平成 26 年度電気関係学会四国支部連合大会 講演論文集 （2014 徳島大学）
2014 SHIKOKU-SECTION JOINT CONVENTION RECORD OF THE INSTITUTES OF ELECTRICAL AND RELATED ENGINEERS (TOKUSHIMA)

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Particle Swarm Optimization with Two Predators
Norio INUKAI1

Takuya INOUE1 Yoko UWATE1(1 Tokushima University)

1. Introduction
Particle Swarm Optimization (PSO) is known as one of
Swarm Intelligence. PSO algorithm is based on the behavior of fish school, bird flock and so on. It is simple andeasily possible to find solutions of optimization problems.
However, the standard PSO is hard to get out from localminimum.
Therefore, we have proposed PSO with Predator (PSOP). PSO-P algorithm is specific fish school (particles) algorithm that is added big fish (predator) by the standard
PSO. PSO-P is improved for PSO that particles are eaten
by predator.
In this study, we propose PSO with Two Predators.
This is added two predators for PSO-P. We compare PSOP and the standard PSO by using computer simulation.

2. PSO-P algorithm
PSO algorithm uses two expression from Eqs. (1), (2).

Yoshifumi NISHIO1

The standard PSO algorithm repeats Step 2, 3, 5.
PSO-P algorithm repeats Step 2–5.
In this study, we fix the parameters as follows;a = 0.6, b1 = b2 = 1.7, c = d = 1.

3. Numerical Experiments
In order to confirm the performance, we apply PSO andPSO-P algorithm to computer simulation. We use for theoptimization of Rosenbrock function Eq. (4).
f (x) =n−1∑(100(xi+1 − xi 2 )2 + (xi − 1)2(4)i=1Function dimension is 30. Population sizes is 30 particles. We change the predation radius, 0.1 to 2.0 with
0.1 step size. The predation radius equal 0.0 means thestandard PSO. Predator’s strategic move patterns are considered 3 kinds (Table 1).

Table 1: Move pattern⃗vk+1 = ⃗a ⊗⃗vk +⃗b1 ⊗⃗r1 ⊗ (⃗p1 −⃗xk ) +⃗b2 ⊗⃗r2 ⊗ (⃗p2 −⃗xk ) (1)⃗xk+1 = ⃗c ⊗ ⃗xk + d⃗ ⊗ ⃗vk+1(2)

In this time, expression values are decide.

⃗vk : particle velocity




⃗
xk : particle position

Pattern 0
Pattern 1
Pattern 2

Access optimum point
Access one time ago optimum point
Intermediate between‘Pattern 0’ and ‘Pattern 1’

The results are shown in Fig. 1. The cost is defined by
the following formula Eq. (5).
P article of number × Average(5)
Cost =Success ratep⃗1 : own previous best positionp⃗2 : globally best position in the whole swarm




⃗
a, ⃗b1 , ⃗b2 , ⃗c, d⃗ : coeﬃcient⃗r1 , ⃗r2 : random numbers

The algorithm of the standard PSO and PSO-P are described below;
Step 1 { Decide for ⃗v0 , ⃗x0 , p⃗1 , p⃗2 }⃗v0 and ⃗x0 decide random number for all particle. p⃗1and p⃗2 decide from Eq. (3).
p
⃗1 = min{⃗xk }, p⃗2 = min{⃗
p1 }

(3)

Step 2 { Update for ⃗vk , ⃗xk }⃗vk and ⃗xk are decided update for using Eqs. (1), (2).
Step 3 { Update for p⃗1 , p⃗2 }p⃗1 and p⃗2 are decided update for using Eq. (3).
Step 4 { Predator section }Predation decision do for particle around predator. If
it is true, we reposition the half of particle that are preyedparticle.
In PSO with Two Predators, this step executes twice.
Step 5 { End decision }If p⃗2 is smaller than the threshold value, it ends tosearch solution. Also, if loop count measure up to thethreshold value, it ends to search solution.

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Fig. 1: Rosenbrock results.
PSO with Two Predators is lower cost than the standard PSO. Notably, if predation radius is more, thensearch solution is low cost. Especially, the results of ‘Pattern 2’ of predator strategy show the lowest cost.

4. Conclusions
In this study, we proposed PSO with Two Predators.
We investigated behavior of PSO-P by the simulation andconfirmed the eﬃciency.
In the future work, we would like to adapt other functions in PSO-P.