平成22年度電気関係学会四国支部連合大会

308

18-9

Particle Swarm Optimization
Containing Cooperative Particles
Haruna MATSUSHITA Yoshifumi NISHIO(Hosei University)(Tokushima University)+c1 r1 {pid − xid (t)}+c2 r2 {pgd − xid (t)} ,(1)

3

10
PSO
PSOC

PSO
PSOC

0

g

f (P )

10-20

2

Gbest

10-40

-60

1

10100

500

1000

1500

2000

0(a)

1500

2000

(b)

44

1010
PSO
PSOC

2PSO
PSOC

gf (P )

100103-2

1010-4102100[PSOC5] Update X i depending on its V c and V i ;1000
Generation ( t )-6where r1 and r2 are two random variables distributed
uniformly on [0, 1], w is an inertia weight of all particles, and c1 and c2 are positive acceleration coeﬃcients.
[PSOC4]
All the particles shared V c=(vc1 , vc2 , ..., vcD ). Let V c represent the average velocity of all the particles;
M1 ∑(2)
vcd =vid
M i=1500

Generation ( t )10xid (t + 1) = xid (t) + cvcd (t + 1) + vid (t + 1),

1010Gbestvid (t + 1) = wvid

2010Gbest[PSOC1] (Initialization) Let a generation step t =0. Randomly initialize the particle i = (1, 2, ..., M )position X i = (xi1 , xi2 , ..., xiD ) and its velocity V i =(vi1 , vi2 , ..., viD ) for all particles i and initialize P i =(pi1 , pi2 , ..., piD ) with a copy of X i .
[PSOC2] Evaluate the current cost f (X i ). Update
the personal best position pbest P i = (pi1 , pi2 , ..., piD )for each particle i and the global best position gbest
P g = (pg1 , pg2 , ..., pgD ) among the all particles.
[PSOC3] Update V i of each particle i depending on
its pbest and its swarm best gbest;f (Pg)

2. PSOCalgorithms that PSO and PSOC. PSO is the standard
PSO and PSOC is the proposed algorithm. The inertia weight w is 0.5. We carry out the simulation 30
times for two optimization functions with 2000 generations. Figures 1(a), (b), (c) and (d) show the mean
gbest values of every generation over 30 runs for Spherefunction and Rastrigin function with 30-dimension and100-dimension. The optimum function values f (x∗ ) of
the two functions are 0. From these results, we canconﬁrm that the mean values of PSOC are the best
among four problems. Therefore, we can conﬁrm that
PSOC algorithm is the most eﬀective.

Gbest

Particle Swarm Optimization (PSO) [1] is a popular
optimization technique for the solution of object function and is an algorithm to simulate the movement of
ﬂock of birds and the movement of a school of ﬁshtoward foods.
In this study, we propose PSO containing cooperative particles (PSOC). The important feature of PSOC
is that each particle of PSOC shares the same velocity information. We investigate the behavior of PSOC
and conﬁrm its eﬃciency.

g1. Introductionf (P )

Masaki SUGIMOTO(Tokushima University)

500

1000

1500

Generation ( t )

(c)

2000

0500

1000

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2000

Generation ( t )(d)Figure 1: Mean gbest value of every generation for
four problems. (a) Sphere function (30-dimension,).
(b) Rastrigin function (30-dimension). (c) Spherefunction (100-dimension). (d) Rastrigin function (100dimension).

4. Conclusions
In this study, we have proposed PSOC. We haveinvestigated its behavior with the simulation and have
conﬁrmed the eﬃciency.

(3)

where c is an cooperation coeﬃcients. In other words,
the particles combine the action of individual and cooperation.
[PSOC6] Let t = t + 1. Go back to [PSOC2], andrepeat until t = T .

3. Numerical Experiments
In order to evaluate the eﬃciency of PSOC and investigate the behavior of PSOC, we compare the two

References[1] J. Kennedy and R. Eberhart, “Particle swarm optimization”, Proc. IEEE Int. Conf. Neural Netw., vol. 4,pp. 1942–1948, 1995.
[2] M. Sugimoto, T. Haraguchi, H. Matsushita andY. Nishio, “Particle swarm optimization containing
plural swarms”, Proc. RISP Int. Workshop on Nonlinear Circuits and Signal Processing, pp. 419–422, 2009.