平成22年度電気関係学会四国支部連合大会

333

18-34

Pheromone-Based Bees Algorithm
Yudai SHIRASAKISho SHIMOMURA
Masaki SUGIMOTO
Yoko UWATE
Yoshifumi NISHIO(Tokushima University)

1. Introduction[PBBA2], and repeat until t = T .

Bees Algorithm (BA) is a popular optimization
method for the solution of object function and is anevolutionary algorithm to simulate the food foraging
behavior of honey bees. In BA, the algorithm performs
a kind of neighbourhood search combined with random
search and can be used for both combinatorial optimization problems and functional optimization problems.
In this study, we propose Pheromone-Based BA(PBBA). The important feature of PBBA is that allbees are influenced by using the pheromone. We apply
PBBA to functional optimization problems and confirm
its effectiveness.

3. Numerical Experiments

rij = xi (t) + ∆φij (t),∆φij = (Si (t)Qij , θij ),(1)(2)

where ∆φij is the polar coordinate. Qij is the random variables distributed uniformly on [0,1]. θij is theamplitude and is the random variables distributed uniformly on [0,2π]. Si is the largest search range.

41010100PSOBAPBBAg[PBBA2] Dispose the recruit bees j = (1, 2, ..., N )around each X i . The recruit bees position rij is decided byGbest log( f (P ))[PBBA1] (Initialization): Let the generation step t =0 and the converge step tRi = 0. Randomly initialize the search bees i = (1, 2, ..., M ) position X i =(xi1 , xi2 , ..., xiD ). D is dimension parameters.

Gbest log( f (Pg ))2. Pheromone-Based Bees Algorithm

In order to evaluate the performance of PBBA, we apply PBBA to two functional optimization problems andcompare PBBA with existing two algorithms. One isthe standard BA and the other is the standard Particle Swarm Optimization (PSO). PSO is based onpheromone action as similar to PBBA.
We carry out the simulation 10 times for two optimization functions; Sphere function and Rastrigin function, with 2000 generations. A dimension is 100. The
optimum function values of the two functions are 0.
Fig. 1(a) shows the mean value of gbest for Spherefunction and Fig. 1(b) shows the mean value of gbest
for Rastrigin function. From these results, we can seethat the mean values of PBBA are the best for the twoproblems.

10-10

10-20

10PSOBAPBBA-30

103102-40

10100500

1000

Generation ( t )

(a)

1500

2000

0500

1000

1500

2000

Generation ( t )(b)[PBBA3] Evaluate the all current recruit bees costf (Rij ). Update the search bees position X i for each i.

Figure 1: Mean gbest value of every generation.
(a) Sphere function. (b) Rastrigin function.

[PBBA4]
If X i (t + 1) ≤ X i (t): perform [PBBA5].
If X i (t + 1) > X i (t): Update each X i , let tRi = 0 and
perform [PBBA6].

4. Conclusions[PBBA5]
If tRi < TR : Let tRi = 0 and initialize Si .
If tRi > TR : Si (t + 1) = 0.9Si (t).
[PBBA6] Evaluate the current cost X i . Update theglobal best position xgbest among all X i . X i (t + 1)
is updated according to X gbest . The important feature of PBBA is that the all bees X are influenced bya pheromone. A pheromone is disposed in the wholegroup’s best position X gbest . The X i is updated depending on the best position X gbest .
X i (t + 1) = X i (t) + cQ(xgbest − xi ),(3)where the parameter c is positive acceleration coefficients.
[PBBA7] Let t = t + 1 and tRi = tRi + 1. Go back to

In this study, we have proposed Pheromone-Based
Bees Algorithm (PBBA) and have solved two functional
optimization problems. We have confirmed that PBBA
obtained better results than the standard BA and thestandard PSO.

References[1] D. T. Pham, A. Ghanbarzadeh, E. Koc, S. Otri, S.
Rahim, M. Zaidi, The Bees Algorithm - A Novel Tool for
Complex Optimization Problems, Cardiff University, UK,
2006.
[2] K. Guney, M. Onay, “Bees Algorithm for Interference
Suppression of Linear Antenna Arrays by Controlling thePhase-Only and Both the Amplitude and Phase”, Expert
Systems with Applications, vol. 37, no. 4, pp. 3129-3135,
april 2009.