6th International Forum on Advanced Technologies
March 9th-10 th, 2020,Tokushima, Japan

Modification of Artificial Bee Colony Algorithm
for Various Requirements
Ken Kamiyotsumoto1*, Yoko Uwate1, Thomas Ott2 and Yoshifumi Nishio1
Tokushima University, Tokushima 770-8501, Japan* E-mail: kamiyotsumoto@tokushima-u.ac.jp
2 Zurich University of Applied Sciences
Einsiedlerstrasse 31a, 8820 Waedenswil, Switzerland

1. Introduction
Optimization is to search optimal solution under condition. Beneﬁt of optimization is high eﬃciency.
Optimization is needed in various scenes. Combinatorial optimization problem is often solved by metaheuristicoptimization algorithms.
Many combinatorial optimization problems often results in local optima. Metaheuristic optimization
algorithms are provided good-quality solutions which are close to the optimal solution with less computationaleﬀort in these problems. These algorithms are developed to solve more efﬁciency and larger problems.
Metaheuristic optimization algorithms have Evolutionary Algorithm (EA), Swarm Intelligence (SI) algorithm,
local search, etc. In our study, we choose the SI.
SI is one of the artiﬁcial intelligence techniques. SI was born from swarm of insect. Examples existing innature are ant, bee and ﬁreﬂy, etc. In insect colonies, each insect has its the group in total appears to be highlyorganized. The applications of SI technique are a self-driving car and data mining. The good points of thistechnique are smaller control system and multi control by simple systems. SI algorithms have Artiﬁcial Bee
Colony Algorithm (ABC), Ant Colony Optimization(ACO), Particle Swarm Optimization (PSO), Fireﬂy
Algorithm (FA), etc [1]. ABC is used by our propose method.
ABC is idealized the social behavior of bees based on their feeding characteristics. ABC was proposed byKaraboga Dervis in 2005 [2]. Artiﬁcial intelligence algorithms have been demonstrated to show eﬀectivenessand eﬃciency to solve diﬃcult optimization problems [3]. ABC performs higher ability in high dimensional
optimization problem than other SI algorithms. However, demerit of ABC is that it can not search time-varying
function.
In previous study, we modiﬁed ABC for time-varying function (ABCTV) [4]. However, we can not ﬁnd
accurate solution. [5]In this study, we propose ABCTV in which the employed bee is improved by predictive value. We compare thebest value of the solution with ABC, ABCTV and the proposed method.
2. Experimental setup
The most of algorithms exclude time-varying solution. However, when we search optimal solution, we need toapply the both solutions (time-varying and not time-varying). In case of ABC, it can not be performed adapted
to environmental changing such as shifts in the optimal solution or variations of the cost function. The artiﬁcial
bee colony algorithm for time-varying solution (ABCTV) is proposed. ABCTV was modiﬁed 2 points. First,
when employed bee compares ﬁtness function values between 2 locations, previous location is re-evaluated foreach simulation count. Second, we calculate best ﬁtness function value for each simulation count. According tothese modiﬁcation, ABCTV can search time-varying solution. However, ABCTV can not search accurate
solution than the standard ABC.
We propose ABCTV in which the employed bee improves by prediction. The employed bee searches a newlocation by Eq. (1) in the standard ABC. However, ABC has problem point that the best solution follow foroptima. Therefore, we modify that the employed bee searches new location by the prediction position. Theprediction position is calculated diﬀerence of the employed bee between current best location and the previous
best location. According to we assume the optimal solution is uniform motion, we predict the location of thenext optimal solution from the diﬀerence between the two locations. Furthermore, we use equation of PSO toappend the predictive value. In PSO, position is calculated by Eq. (2).

6th International Forum on Advanced Technologies
March 9th-10 th, 2020,Tokushima, Japan𝑣𝑖𝑑 (𝑡 + 1) = 𝑥𝑖𝑑 (𝑡) + 𝜑𝑖𝑑 (𝑥𝑖𝑑 (𝑡) − 𝑥𝑘𝑑 (𝑡))𝑣𝑖𝑑 (𝑡 + 1) = 𝑥𝑖𝑑 (𝑡) + 𝜑 (𝑥𝑖𝑗 (𝑡) − 𝑥𝑘𝑗 (𝑡)) + 𝜓 (𝑦𝑗 (𝑡) − 𝑥𝑖𝑗 (𝑡))

(1)
(2)

where 𝑦𝑗 is information of global best solution and 𝑥𝑘𝑗 is information of local best solution. PSO use
information of global best solution to guide searching. This convert the predictive value. From the beginning of
the simulation employed bee searches new location by using Eq. (3).
𝑣𝑖𝑑 (𝑡 + 1) = 𝑥𝑖𝑑 (𝑡) + 𝜑1𝑖𝑑 (𝑥𝑖𝑑 (𝑡) − 𝑥𝑘𝑑 (𝑡)) + 𝜑2𝑖𝑑 (𝑥𝑝𝑟𝑒𝑑𝑖𝑐𝑡 (𝑡) − 𝑥𝑘𝑑 (𝑡))(3)

