Bat Algorithm: Literature Review and Applications

Abstract

Bat algorithm (BA) is a bio-inspired algorithm developed by Xin-She Yang in 2010 and BA has been found to be very efficient. As a result, the literature has expanded significantly in the last three years. This paper provides a timely review of the bat algorithm and its new variants. A wide range of diverse applications and case studies are also reviewed and summarised briefly here. In addition, we also discuss the essence of an algorithm and the links between algorithms and self-organisation. Further research topics are also discussed.

Full text

Int. J. Bio-Inspired Computation, Vol. 5, No. 3, 2013 1
Bat Algorithm: Literature Review and
Applications
Xin-She Yang
School of Science and Technology, Middlesex University, The Burroughs, London
NW4 4BT, United Kingdom.
Xingshi He
School of Science, Xian Polytechnic University, No. 19 Jinhua South Road, Xian
710048, China
Abstract: Bat algorithm (BA) is a bio-inspired algorithm developed by Xin-She Yang
in 2010 and BA has been found to be very efficient. As a result, the literature has
expanded significantly in the last three years. This paper provides a timely review of the
bat algorithm and its new variants. A wide range of diverse applications and case studies
are also reviewed and summarized briefly here. In addition, we also discuss the essence
of an algorithm and the links between algorithms and self-organization. Further research
topics are also discussed.
Keywords: Algorithm; bat algorithm; cuckoo search; firefly algorithm; eagle strategy;
nature-inspired algorithm; optimisation; metaheuristics.
Reference to this paper should be made as follows: Yang, X.-S., and He, X., (2013) ‘Bat
Algorithm: Literature review and applications’, Int. J. Bio-Inspired Computation, Vol. 5,
No. 3, pp.141–149.
1 Introduction
Modern optimisation algorithms are often nature-
inspired, typically based on swarm intelligence. The
ways for inspiration are diverse and consequently
algorithms can be many different types. However, all
these algorithms tend to use some specific characteristics
for formulating the key updating formulae. For example,
genetic algorithms were inspired by Darwinian evolution
characteristics of biological systems, and genetic
operators such as crossover, mutation and selection of
the fittest are used. Solutions in genetic algorithms
are represented as chromosomes or binary/real strings.
On the other hand, particle swarm optimisation (PSO)
was based on the swarming behaviour of birds and
fish, and this multi-agent system may have emergent
characteristics of swarm or group intelligence (Kennedy
and Eberhart, 1995). Many variants of PSO and
improvements exist in the literature, and many new
metaheuristic algorithms have been developed (Cui,
2009; Yang, 2010; Yang and Deb, 2010b; Yang et al.,
2011; Yang et al., 2013).
Algorithms such as genetic algorithms and PSO can
be very useful, but they still have some drawbacks
in dealing with multimodal optimization problems.
One major improvement is the firefly algorithm (FA)
which was based on the flashing characteristics of
tropical fireflies (Yang, 2008a; Yang, 2013b). The
attraction behaviour, light intensity encoding, and
distance dependence provide a surprising capability to
enable firefly algorithm to handle nonlinear, multimodal
optimization problems efficiently. Furthermore, cuckoo
search (CS) was based on the brooding behaviour
of some cuckoo species (Yang and Deb, 2009; Yang
and Deb, 2010b; Yang and Deb, 2013; Gandomi et
al, 2013b) which was combined with L´evy flights.
The CS algorithm is efficient because it has very
good convergence behaviour that can be proved using
Markovian probability theory. Other methods such as
eagle strategy are also very effective (Yang and Deb,
2010a; Gandomi et al, 2012). In many cases, efficient
randomisation techniques can help to enhance the
performance of an algorithm (Yang, 2011b; Gandomi et
al., 2013a).
As a novel feature, bat algorithm (BA) was based on
the echolocation features of microbats (Yang, 2010), and
BA uses a frequency-tuning technique to increase the
diversity of the solutions in the population, while at the
same, it uses the automatic zooming to try to balance
exploration and exploitation during the search process
by mimicking the variations of pulse emission rates and
loudness of bats when searching for prey. As a result,
it proves to be very efficient with a typical quick start.
Obviously, there is room for improvement. Therefore,
this paper intends to review the latest developments of
Copyright
c
 2008 Inderscience Enterprises Ltd.
Copyright
c
 2009 Inderscience Enterprises Ltd.
Pages 141-149 (2013).

