THE JOURNAL OF CHINA UNIVERSITIES OF POSTS AND TELECOMMUNICATIONS
Volume 15, Issue 2, June 2008
XU Jun-jie, YUE Xin, XIN Zhan-hong
Research of stochastic weight strategy for extended particle
swarm optimizer
CLC number TP301 Document A Article ID 1005-8885 (2008) 02-0122-03
Abstract To improve the performance of extended particle
swarm optimizer, a novel means of stochastic weight deployment
is proposed for the iterative equation of velocity updation. In
this scheme, one of the weights is specified to a random
number within the range of [0, 1] and the other two remain
constant configurations. The simulations show that this weight
strategy outperforms the previous deterministic approach with
respect to success rate and convergence speed. The experi-
ments also reveal that if the weight for global best neighbor is
specified to a stochastic number, extended particle swarm
optimizer achieves high and robust performance on the given
multi-modal function.
Keywords particle swarm optimization, evolutionary computation,
stochastic weight, function optimization
1 Introduction
Particle swarm optimization (PSO) is a promising function
optimization algorithm developed by Kennedy and Eberhart [13].
Through the simulation of bird flocking, the approach has
achieved success in probing for the optima of continuous
nonlinear functions. The canonical particle swarm algorithm
works by probing iteratively in a region that is defined by each
particle’s best previous success, the best previous success of
any of its neighbors, the particle’s current position, and its
previous velocity. Two versions of canonical particle swarm
are often performed in optimization; one is Gbest and the
other is Lbest. The former chooses its best neighbor in the
whole swarm, whereas the later chooses it in a pre-defined and
local sub-swarm.
Supposing that the object function has D dimensions and m
particles are created in the swarm, each particle i holds three
Received date: 2007-07-21
XU Jun-jie ( )
Economics and Management College, Anqing Teachers College,
Anqing 246133, China
E-mail: xu0926@gmail.com
YUE Xin, XIN Zhan-hong
School of Economics and Management, Beijing University of Posts and
Telecommunications, Beijing 100876, China
basic vectors: current velocity v
i
=(v
i1
, v
i2
,…, v
iD
), current
position x
i
=(x
i1
, x
i2
,…, x
iD
), and its best location, which has
been found to be thus far represented as p
i
=(p
i1
, p
i2
,…, p
iD
).
The global best position p
g
=(p
g1
, p
g2
,…, p
gD
) in Gbest or the
local best p
l
=(p
l1
, p
l2
,…, p
lD
) in Lbest found so far is also
recorded. In Gbest, when particle i flies through the hyperspace,
its velocities and positions iterate as Eq. (1) :
1 1 2 2
( ) ( )
id id id id gd id
id id id
v v c r p x c r p x
x x v
(1)
where c
1
and c
2
are two positive constants and r
1
and r
2
are
random samples in the range [0, 1]. The updating rule of Lbest
is similar to that of Gbest, while p
gd
in Eq. (1) is substituted by
p
ld
.
Paradigms of PSO are easy to implement. Many research
studies on PSO have been proposed over the past ten years. In
most PSO paradigms, only the best neighbor has social influence
on velocity adjustment of each particle; one straightforward idea
is to consider the experience of all members in the neighborhood,
which is the fully informed particle swarm (FIPS) [45]. FIPS
has a stronger social influence than the canonical version. The
disadvantage of FIPS is obvious in that it requires more
computations in velocity updation.
In our previous work [67], we studied an extended particle
swarm optimizer (EPSO) which combined Gbest with Lbest in
velocity updating rule to achieve a compromised computation
result. When weights in the velocity updating equation of
EPSO were deployed in deterministic configurations, EPSO
presented a better performance on most benchmarks, and it
markedly reduced the iteration number, with success rate
relatively higher than that of Lbest. However, it failed in case
of multi-modal functions unless the three weights were
specifically assigned. This article focuses on the configuration
of those weights in EPSO and proposes a stochastic weight
strategy to acquire a robust and high performance.
The rest of this article is organized as follows: Section 2
briefly describes EPSO with deterministic weights. Section 3
introduces the stochastic weight strategy in the velocity
updating equation for EPSO. Section 4 shows the simulation
results on a multi-modal function based on the proposed new
weight approach, and the last section presents the conclusions.