平成 30 年度電気関係学会四国支部連合大会 講演論文集 (2018 愛媛大学)
2018 SHIKOKU-SECTION JOINT CONVENTION RECORD OF THE INSTITUTES OF ELECTRICAL AND RELATED ENGINEERS (EHIME)

1-19

High Performance Artificial Bee Colony Algorithm for Time-Varying Solutions
Ken KAMIYOTSUMOTO† , Thomas OTT‡ , Yoko UWATE† and Yoshifumi NISHIO†( Tokushima University† , Zurich University of Applied Sciences‡ )1. Introduction

improve the artificial bee colony for time-varying solution(ABCTV) [1]. The ABCTV can not search locally. We
propose the ABCTV modified fitness function(ABCTVD).
We calculate pi for the diﬀerence between evaluate valueof present location and previous location. Therefore pi iscalculated Eq. (3).
ne∑pi = (fi+1 − fi )/(fn+1 − fn )(3)

Recently, nature-inspired metaheuristic optimization algorithms such as Artificial Bee Colony (ABC) algorithm isdeveloped. ABC is based on a particular intelligent foraging behavior of honeybee.
In this study, we propose ABC applied time-varying solution. We compare the optimal solution with ABC and theproposed method.

i=12. Artificial Bee Colony algorithm

According to this modification, we expect that ABCTVD
obtains better performance.

Karaboga has proposed an Artificial Bee Colony (ABC)algorithm in 2005. The ABC algorithm is based on real bee
behavior and consist of 3 kinds of honeybee, employed bee,onlooker bee and scout bee. It is suitable when the object
function is high dimension. The procedure for solving anoptimization problem in the ABC algorithm is shown below.

4. Simulation result
We compare the result of Eq. (4).
(x1 − 250 − 125sinαk)22 · 402(4)(x2 − 250 + 125sinαk)2−].
22 · 40Equation (4) simulates a visual tracking problem. The optimal function value is 0, and position along a circle of radius
125 centered at (x1 , x2 ) = (250, 250), then return its original position in (2π/α) steps. We express the constant value
to use for simulation in Eq. (5).
g(x1 , x2 , t) = 1 − exp[−

Step0. Initialize each total number of employed bees ne
and onlooker bee no , the colony size N = ne + no andthe total number of iterations tmax .
Step1. (1) Set the locations of the xi . i is the number ofthe employed bee.
(2) Calculate the fitness fi in the initial arrangement by Eq. (1). The best fi and initial arrangement
are stored.

ne = no = 100, tmax = 500000,(5)

We compare the best value for 3 kinds α. Table 1 showsthat the best value of each method.

Step2. (1) New locations vi is generated and calculated
the fitness function value.
(2) Based on the fitness, the best location and fitness update.

Table 1: Simulation resultsα

step3. (1) Based on the fitness, the probability pi is calculated by Eq. (2).
(2) Select the number of employed bee i based onpi , and Step1 is applied. When this procedure has
been repeated no times.

ABCABCTVABCTVD

0.01

0.05

2.76e-05
5.12e-04
3.58e-05

6.59e-06
1.58e-02
1.55e-03

0.1
1.23e-06
7.96e-03
9.73e-03

step4. If function value of each i is better than function
value of all bees, the solution and the function bestvalue are updated.
step5. The employed bee which has not been generate thenew location.

(a) ABC．

Step6. Repeat steps 1 to 4 and output the solution.

fipi==fi /1
1 + g(xi )1 + |g(xi )|ne∑

if g(xi ) ≥ 0

From Table 1, the best value of TBCTVD is better
than the best value of ABCTV. Furthermore, Fig. 1 expresses that ABCTVD can search time-varying solution.

5. Conclusion(1)

otherwisefn ,(c) ABCTVD．

Figure 1: shape of solutions when α is 0.01.

Fitness function fi and evaluations value a are given byfollowing equations:{(b) ABCTV．

This study introduced the ABC modified fitness function. We tried improvement of ABC, where fitness function
modified the diﬀerence of 2 locations. We compared thebest values of ABCTVD ABCTV and ABC. As a result,
ABCTVD performed better than other algorithms.

(2)

i=1

where, g(xi ) expresses the objective function.

3. Propose method

Reference

The most of algorithms exclude time-varying solution.
However, when we search optimal solution, we need to apply
the both solutions (time-varying and not time-varying). We[1] Takeshi Nishida, “ Modification of ABC Algorithm for
Adaptation to Time-Varying Functions,” Electronics andCommunications in Japan, 2012.

19