2 Bat Algorithm: Literature Review and Applications
the bat algorithm. The paper is organized as follows:
Section 2 introduces the self-organization characteristics
of algorithms. Section 3 introduces the basic behaviour
of echolocation and the standard formulation of the bat
algorithm. Section 4 provides a brief description of the
variants of BA, and Section 5 highlights the diverse
applications of bat algorithm and its variants. Finally,
Section 6 provides some discussions and topics for further
research.
2 Magic Formula for Algorithms?
2.1 Essence of An Algorithm
In essence, an algorithm is a procedure to generate
outputs from given inputs. Numerically speaking, an
optimization algorithm generates a new solution x
t+1
to
a given problem from a known solution x
t
at iteration
or time t. In general, we have
x
t+1
= A(x
t
, p(t)), (1)
where A is a nonlinear mapping from a given solution, or
d-dimensional vector, x
t
to a new solution vector x
t+1
.
The algorithm A has k algorithm-dependent parameters
p(t) = (p
1
, p
2
, ..., p
k
) that can be time-dependent and
can thus be tuned if necessary.
2.2 Self-Organizing Systems
Self-organization may occur in many systems, from
physical and chemical to biological and artificial
systems. Emergent phenomena such as Releigh-B´enard
convection, Turing pattern formation, and organisms
and thunderstorms can all be called self-organization
(Ashby, 1962; Keller, 2009). Though there is no universal
theory for self-organizing processes, some aspects
of self-organization can partly be understood using
theories based on nonlinear dynamical systems, far-from-
equilibrium multiple interacting agents (Prigogine and
Nicolois, 1967), and closed-system under unchanging
laws (Ashby, 1962). As pointed out by cyberneticist and
mathematician Ross Ashby, every isolated determinate
dynamic system, obeying unchanging laws, will
ultimately develop some sort of ‘organisms’ that are
adapted to their ‘environments’ (Ashby, 1962).
Going to equilibrium is trivial for simple systems.
However, for a complex system, if its size is so large
that its equilibrium states are just a fraction of the vast
number of possible states, and if the system is allowed
to evolve long enough, some self-organized structures
may emerge. The changes in environments can apply
pressure on the system to re-organize and adapt to such
changes. If the system have sufficient perturbations or
noise, often working at the edge of the chaos, some
spontaneous formation of structures will emerge as the
systems move, far-from-equilibrium, and select some
states, thus reducing the uncertainty or entropy.
Mathematically speaking, the state set S of a complex
system such as a machine, may change from initial states
S(ψ) to other states S(φ), subject to the change of a
parameter set α(t) which can be time dependent. That
is,
S(ψ)
α(t)
−→ S(φ), (2)
where α(t) must come from external conditions such as
the heat flow in Raleigh-B´enard convection, not from
the states S themselves. Obviously, S + α(t) can be
considered as a larger, closed system (Ashby, 1962). In
this sense, self-organization is equivalent to a mapping
from some high-entropy states to low-entropy states.
An optimization algorithm can be viewed as a
complex, dynamical system. If we can consider the
convergence process as a self-organizing process, then
there are strong similarities and links between self-
organizing systems and optimization algorithms.
2.3 Algorithms as Self-Organization
To find the optimal solution x
∗
to a given optimization
problem S with often an infinitely number of states is to
select some desired states φ from all states ψ, according
to some predefined criterion D. We have
S(ψ)
A(t,D,p)
−→ S(φ(x
∗
)), (3)
where the final converged state φ corresponds to an
optimal solution x
∗
to the problem of interest. The
selection of the system states in the design space is
carried out by running the optimization algorithm A.
The behavior of the algorithm is controlled by p, the
initial solution x
t=0
and the stopping criterion D. We
can view the combined S + A as a complex system with
a self-organizing capability.
The change of states or solutions of the problem
of interest is controlled by the algorithm A. In
many classical algorithms such as hill-climbing, gradient
information is often used to select states, say, the
minimum value of the landscape, and the stopping
criterion can be a given tolerance or accuracy, or zero
gradient, etc.
Alternatively, an algorithm can act like a tool to tune
a complex system. If an algorithm does not use any
state information of the problem, then it is more likely
to be versatile to deal with many types of problems.
