令和元年度電気関係学会四国⽀部連合⼤会 講演論⽂集 (2019 新居浜⾼専)
2019 SHIKOKU-SECTION JOINT CONVENTION RECORD OF THE INSTITUTES OF ELECTRICAL AND RELATED ENGINEERS (NIIHAMA)

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Artificial Bee Colony Algorithm for Optimization with Time-Variable Function
Ken KAMIYOTSUMOTO† , Yoko UWATE† , Thomas OTT‡ and Yoshifumi NISHIO†( Tokushima University† , Zurich University of Applied Sciences‡ )1. Introduction

3. Propose method

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 previous study, we proposed ABC applied time-varying
solution. However, we can not search accurate solution.
In this study, we propose ABC used predictive valueand Particle Swarm Optimization (PSO) for time-varying
solution. We compare the optimal solution with ABC, theprevious method and the propose method.

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).
Nishida improves the artificial bee colony for time-varying
solution (ABCTV) [1]. The ABCTV can not search locally.
We propose the ABCTV modified employed bee. We calculate v by the predictive value. The predictive value iscalculated by diﬀerence between best solutions by assumeing that the optimal solution is constant motion. Therefore,
v is calculated by Eq. (4).

2. Artificial Bee Colony algorithmvid (t + 1) = xid (t) + ϕid (xid (t) − xk d (t))+ψid (xpredict (t) − xk d (t)).

Karaboga has proposed an Artificial Bee Colony (ABC)algorithm in 2005. The ABC algorithm is based on real beebehavior and consist of 3 kinds of honeybee, employed bee,onlooker bee and scout bee. It has high performance when
the object function is high dimension. The procedure forsolving an optimization problem in the ABC algorithm isshown below.

(4)

According to this modification inspired by PSO, we expectthat the propose method obtains better performance.

4. Simulation result
We compare the result of Eq. (5).

Step 0. Initialize each total number of employed bees neand onlooker bee no , the colony size N = ne + no andthe total number of iterations tmax .

(x1 − 250 − 125 sin αt)22 · 402(x2 − 250 + 125 sin αt)2].
−2 · 402g(x1 , x2 , t) = 1 − exp[−Step 1. (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.

(5)

Equation (5) 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 parameters touse for simulation in Eq. (6).

Step 2. (1) New locations vi is generated by Eq. (2) andcalculated the fitness function value.
(2) Based on the fitness, the best location and fitness update.

ne = no = 50, tmax = 100, 000,

(6)

We compare the best value for 3 kinds movement speed of
optimal solution α. Table 1 shows that the best value ofeach method.

Step 3. (1) Based on the fitness, the probability pi is calculated by Eq. (3).
(2) Select the number of employed bee i based onpi , and Step1 is applied. This procedure has been repeated no times.

Table 1: Simulation results

Step 4. If function value of each i is better than function
value of all bees, the solution and the function bestvalue are updated.

α0.01

0.05

0.1

ABCABCTV
proposed method

1.08e-08
4.12e-07
4.28e-09

1.11e-06
3.34e-06
4.28e-09

4.11e-06
9.96e-05
3.52e-06

Step 5. The employed bee which has not been generate
the new location.

From Table 1, the best value of the propose method isbetter than the best value of ABCTV.

Step 6. Repeat steps 1 to 4 and output the solution.

5. Conclusion

Fitness function fi , new location vi and evaluations value
a are given by following equations:This study introduced the modified ABC for accurate
time-varying solution. We tried improvement of ABC, whereemployed bee modified by the diﬀerence of best locations
and the equation of Particle Swarm Optimization. We compared the best values of propose method, ABCTV andABC. As a result, the propose method performed better
than the other algorithms.

{fivid (t + 1)pi===

1
1 + g(xi )1 + |g(xi )|if g(xi ) ≥ 0

xid (t) + ϕid (xid (t) − xk d (t))
fi /ne∑(1)otherwisefn ,(2)

Reference(3)[1] Takeshi Nishida, “ Modification of ABC Algorithm for
Adaptation to Time-Varying Functions,” Electronics andCommunications in Japan, 2012.

i=1

where, g(xi ) expresses the objective function.

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