𝜑 is a uniform random parameter in [0, C], where C is a nonnegative constant. In this study, we set 5 kinds C(0.5, 1.0, 2.0, 3.0, 4.0). Furthermore, the proposed method is expected to have better performance by combining
improved ABCTV and ABC.
3. Results and discussion
Firstly, in order to evaluate the performance of the propose method, we compare the result of Eq. (4). Figure 1shows the shape of this function.
(𝑥1 − 250 − 125𝑠𝑖𝑛𝛼𝑡) (𝑥2 − 250 + 125𝑐𝑜𝑠𝛼𝑡)𝑔(𝑥1 , 𝑥2 , 𝑡) = 1 − 𝑒𝑥𝑝 [−−]
(4)
2・402
2・402
Equation (4) simulates a visual tracking problem. The
distribution of the minimum value represented by a Gaussianfunction moves continuously in the ﬁgure, and the problem of
tracking this movement is assumed. The optimal function
value is 0, and position along a circle of radius 125 centeredat (𝑥1 , 𝑥2 ) = (250, 250), then return its original position in(2π/α) steps. k means time that is approximated by simulation
count. We express the constant value to use for simulation inEq. (5).
𝑣𝑖𝑑 (𝑡 + 1) = 𝑥𝑖𝑑 (𝑡) + 𝜑𝑛𝑒 = 𝑛𝑜 = 50, 𝑡𝑚𝑎𝑥 = 100000 (5) Fig. 1. Shape of unimodal time-varying function
We compare the best value for 7 kinds movement speed of optimal solution α (α = 0.01, 0.05, 0.10, 0.15, 0.20,0.25, 0.30). The best solution is the smallest value in results of 15 times simulations. Table 1 shows that the bestvalue of each method. From Table I, the best value of the propose method is better than the best value of ABCTV.
Especially, the propose method when C = 3.0 has best performance. However, many of the proposed methods
become less effective as α increases. This is reason that the movement of the solution becomes discrete as αincreases.
Table 1. Simulation result (unimodal time-varying)
function6th International Forum on Advanced Technologies
March 9th-10 th, 2020,Tokushima, Japan
Secondly, we confirm the proposed method has the ability to search for multimodal time-varying solutions. We
compare the result of Eq. (6).

𝑔(𝑥1 , 𝑥2 , 𝑡) = 1 − [+sin 𝛽𝑡 + 121 (𝑥1 − 125)2 (𝑥2 − 375)2
𝑒𝑥𝑝 {− (+)}
2402
402

sin(−𝛽𝑡) + 1
21 (𝑥1 − 375)2 (𝑥2 − 125)2
𝑒𝑥𝑝 {− (+)}]
2402402(6)

Figure 4 shows the shape of this function. Multiple
depressed area expressed by Gaussian function
move discontinuously by repeating appearance anddisappearance. Optimal value is assumed to be
between 0 and 0.5. The optimal position is switchedbetween (125,375) and (375,125) in a set period.
𝛽 means variation of object function for each step.
From Table 2, the best value of the propose method
is better than the best value of ABCTV and ABC.
Especially, the propose method when C = 0.5 hasbest performance.
Fig. 2. Shape of multimodal time-varying function
Table 2. Simulation result (multimodal time-varying)
function

4. Conclusion
This study shows ABC modified that employed bee is changed by predictive value because this algorithm do
not applied for accurate time-varying solution. We tried improvement of ABC, where employed bee searches
new position by predictive value. The predictive value is calculated by difference between best solutions byassuming that optimal solution is constant motion. Furthermore, the predictive value is append searchingequation of employed bee by inspired from PSO. We set the proposed method has 5 kinds of range of random
value. We compared the best values of the proposed method, the previous method and ABC. As a result, even if
optimal solution is discrete, the proposed method could search better value than other algorithms. Therefore, theproposed method is better performance than other methods. In the future work, we would like to investigate themechanism of the proposed method in detail. Furthermore, we try to search high dimensional problems.
References[1] X. S. Yang, “Nature-Inspired Metaheuristic Algorithms Second Edition,”Luniver Press, 2010.
[2] D. Karaboga, “An idea based on honeybee swarm for numerical optimization,” Technical Report TR06, 2005.
[3] I. Iimura and S. Nakayama, “Search Performance Evaluation of Artificial Bee Colony Algorithm on HighDimensional Function Optimization,” Transactions of the Institute of Systems, Control and Information
Engineers, vol. 24, pp. 97-99, 2011.
[4] T. Nishida, “Modification of ABC Algorithm for Adaptation to Time-Varying Functions,” Electronics andCommunications in Japan, vol. 96,2013.
[5] K. Kamiyotsumoto, T. Ott, Y. Uwate and Y. Nishio, “Artificial Bee Colony Algorithm for Time-Varying
Optimization,” Proceedings of RISP International Workshop on Nonlinear Circuits, Communications and Signal
Processing (NCSP’19), pp. 382-385, 2019.