However, such black-box approaches can also imply
that the algorithm may not be efficient as it could
be for a given type of problem. For example, if the
optimization problem is convex, algorithms that use
such convexity information will be more efficient than
the ones that do not use such information. In order to
select states/solutions efficiently, the information from
the search process should be used to enhance the search
process. In many cases, such information is often fed into
the selection mechanism of an algorithm. By far the most
widely used selection mechanism is to identify and keep

X. S. Yang 3
the best solution found so far. That is, some form of
‘survival of the fitness’ is used.
Optimization algorithms can very diverse. There are
several dozens of widely used algorithms. The main
characteristics of different algorithms will only depend
on the actual, often highly nonlinear or implicit, forms
of A(t) and their parameters p(t).
In many situations concerning optimization, the
generation and verification of the new solutions
can often involve computationally expensive computer
simulations or even measurements of the physical
system. In such cases, the expensive model of the
system under consideration is often replaced by its
cheaper representation, so-called surrogate model, and
the algorithm A uses that model to produce a new
solution. The parameters p(t) may then include variables
that are used to align the surrogate with the expensive
model to make it reliable representation of the latter
(Koziel and Yang, 2011).
2.4 An Ideal Algorithm?
In an ideal world, we hope to start from any initial guess
solution and wish to get the best solution in a single
step. That is, to use the minimal computational effort. In
other words, this is essentially saying that the algorithm
simply has to tell what the best answer is to any given
problem in a single step! You may wonder if such an
algorithm exists. In fact, the answer is yes, for a very
specific type of problem — quadratic, convex problems.
We know Newton-Raphsons method is a root-finding
algorithm. It can find the roots of f(x) = 0. As the
minimum or maximum of a function f(x) has to
satisfy the critical condition f (x) = 0, therefore, this
optimization problem now becomes a problem of finding
the roots of f(x). Newton-Raphson method provides the
following iteration formula
x
t+1
= x
t
−
f
0
(x
t
)
f
00
(x
t
)
. (4)
For a quadratic function, for example, f (x) = x
2
, if we
start from a fixed location, x
0
= a at t = 0, we have
f
0
(a) = 2a and f
00
(a) = 2. Then, we have
x
1
= x
0
−
f
0
(x
0
)
f
00
(x
0
)
= a −
2a
2
= 0, (5)
which is exactly the optimal solution f
min
= 0 at x
∗
= 0.
This solution is also globally optimal. That is to say,
we have found the global optimum in a single step. In
fact, for any quadratic functions that are also convex,
Newton-Raphson is an ideal algorithm. However, the
world is not convex and certainly not quadratic, real-
world problems are often highly nonlinear, and therefore
there is no ideal algorithm in general.
For non-deterministic polynomial-time (NP) hard
problems, or NP-hard problems, there is no known
efficient algorithm at all. Such hard problems require
a huge amount of research efforts to search for specific
techniques that are still not satisfactory in practice.
These challenges can also be a driving force for more
active research.
2.5 The Magic Formulae?
The ultimate aim for optimization and algorithm
researchers is to find a magic formula or method that
works for many problems, like the Newton-Raphson
method for quadratic functions. We wish it could work
like a ‘magic’ to provide the best solution for any
problem in a few steps. However, such formulae may
never exist.
As optimization algorithms are iterative, an
algorithm to solve a given problem Q can be written as
the following generic formula
x
t+1
= g(x
t
, p, Q), (6)
which forms a piece-wise trajectory in the search space.
This algorithm depends on a parameter p, starting with
initial guess x
0
. This iterative path will depend on the
problem (Q) or its objective function f(x). However,
as algorithms nowadays tend to use multiple agents as
those in swarm intelligence, we have to extend the above
equation to a population of n agents/solutions
[x
1
, x
2
, x
3
, ..., x
n
]
t+1
= g([x
1
, x
2
, x
3
, ..., x
n
]
t
, [p
1
, p
2
, p
3
, ..., p
k
]
t
, Q), (7)
which has a population size of n and depends
on k different algorithm-dependent parameters. Each
iteration will produce n new, often different, solutions
[x
1
, ..., x
n
]. Modern metaheuristic algorithms have
stochastic components, which means some of these
k parameters can be drawn from some probability
distributions. If we wish to express the randomness more
explicitly, we can rewrite the above as
[x
1
, x
n
, ..., x
n
]
t+1
= g([x
1
, x
2
, ..., x
n
]
t
,
[p
1
, ..., p
k
]
t
, [
1
, ..., 
m
]
t
, Q), (8)
where m is the number of random variables that
are drawn from some probability distributions such as
uniform, Gaussian or L´evy distributions (Yang, 2008a;
Yang, 2008b; Yang, 2008c; Yang, 2013a; Yang et al.,
2013). In some cases as those in cuckoo search, these
random variables can also be drawn from a L´evy
distribution (Yang and Deb, 2009; Yang and Deb,
2010b).
