of GM (1, 1) model, which has been strictly proved to
have the white exponential superposition and the white coefficient
superposition in theory. The normal exponential series and a practical example
are also given to show that the new model has the very high simulation and
prediction precisionn.

Keywords: GM(1, 1); Optimization; Background.

1 Introduction

Grey prediction model GM (1, 1) has been widely applied in many fields since it was
introduced. In order to improve the precision of the model, literatures [3] and [4]
derived the integral form of the background value from the white differential
equation, which greatly improve the prediction precision. In literatures [5] and [6], the
authors used the least square method to optimize coefficient, avoiding the error
brought out by the initial condition. Due to the recuperating value of GM (1, 1) model
has the homogeneous exponential form xk −

ˆ

(0) ak

, therefore, if only working out
a and c , we could obtain the recuperating value. According to the new background
value derived in literature [4], we can work out development coefficient a ; according
to the smallest principle that the difference quadratic sum between actual values and
recuperating values, we could utilize the least square method to obtain c , thereby a
new optimized GM(1, 1) method is presented in this paper.

() =

2 Optimized Method and Its Properties

Lemma 1. Let be the raw series, be the

x

( 0 )

= ( x

( 0

( ), L , x

( 0 )

( n )) x

(

= ( x

(

( ), L , x

(

( n ))

(0) (1) ()

1- AGO series of x , zk be background value. Let