平成24年度 電気関係学会四国支部連合大会

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Artificial Bee Colony Algorithmwith Two Kinds of Colonies
Yudai SHIRASAKI,

Yoko UWATE and Yoshifumi NISHIO(Tokushima University)

1. Introduction
Artiﬁcial Bee Colony (ABC) is known as a optimization
technique by modeling the intelligent foraging behavior ofhoneybee swarms.
In this study, we propose Artiﬁcial Bee Colony withTwo Kinds of Colonies (ABCTKC). It has diﬀerent characteristic each colony. We investigate the performance ofABCTKC for four benchmark functions.

2. The flow of ABCTKCABCTKC has two types colonies. Colony1 is samesearching method as ABC. Colony2 searches by using
informations of Colony1. And, Colony2 has the characteristic of high convergence by assembling Colony2 tocenter of Colony2. ABCTKC can eﬃciently search bycombining two types colonies.
Step 1 (Initialization)
Let a generation step t = 0, the converge step tRi = 0
and the exchange step te . After the employed bees
are divided two colonies. The employed bees i =(1, 2, ..., Me ) search food sources at random.
Step 2 (Search by employed bee)
Employed bees search new food source in eachcolony.
(Colony1)
In order to search better food source, the employed
bee uses the following equation:
Xid (t + 1) = Xid (t) + Φid (Xid (t) − Xkd (t))(1)

where X i (t) = (xi1 , xi2 , ..., xid ) is position informations of employed bees. k ∈ {1, 2, ..., Me } is randomly chosen indexes for each colony. Although kis determined randomly from excluding the chosen i.
Φid is a random number between [−1,1]. d is numberof dimensions.
(Colony2)
In Colony2, employed bees use the searched information of Colony1. The searching method of employed
bee is described by the following equation:
Xid (t + 1) =id (t) + rand[0, 1](Xid (t) − Xbest,d (t))− rand[0, 1](Xid (t) − Xave,d (t))

Step 3 (Evaluation of employed bee)
Evaluate X i (t) and compare of the current employed
bee ﬁtness value f (X i (t)).
If f (X i (t)) ≤ f (X i (t + 1)): Let tRi = tRi + 1.
If f (X i (t)) > f (X i (t + 1)): Update the position
information on each X i , and tRi = 0.
Step 4 (Search by onlooker bee)
Onlooker bee searches new food sources dependingon evaluation values of employed bees. The chosenprobability Pi is calculated by the following equation:

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Yjd (t) = Xid (t) + Φid (Xid (t) − Xkd (t))(4)

where Y j (t) = (xi1 , xi2 , ..., xid ) is position informations of onlooker bees.
Step 5 (Evaluation of onlooker bee)If f (X i (t)) ≤ f (Y j (t)): Let tRi = tRi + 1.
If f (X i (t)) > f (Y j (t)): Update the current foodsource X i to new food source Y j , and tRi = 0.
Step 6 (Search by scout bee)
If Tlimit < tRi , initialize X i and tRi = 0. New X i issearched at random by scout bee.
Step 7 (Exchange of employed bee)If Te ≥ te : Exchange employed bee between colonies
and te = 0. The selection probability Ei is calculatedby the following equation:( T 1 )3
Ei = ∑Mg Ri13
n=1 ( TRi )(5)

Step 8Let t = t + 1, go back to [Step 2] and repeat until
T = t.

3. Simulations
In order to investigate the performance of ABCTKC,
we apply to four benchmark functions for d = 20. The
simulation is 100 times and the generation number isT = 10000 times. ABCTKC uses best parameters eachfunction.
As shown in Table 1, ABCTKC is better results than
ABC in Sphere and Rosenbrock functions. In Rastriginfunction, because the diﬀerence of Max and Min in ABCTKC is smaller than ABC’s, ABCTKC obtains better results with small number of trials. From these results, weconﬁrmed that ABCTKC can eﬃciently search by combining two type colonies.

(2)

where Xbest,d (t) is the best food source in current
generation t into Colony1. Xave,d (t) is the average
position of whole Colony2.

f (Xi )Pi = ∑Mg
n=1 f (Xn )The searching methods of onlooker bee is describedby following equation:(3)

Table 1: The simulation results of ABC and ABCTKC
for four functions.
Function
SphereRosenbrock
Rastrigin
Griewank

Algorithm
ABC
ABCTKCABC
ABCTKCABC
ABCTKCABC
ABCTKCAve
8.71E-255
4.33E − 289
1.29
0.94
0.25
0.800Min
4.34E-261
4.82E-300
0.78
0.47
0000Max
4.65E-253
3.21E-251
2.01
1.42
18.7
3.19
00

4. Conclusions
In this study, we have proposed Artiﬁcial Bee Colony
with Two Kinds of Colonies. We have conﬁrmed thatABCTKC obtains better result than ABC for some functions. In future works, we would like to apply to higher
dimensions and conﬁrm new behaviors.