Though there is no magic formula, each algorithm
strives to use fewer iterations (or smaller t) as possible.
The only difference among algorithms is the exact form
of g(.). In fact, sometimes, the procedure g(.) can be
divided into many sub-steps or procedures with different
branches, so that these branches can be used in a
random manner during iterations, and one good example
is the Eagle Strategy that uses a two-stage iterative
strategy (Yang and Deb, 2010a). That is the essence
of all contemporary swarm intelligence and bio-inspired
metaheuristic algorithms.

4 Bat Algorithm: Literature Review and Applications
3 The Standard Bat Algorithm
The standard bat algorithm, developed by Xin-She
Yang in 2010, was based on the echolocation or bio-
sonar characteristics of microbats (Yang, 2010). Before
we outline the details of the algorithm, let us briefly
introduce the echolocation.
3.1 Echolocation of Microbats
There are about 1000 different species of bats (Colin,
2000). Their sizes can vary widely, ranging from the tiny
bumblebee bats of about 1.5 to 2 grams to the giant
bats with a wingspan of about 2 m and may weight up
to about 1 kg. Most bats uses echolocation to a certain
degree; among all the species, microbats use echolocation
extensively, while megabats do not.
Microbats typically use a type of sonar, called,
echolocation, to detect prey, avoid obstacles, and locate
their roosting crevices in the dark. They can emit a very
loud sound pulse and listen for the echo that bounces
back from the surrounding objects (Richardson, 2008).
Their pulses vary in properties and can be correlated
with their hunting strategies, depending on the species.
Most bats use short, frequency-modulated signals to
sweep through about an octave, and each pulse lasts a
few thousandths of a second (up to about 8 to 10 ms)
in the frequency range of 25kHz to 150 kHz. Typically,
microbats can emit about 10 to 20 such sound bursts
every second, and the rate of pulse emission can be
sped up to about 200 pulses per second when homing
on their prey. Since the speed of sound in air is about
v = 340 m/s, the wavelength λ of the ultrasonic sound
bursts with a constant frequency f is given by λ = v/f,
which is in the range of 2mm to 14mm for the typical
frequency range from 25kHz to 150 kHz. Interestingly,
these wavelengths are in the same order of their prey
sizes.
Though in reality microbats can also use time delay
between their ears and loudness variations to sense three-
dimensional surroundings, we are mainly interested in
some features of echolocation so that we can some link
them with the objective function of an optimization
problem, which makes it possible to formulate a smart,
bat algorithm.
3.2 Bat Algorithm
Based on the above description and characteristics of
bat echolocation, Xin-She Yang (2010) developed the bat
algorithm with the following three idealised rules:
1. All bats use echolocation to sense distance, and
they also ‘know’ the difference between food/prey
and background barriers in some magical way;
2. Bats fly randomly with velocity v
i
at position x
i
with a frequency f (or wavelength λ) and loudness
A
0
to search for prey. They can automatically
adjust the wavelength (or frequency) of their
emitted pulses and adjust the rate of pulse emission
r ∈ [0, 1], depending on the proximity of their
target;
3. Although the loudness can vary in many ways,
we assume that the loudness varies from a large
(positive) A
0
to a minimum constant value A
min
.
For simplicity, we do not use ray tracing in
this algorithm, though it can form an interesting
feature for further extension. In general, ray tracing
can be computationally extensive, but it can be a
very useful feature for computational geometry and
other applications. Furthermore, a given frequency is
intrinsically linked to a wavelength. For example, a
frequency range of [20kHz, 500kHz] corresponds to a
range of wavelengths from 0.7mm to 17mm in the
air. Therefore, we can describe the changes either in
terms of frequency f or wavelength λ to suit different
applications, depending on the ease of implementation
and other factors.
