Artificial Bee Colony Algorithm withHigh Robustness for Time-Variable Solutions†K. Kamiyotsumoto, †Y. Uwate , ‡T. Ott and †Y. Nishio†Tokushima University{kamiyotsumoto,uwate,nishio}@ee.tokushima-u.ac.jp‡Zurich University of Applied Sciences‡thomas.ott@zhaw.ch
Recently, optimization problems have drawn attention. Optimization is to search for an optimalsolution under condition. The advantage of optimization is to design or plan high eﬃciently. Theseproblems are very diﬃcult to solve because many problems have nonlinearity and are solved muchtime generally. Thus, optimization problem is often solved by eﬃcient optimization algorithms.
Metaheuristic optimization algorithms are provided good-quality solutions which are close tothe optimal solution with less computational eﬀort in these problems. These algorithms are developed to solve more eﬃciency and larger problems. Metaheuristic optimization algorithms havecharacteristics that are easy to improve in order to solve many problems. Metaheuristic optimization algorithms have Evolutionary Algorithm (EA), Swarm Intelligence (SI) algorithm, local
search, etc.
SI is one of the artificial intelligence techniques. SI aims to design algorithms with inspirationin the collective and intelligent behavior of insects and other animals. SI algorithms have Ant
Colony Optimization (ACO), Particle Swarm Optimization (PSO), Artificial Bee Colony (ABC)algorithm, etc [1]. Karaboga has proposed an Artificial Bee Colony (ABC) algorithm in 2005. TheABC 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 [2]. The
procedure for solving an optimization problem in the ABC algorithm is shown below.
Step 0. Initialize each total number of employed bees ne and onlooker bee no , the colony size
N = ne + no and the total number of iterations tmax .
Step 1. (1) Set the locations of the xi . i is the number of the employed bee.
(2) Calculate the fitness fi in the initial arrangement by Eq. (1). The best fi and initialarrangement are stored.
Step 2. (1) New locations vi is generated by Eq. (2) and calculated the fitness function value.
(2) Based on the fitness, the best location and fitness update.
Step 3. (1) Based on the fitness, the probability pi is calculated by Eq. (3).
(2) Select the number of employed bee i based on pi , and Step1 is applied. This procedure
has been repeated no times.
Step 4. If function value of each i is better than function value of all bees, the solution and thefunction best value are updated.
Step 5. The employed bee which has not been generate the new location.
Step 6. Repeat steps 1 to 4 and output the solution.
14

Fitness function fi , new location vi and evaluations value a are given by following equations:

1if g(xi ) ≥ 0
fi =  1 + g(xi ) 1 + |g(x )|otherwise
ivid (t + 1) = xid (t) + ϕid (xid (t) − xkd (t))
ne∑pi = f i /

fn ,

(1)
(2)
(3)

i=1

where, g(xi ) expresses the objective function.
The most of algorithms exclude time-varying solution. However, when we implement SI algorithm in the system, we need to apply the both solutions (time-varying and not time-varying)for high robustness of the system. It is important to search optimal solution under various conditions. Thus, Nishida improves the artificial bee colony for time-varying solution (ABCTV) [3].
The ABCTV can not search locally. We propose the ABCTV modified employed bee. We calculate optimal solution by the predictive value. The predictive value is calculated by diﬀerence
between best solutions by assumeing that the optimal solution is constant motion. Therefore, v iscalculated by Eq. (4).
vid (t + 1) = xid (t) + ϕid (xid (t) − xkd (t))+ψid (xpredict (t) − xkd (t)).

(4)

According to this modification, we expect that the propose method obtains better performance.
We compare the optimal solution with ABC, the previous method and the propose method.

References[1] X. S. Yang, “Nature-Inspired Metaheuristic Algorithms Second Edition,” Luniver Press, 2010.
[2] Guopu Zhu, Sam Kwong, “Gbest-guided artificial bee colony algorithm for numerical function
optimization,”Applied Mathematics and Computation, pp.3166-3173, 2010.
[3] Takeshi Nishida, ”Modification of ABC Algorithm for Adaptation to Time-Varying Functions,” IEEJ Transactions on Electronics, Information and Systems, pp.584-591, 2011.

15