METHODOLOGIES AND APPLICATION
Dynamic characteristic of a multiple chaotic neural network
and its application
Gang Yang
•
Junyan Yi
Published online: 26 October 2012
Ó Springer-Verlag Berlin Heidelberg 2012
Abstract Based on chaotic neural network, a multiple
chaotic neural network algorithm combining two different
chaotic dynamics sources in each neuron is proposed. With
the effect of self-feedback connection and non-linear delay
connection weight, the new algorithm can contain more
powerful chaotic dynamics to search the solution domain
globally in the beginning searching period. By analyzing
the dynamic characteristic and the influence of cooling
schedule in simulated annealing, a flexible parameter tun-
ing strategy being able to promote chaotic dynamics con-
vergence quickly is introduced into our algorithm. We
show the effectiveness of the new algorithm in two difficult
combinatorial optimization problems, i.e., a traveling
salesman problem and a maximum clique problem.
Keywords Chaotic dynamics Annealing strategy
Combinatorial optimization Neural network
1 Introduction
Recently, chaotic behaviors existing widely have been
observed in human brains and animals neural systems. To
realize flexible intelligent information processing that
mimics the human brains, a wide variety of artificial neural
networks (ANNs) algorithms embedded with chaotic
dynamics are proposed (Aihara 2002; Klotz and Brauer
1999; Lin 2001; Nozawa 1992; Cao et al. 2006). Aimed to
combinatorial optimization problems (Hasegawa et al.
1995; Kwok and Smith 2000), ANNs with chaotic dynamics
use the complex evolutive characteristic of chaos to search
the solution domains globally. These methods reserve the
basic evolution theory of Hopfield network, and obtain
more efficient problem solving ability by introducing cha-
otic signals generated externally or internally. Embedded
with an external chaotic noise, some Hopfield-type neural
networks (Hopfield and Tank 1985, 1986), such as a chaotic
simulated annealing method with decaying chaotic noise
proposed by He (2002), get complex dynamics and hold
superior capability to find solutions. The typical chaotic
neural networks with internal signals are transiently chaotic
neural network (TCNN) proposed by Chen-Aihara (1995)
and the chaotic simulated annealing (CSA) algorithm pre-
sented by Wang-Smith (1998). Chaos generated by the
internal dynamics in a large neural network can be corre-
lated over large spatial scales (Hansel and Sompolinsky
1992). That means chaotic neural networks with internally
generated chaos have more reasonable capability to search
large domains containing optimal solutions.
Various types of Hopfield-type chaotic neural networks
have been presented and analyzed on combinatorial opti-
mization problem since Aiharas works. In 1990, Aihara
et al. presented a basic chaotic network model based on
chaotic properties of biological neurons, then Chen and
Aihara (1995) proposed ‘‘chaotic simulated annealing’’ to
demonstrate the characteristic and solving capability of a
transiently chaotic neural network on optimization prob-
lems. By introducing a negative self-feedback internal
Communicated by Y. Jin.
G. Yang
Key Laboratory of Data Engineering and Knowledge
Engineering, Renmin University of China, MOE,
Beijing 100872, People’s Republic of China
J. Yi
Department of Computer Science and Technology,
Zhejiang University of Technology, Chaowang Road 18,
Hangzhou 310026, Zhejiang Province,
People’s Republic of China
123
Soft Comput (2013) 17:783–792
DOI 10.1007/s00500-012-0948-8