3.3 Bat Motion
Each bat is associated with a velocity v
t
i
and a location
x
t
i
, at iteration t, in a d-dimensional search or solution
space. Among all the bats, there exists a current best
solution x
∗
. Therefore, the above three rules can be
translated into the updating equations for x
t
i
and
velocities v
t
i
:
f
i
= f
min
+ (f
max
− f
min
)β, (9)
v
t
i
= v
t−1
i
+ (x
t−1
i
− x
∗
)f
i
, (10)
x
t
i
= x
t−1
i
+ v
t
i
, (11)
where β ∈ [0, 1] is a random vector drawn from a uniform
distribution.
As mentioned earlier, we can either use wavelengths
or frequencies for implementation, we will use f
min
=
0 and f
max
= O(1), depending on the domain size of
the problem of interest. Initially, each bat is randomly
assigned a frequency which is drawn uniformly from
[f
min
, f
max
]. For this reason, bat algorithm can be
considered as a frequency-tuning algorithm to provide
a balanced combination of exploration and exploitation.
The loudness and pulse emission rates essentially provide
a mechanism for automatic control and auto-zooming
into the region with promising solutions.
3.4 Variations of Loudness and Pulse Rates
In order to provide an effective mechanism to control the
exploration and exploitation and switch to exploitation
stage when necessary, we have to vary the loudness A
i
and the rate r
i
of pulse emission during the iterations.
Since the loudness usually decreases once a bat has found
its prey, while the rate of pulse emission increases, the
loudness can be chosen as any value of convenience,
between A
min
and A
max
, assuming A
min
= 0 means that

X. S. Yang 5
a bat has just found the prey and temporarily stopped
emitting any sound. With these assumptions, we have
A
t+1
i
= αA
t
i
, (12)
and
r
t+1
i
= r
0
i
[1 − exp(−γt)], (13)
where α and γ are constants. In essence, here α is similar
to the cooling factor of a cooling schedule in simulated
annealing. For any 0 < α < 1 and γ > 0, we have
A
t
i
→ 0, (14)
and
r
t
i
→ r
0
i
, as t → ∞. (15)
In the simplest case, we can use α = γ, and we have used
α = γ = 0.9 to 0.98 in our simulations.
3.5 How to Discretize
The standard bat algorithm is for continuous
optimization. In order to deal with combinatorial
problems effectively, some modifications are needed.
Nakamura et al. (2012) extended the standard bat
algorithm to the so-called binary bat algorithm (BBA)
for feature selection. A key step is to convert continuous-
valued positions of bats into binary values using a
sigmoid funciton
S(x
t
i
) =
1
1 + exp[−x
t
i
]
, (16)
which leads to
x
t
i
=



1 if S(x
t
i
) > σ,
0 otherwise,
(17)
where σ is a random variable that can be drawn from
a uniform distribution U(0, 1). This transformation will
generate only binary states in a vast Boolean lattice,
and consequently it can deal with feature selection very
effectively (Nakumura et al., 2012).
4 Variants of Bat Algorithm
The standard bat algorithm has many advantages, and
one of the key advantages is that it can provide very
quick convergence at a very initial stage by switching
from exploration to exploitation. This makes it an
efficient algorithm for applications such as classifications
and others when a quick solution is needed. However, if
we allow the algorithm to switch to exploitation stage
too quickly by varying A and r too quickly, it may lead to
stagnation after some initial stage. In order to improve
the performance, many methods and strategies have
been attempted to increase the diversity of the solution
and thus to enhance the performance, which produced a
few good and efficient variants of bat algorithm.
From a quick literature survey, we found the following
bat algorithm variants:
• Fuzzy Logic Bat Algorithm (FLBA): Khan et al.
(2011) presented a variant by introducing fuzzy
logic into the bat algorithm, they called their
variant fuzzy bat algorithm.
• Multiobjective bat algorithm (MOBA): Yang
(2011a) extended BA to deal with multiobjective
optimization, which has demonstrated its
effectiveness for solving a few design benchmarks
in engineering.
