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and new selection schemes
Konrad Diwold · Andrej Aderhold ·
Alexander Scheidler · Martin Middendorf
Received: 22 November 2010 / Accepted: 7 July 2011 / Published online: 24 July 2011
© Springer-Verlag 2011
Abstract The artificial bee colony optimization (ABC) is
a population-based algorithm for function optimization that
is inspired by the foraging behavior of bees. The population
consists of two types of artificial bees: employed bees (EBs)
which scout for new, good solutions and onlooker bees (OBs)
that search in the neighborhood of solutions found by the
EBs. In this paper we study in detail the influence of ABC’s
parameters on its optimization behavior. It is also investigated
whether the use of OBs is always advantageous. Moreover,
we propose two new variants of ABC which use new methods
for the position update of the artificial bees. Extensive
empirical tests were performed to compare the new variants
with the standard ABC and several other metaheuristics on a
set of benchmark functions. Our findings show that the ideal
parameter values depend on the hardness of the optimization
goal and that the standard values suggested in the literature
should be applied with care. Moreover, it is shown that in
some situations it is advantageous to use OBs but in others it
is not. In addition, a potential problem of the ABC is identified,
namely that it performs worse on many functions when
the optimum is not located at the center of the search space.
K. Diwold (B) · M. Middendorf
Department of Computer Science,
University of Leipzig, Leipzig, Germany
e-mail: kdiwold@informatik.uni-leipzig.de
M. Middendorf
e-mail: middendorf@informatik.uni-leipzig.de
A. Aderhold
School of Biology, University of St. Andrews,
St. Andrews, Fife, UK
e-mail: aa796@st-andrews.ac.uk
A. Scheidler
IRIDIA, CoDE, Université Libre de Bruxelles, Brussels, Belgium
e-mail: ascheidler@iridia.ulb.ac.be
Finally it is shown that the new ABC variants improve the
algorithm’s performance and achieve very good performance
in comparison to other metaheuristics under standard as well
as hard optimization goals.
Keywords Swarm intelligence · Artificial bee colony
optimization · Function optimization
1 Introduction
Bio-inspired computation, i.e., the application of biological
principles in the context of computation, is as old as computer
science itself. Based on biological principles, several
prominent computational frameworks such as evolutionary
computation and neural networks have been developed (for
an extensive review of bio-inspired computation the interested
reader should refer to [13]).
A prominent subfield of bio-inspired computation is
swarm intelligence [8]. It applies concepts found in the collective
behavior of swarms such as fish shoals, bird flocks or
social insects to problems in various domains such as robotics
or optimization [7]. In optimization, swarm intelligence is
probably best known for ant colony optimization [11], which
utilizes the concept underlying the pheromone laying behavior
of ants; and particle swarm optimization (PSO), which
uses group flight guidance for optimization purpose [27].
In recent years bee-inspired algorithms have emerged
in the field of swarm intelligence. These algorithms are
based on mechanisms underlying the behavior of honeybees
and have been successfully applied to various problem
domains such as optimization [4], robotics [38], network
routing [44], multi-agent systems [31], and protein structure
prediction [3].
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150 Memetic Comp. (2011) 3:149–162
Bee-inspired algorithms do not have a unified foundation,
but are based on different behavioral concepts
(see [21] or [10] for an in-depth review on bee-inspired optimization
approaches). In general one can distinguish between
two classes of algorithms: algorithms based on the mating
behavior of honeybees, and algorithms based on their foraging
behavior. Furthermore, a recent study [9] suggests that the
nest-site selection behavior of honeybees involves principles
that are interesting from an optimization point of view.
Mating-inspired algorithms draw their inspiration from
the genetic diversity underlying a bee colony. Genetic diversity
has been shown to be a driving factor in the ecological
success of bees [33] and is due to the polyandrous behavior
of a young queen on her maiden flight.Mating inspired algorithms
are closely related to evolutionary computation and
either introduce new bee-inspired mutation/crossover operators
in that context (e.g., [26,37]) or evolve populations by
imitating a queen’s maiden flight (e.g., [1,32]).
