平成21年度電気関係学会四国支部連合大会

358

18-34

Particle Swarm Optimization
Containing Plural Swarmswith Inﬂuence
Masaki SUGIMOTO(Tokushima University)

Taku HARAGUCHI(Tokushima University)

1. Introduction
Particle Swarm Optimization (PSO) [1] is a popular
optimization technique for the solution of object function and is an algorithm to simulate the movement ofﬂock of birds and the movement of a school of ﬁsh toward foods. In this study, we propose PSO containing
plural swarms with inﬂuence (PPSO). The importantfeature of PPSO is that each particle of PPSO belongs
to one of plural swarms, which have diﬀerent characteristics and inﬂuence other swarms. We investigate
the behavior of PPSO and conﬁrm its eﬃciency.

2. PPSO[PPSO1] (Initialization) Let a generation step t = 0
and tc = 0, i.e., tc is the time step for update theinertia weight wk of each swarm Sk . Randomly initialize the particle position X i and its velocity V i forall particles i and initialize P i = (pi1 , pi2 , ..., piD ) witha copy of X i . Attach each particle i to any swarm Skat random.
[PPSO2] Evaluate the current cost f (X i ). Update
the personal best position pbest P i for each particle iand the global best position gbest P g among the allparticles in all the swarms so far.
[PPSO3] Let P sk represents the swarm best position
with the best cost among the particles belonging to
the swarm Sk so far (called sbest). Update P sk foreach swarm Sk , if needed. [PPSO4] Updated V i andX i of each particle i depending on its pbest, its swarm
best sbest and gbest;

Haruna MATSUSHITA Yoshifumi NISHIO(Tokushima University)(Tokushima University)
wtop is an inertia weight of the swarm containing gbest.
Q is the rate of change of the inertia weight. And also,reset tc = 0.
[PPSO7] Let t = t + 1 and tc = tc + 1. Go back to[PPSO2], and repeat until t = T .

3. Numerical Experiments
In order to evaluate the eﬃciency of PPSO andinvestigate the behavior of PPSO, we compare thefour algorithms that PSO, PPSO1, PPSO2 and PPSO.
PSO is the standard PSO and PPSO is the proposedalgorithm. PPSO1 and PPSO2 algorithms are PPSO
algorithm which does not perform [PPSO6]. The inertia weight wk of PPSO1 is all the same as the inertia
weight w of PSO. PPSO2 uses diﬀerent inertia weightwk depending on each swarm, however they are constant values unlike PPSO. We carry out the simulation 30 times for two optimization functions with 3000generations. Figures 1(a) and (b) show the mean gbest
values of every generation over 30 runs for Sphere function and Rastrigin function with 30-dimension. Fromthese results, we can conﬁrm that the mean values ofPPSO are the best for two problems. Therefore, wecan conﬁrm that PPSO algorithm is the most eﬀective.

vid (t + 1) = wk vid + c1 r1 {pid − xid (t)}+c2 r2 {psk d − xid (t)} + c3 r3 {pgd − xid (t)} ,xid (t + 1) = xid (t) + vid (t + 1),(1)where r1 , r2 and r3 are three random variables distributed uniformly on [0, 1], and c1 , c2 and c3 are positive acceleration coeﬃcients. wk is an inertia weightof each swarm Sk . In other words, the particles behave
in a diﬀerent way according to the inertia weight wkof each swarm.
[PPSO5] If tc = Tc , perform [PPSO6]. If not, perform[PPSO7]. Thus, perform [PPSO6] every Tc generation.
Tc is a ﬁxed parameter and is the number of generations to reconstitute the swarms.
[PPSO6] Update the inertia weight wk of each swarm
Sk aswk (t + 1) = wk (t) − (wk (t) − wtop ) × Q,

(2)

(a)

(b)

Figure 1: Mean gbest value of every generation for
30-dimensional two functions. (a) Sphere function.
(b) Rastrigin function.

4. Conclusions
In this study, we have proposed PPSO. We haveinvestigated its behavior with the simulation and have
conﬁrmed the eﬃciency.
Reference[1] J. Kennedy and R. Eberhart, “Particle swarm optimization”, Proc. of IEEE Int. Conf. Neural Networks, vol. 4, pp. 1942–1948, 1995.