平成 27 年度電気関係学会四国支部連合大会 講演論文集 (2015 高知工科大学)
2015 SHIKOKU-SECTION JOINT CONVENTION RECORD OF THE INSTITUTES OF ELECTRICAL AND RELATED ENGINEERS (KOCHI)

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Firefly Algorithm Distinguishing
between Males and Females
Masaki TAKEUCHI† Haruna MATSUSHITA‡ Yoko UWATE†
Yoshifumi NISHIO††‡( Tokushima UniversityKagawa University)
In this study, males are attracted to all of firefly, whilefemales are attracted to only males. In addition, males movethe same as fireflies of FA.

1. Introduction
The swarm intelligence algorithm is based on behaviorof animals and insects. Representative examples are Particle Swarm Optimization (PSO), Ant Colony Optimization(ACO) and Firefly Algorithm (FA) [1–2]. All fireflies aredefined as unisex on FA. Therefore, we distinguish sex offirefly. The proposed method is called Firefly Algorithm
Distinguishing between Males and Females (FA-DMF). In
this study, we compare FA-DMF to FA with famous threetest functions.

4. Numerical Experiments
We compare FA-DMF to FA with three test functions (seeTable 1). These optimal solutions are f (x) = 0 at x = 0.

Table 1: The Test Functions
nameSphere

2. Firefly Algorithm (FA)
FA is based on the idealized behavior of the flashing
characteristics of firefly. It is suitable for multi-peak optimization problems. Attractiveness is proportional to theirbrightness, and attractiveness and brightness both decreaseas their distance increases. The brightness of firefly is affected by the landscape of the objective function to be optimized. For any two flashing fireflies, the less brighter one
moves toward the brighter one. The brightest firefly moves
randomly. Thus, they search the optimal solution. Attractiveness of firefly β is defined by2
β = β0 e−γrij ,(1)where γ is the light absorption coefficient, β0 is the attractiveness at rij = 0, and rij is the distance between any twofireflies i and j at xi and xj . The movement of the firefly i is attracted to another more attractive firefly j, and isdetermined by
xi = xi + ∆x,(2)Rastrigin
Griewank2−γrij/Wβ = β0 ex = x + ∆x/V.

,(x2i − 10 cos (2πxi ) + 10)
nXnY

1xix2 −cos ( √ ) + 1
4000 i=1 i i=1iname[-5.12,5.12][-600,600]

FAFA-DMF

Sphereaveminmax2.81 × 10−7
1.67 × 10−7
3.75 × 10−7

1.27 × 10−7
6.66 × 10−8
1.94 × 10−7

Rastriginaveminmax

2.66 × 101
1.49 × 101
4.97 × 101

1.53 × 101
4.97 × 100
3.38 × 101

Griewank

aveminmax2.07 × 10−4
1.31 × 10−4
2.85 × 10−4

2.26 × 10−4
1.24 × 10−4
1.72 × 10−2

In Sphere and Rastrigin functions, FA-DMF obtains better results. In Griewank function, FA-DMF also obtains
better result about min, while FA-DMF obtains worse results about ave and max.

5. Conclusions
In this study, we have proposed a new firefly algorithm,
and have compared to the conventional firefly algorithm.
Our numerical experiment results show that FA-DMF issuperior to FA in Sphere and Rastrigin functions. In thefuture works, we improve FA-DMF, and apply multi-peak
optimization problems.

References[1] Yang, X.S., “Nature-Inspired Metaheuristic Algorithms
Second Edition”, Luniver Press, 2010.

t/2tmax,[-5.12,5.12]

Table 2: Numerical Experiment Results

In our proposed method, there are two swarms. The twoswarms represent male and female. We define that half fireflies are males and the rest are females. The movement offemale is modeled from the characteristics of the real firefly. In the real world, females are bigger than males andfemale eyes are smaller than male. Therefore, in our proposed method, females move slower than males, and females
have difficulty finding the flashes of other distant fireflies.
In addition, we change the randomization parameter of female. The female parameters α(t) and β, and the female
movement x is determined with parameters V and W byα(t) = α(0)f (x) =Range

Each numerical experiment is run 100 times. In eachtest function, we define the number of fireflies n = 30, thenumber of dimensions N = 30, tmax = 900, W = 2 andV = 3. Numerical experiment results are shown in Table 2.

3. FA-DMF

104
0.9f (x) =i=1nX
i=1∆x = β(xj − xi ) + αi ,(3)where xi is the position vector of firefly i, i is the vector ofrandom variable, and α(t) is the randomization parameter.
The parameter α(t) is definedbyt/tmax
10−4α(t) = α(0),(4)
0.9where t is the number of iteration.

FormulanXf (x) =x2i

(5)[2] Yang, X.S., “Firefly Algorithm, Stochastic Test Functions and Design Optimization”, Int. J. Bio-Inspired
Computation, vol.2, pp.78-84, 2010.

(6)(7)

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