The second kind of algorithms are inspired by foraging
behavior. Foraging behavior of honeybees constitutes a
decentralized process that works on the basis of decisions of
individual bees. It enables a colony tomaintain a good ratio of
exploitation and exploration of food sources. In addition, foraging
is adaptive, meaning that a colony’s foraging effort can
adapt toward changing needs for resources if necessary [6].
Scouts that successfully locate a resource will return to the
hive and promote that resource by means of awaggle dance in
order to recruit other bees to forage on that resource [39]. As
well as the site’s distance and direction, the bee’s dance can
also encode its quality. Using this mechanism foragers can
distribute themselves over the available resources in terms of
profitability. A recent study [12] has shown that the recruitment
strategies used by honeybees are especially beneficial if
resources are of poor quality, few in number, and of variable
quality. A number of optimization algorithms have been proposed
on the basis of foraging, such as the bees’ algorithm
(BA) [35], the bee colony optimization algorithm (BCO)
[42] and the artificial bee colony optimization algorithm
(ABC) [17].
In this paper (which is an extended version of our
paper “Artificial Bee Colony Optimization: A New Selection
Scheme and Its Performance” at NICSO 2010) the artificial
bee colony optimization algorithm (ABC) is studied.
ABC was introduced by Karaboga in 2005 [17] and constitutes
one of the most prominent approaches in the field of
bee-inspired algorithms. The algorithm has been applied to
various problem domains including the training of artificial
neural networks [19,25], the design of a digital filters [18],
solving constrained optimization problems [22], and the prediction
of the tertiary structures of proteins [3]. Its optimization
performance has been tested and compared to other optimization
methods such as Genetic Algorithms (GA), PSO,
Particle Swarm Inspired Evolutionary Algorithm (PS–EA),
Differential Evolution (DE), and different evolutionary strategies
[23,24,20,2].
The ABC algorithm works with a population of artificial
bees. The bees are divided into two groups—employed bees
(EBs) are responsible for finding and maintaining promising
solutions, and onlooker bees (OBs) for performing local
search at these solutions. The exploration (via the EBs) and
exploitation (via the OBs) is influenced by the qualities of
the solutions currently maintained by the EBs. If an EB’s
solution does not improve over a certain number of steps it
will abandon it’s current solution and choose a new random
solution in the search space (EBs choosing a new random
solution are referred to as scouts).
ABC is clearly one of the most applied bee inspired algorithms
but several interesting properties have not been studied
so far. Therefore, one aim of this paper is to fill this gap
and to examine in detail the influence of several ABC key
parameters (i.e., size of the bee population, the ratio between
the number of employed bees and onlooker bees, and the
solution-abandon limit) on the optimization behavior. Some
of these parameters have been considered before [2,17,24]
and suggestions have been made regarding their parameterization.
However, our study shows that is necessary to reconsider
these settings because good parameter values depend
strongly on the optimization context (e.g., hardness of goal).
Moreover, the ratio between onlooker and employed bees is
studied, which has not been investigated in detail before.We
also test the ABC’s optimization performance in scenarios
where the global optimum is not located in the center of the
search space (which is the typical for applications).
The second aim of this paper is to propose two variants
of the standard ABC algorithm that use new methods for the
selection of new positions. To show the quality of the new
variants of ABC their performance is tested against the standard
ABC and several other population-based optimization
heuristics on several benchmark functions.
This paper is structured as follows. In Sect. 2 the ABC is
described. The newvariants ofABCare introduced in Sect. 3.
The experimental setup is described in Sect. 4 and the experimental
results are presented in Sect. 5. Concluding remarks
and an outlook are given in Sect. 6.
2 Artificial bee colony optimization
The ABC algorithm [17] is a population based algorithm for
function optimization that can be seen as aminimal honeybee
foraging model. The artificial bee population consists of two
types of bees: employed bees (EBs) and onlooker bees (OBs).
In ABC the search space represents the environment and
each point in the search space corresponds to a food source
(solution) that the artificial bees can exploit. The quality of
a food source is given by the value of the function to be