2016年 NOLTAソサイエティ大会
IEICE, NOLTA
東京, 2016年6月12日

Female Percentage in Firefly Algorithm
Masaki Takeuchi1

Haruna Matsushita2

Yoko Uwate1

Yoshifumi Nishio1

Tokushima University, Department of Electrical and Electronic Engineering1
Kagawa University, Department of Electronics and Information Engineering2

1

INTRODUCTION
Swarm intelligence is receiving a lot of attention invarious fields. One of swarm intelligence algorithms isFirefly Algorithm (FA). The conventional FA is composed of one swarm. In nature, it is important to havea diversity in order to fit various environments. Therefore, we distinguish sex of fireflies so that algorithm
has diversity. This proposed algorithm is called Firefly
Algorithm Distinguishing between Males and Females.
In this study, we focus on eﬀect of female percentage.
FIREFLY ALGORITHM (FA)On FA, fireflies search optimal solution according toeach attractiveness. Attractiveness is proportional to
the their brightness. The less brighter(darker) fireflymove towards the brighter one. The brightness of a
firefly is aﬀected by the landscape of the objective function and decrease as distance increases.
Attractiveness of firefly β is defined bymales, and females have diﬃculty finding the flashesof other distant fireflies. In addition, we change therandomization parameter of female.
The female parameters α(t) and β, and the female
movement x is determined with parameters V and Wby(α(t) = α(0)2(1)

where γ is the light absorption coeﬃcient, β0 is the attractiveness at rij = 0, and rij is the distance between
any two fireflies i and j at xi and xj . The movementof the firefly i is attracted to another more attractive
firefly j, and is determined by
xi = xi + ∆x,(2)∆x = β(xj − xi ) + αϵi ,(3)where xi is the position vector of firefly i, ϵi is the vector of random variable, and α(t) is the randomization
parameter. The parameter α(t) is defined by(α(t) = α(0)10−40.9)t/tmax,(4)where t is the number of iteration.
PROPOSED METHOD
In nature, it is important to have a diversity in order to survive and fit various environments. Therefore,
we distinguish sex of fireflies, that is, there are twokinds fireflies in our proposed method. We call ourproposed method Firefly Algorithm Distinguishing between Males and Females (FADMF). In our proposed
method, moving distance of females is shorter than)t/2tmax,(5)

β = β0 e−γrij /W ,(6)x = x + ∆x/V.

(7)

2

2

β = β0 e−γrij

104
0.9

In the proposed method, males are attracted to all
fireflies, while females are attracted to only males.
Males move the same as fireflies of the conventional
FA.
4NUMERICAL EXPERIMENT
We compare FADMF to the conventional FA with 8
composition functions of CEC 2013 benchmark functions. Table1 shows how many times the proposed
FA wins the conventional FA in the comparison for
the 8 composition functions. The dimension N is 30,
the search range of these functions is [−100, 100]N , themaximum number of iteration is 1500, and each numerical experiment is run 50 times.
Table 1 Numerical Experiments
Female Percentage 10 20 30 40 50 60 70 80 90
Num. of Function 4 4 5 5 6 6 3 2 2Table1 indicates female percentage is suitable for 50
or 60. As female percentage increases until 50, thenumber of function increases, and then the number offunction immediately decreases. Females tend to converge slowly because the moving distance of females isshorter than males. We assume that FADMF is more
hardly falling into local optima as female percentage
increases. However, FADMF becomes local search algorithm when female percentage is too large.

35CONCLUSION
We have proposed improved Firefly Algorithm that
distinguishes sex of fireflies. In this study, we focus on
female percentage of our proposed method. We assume
that FADMF is more hardly falling into local optima
when female percentage is suitable value.

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