• K-Means Bat Algorithm (KMBA): Komarasamy
and Wahi (2012) presented a combination of K-
means and bat algorithm (KMBA) for efficient
clustering.
• Chaotic Bat Algorithm (CBA): Lin et al. (2012)
presented a chaotic bat algorithm using L´evy
flights and chaotic maps to carry out parameter
estimation in dynamic biological systems.
• Binary bat algorithm (BBA): Nakamura et al.
(2012) developed a discrete version of bat
algorithm to solve classifications and feature
selection problems.
• Differential Operator and L´evy flights Bat
Algorithm (DLBA): Xie et al. (2013) presented a
variant of bat algorithm using differential operator
and L´evy flights to solve function optimization
problems.
• Improved bat algorithm (IBA): Jamil et al.
(2013) extended the bat algorithm with a good
combination of L´evy flights and subtle variations
of loudness and pulse emission rates. They tested
the IBA versus over 70 different test functions and
proved to be very efficient.
There are other improvements and variants of bat
algorithm. For example, Zhang and Wang (2012) used
mutation to enhance the diversity of solutions and then
used for image matching. In addition, Wang et al.
(2012) also introduced mutation to the bat algorithm,
and Wang and Guo (2013) hybridized bat algorithm
with harmony search and have produced a hybrid
bat algorithm for numerical optimization of function
benchmarks.
On the other hand, Fister Jr et al. (2013) developed
a hybrid bat algorithm using differential evolution as
a local search part of bat algorithm, while Fister et
al. (2013) incorporate quaternions into bat algorithm
and presented a quaternion bat algorithm (QBA) for
computational geometry and large-scale optimization
problems with extensive rotations. It can be expected
that more variants are still under active research.
5 Applications of Bat Algorithm
The standard bat algorithm and its many variants mean
that the applications are also very diverse. In fact, since

6 Bat Algorithm: Literature Review and Applications
the original bat algorithm has been developed (Yang,
2010), bat algorithms have been applied in almost every
area of optimisation, classifications, image processing,
feature selection, scheduling, data mining and others. In
the rest of the paper, we will briefly highlight some of
the applications (Yang, 2010; Parpinelli and Lopes, 2011;
Yang et al., 2012a; Yang, 2012; Yang, 2013; Gandomi et
al., 2013).
5.1 Continuous Optimisation
Among the first set of applications of bat algorithm,
continuous optimisation in the context of engineering
design optimisation has been extensively studied, which
demonstrated that BA can deal with highly nonlinear
problems efficiently and can find the optimal solutions
accurately (Yang, 2010; Yang and Gandomi, 2012;
Yang, 2012; Yang et al., 2012a). Case studies include
pressure vessel design, car side design, spring and beam
design, truss systems, tower and tall building design and
others. Tsai et al. (2011) solved numerical optimisation
problems using bat algorithm.
In addition, Bora et al. (2012) optimised the brushless
DC wheel motors using bat algorithm with superior
results. BA can also handle multiobjective problems
effectively (Yang, 2011a).
5.2 Combinatorial Optimisation and Scheduling
From computational complexity point of view,
continuous optimization problems can be considered as
easy, though it may be still very challenging to solve.
However, combinatorial problems can be really hard,
often non-deterministic polynomial time hard (NP-
hard). Ramesh et al. (2013) presented a detailed study of
combined economic load and emission dispatch problems
using bat algorithm. They compared bat algorithm with
ant colony algorithm (ABC), hybrid genetic algorithm
and other methods, and they concluded that bat
algorithm is easy to implement and much superior to
other algorithms in terms of accuracy and efficiency.
Musikapun and Pongcharoen (2012) solved multi-
stage, multi-machine, multi-product scheduling
problems using bat algorithm, and they solved a class
of NP hard problems with a detailed parametric study.
They also implied that that the performance can be
improved by about 8.4% using optimal set of parameters.
5.3 Inverse Problems and Parameter Estimation
Yang et al. (2012b) use the bat algorithm to
study topological shape optimization in microelectronic
applications so that materials of different thermal
properties can be placed in such a way that the heat
transfer is most efficient under stringent constraints. It
can also be applied to carry out parameter estimation as
an inverse problem. If an inverse problem can be properly
formulated, then bat algorithm can provide better results
than least-squares methods and regularization methods.
Lin et al. (2012) presented a chaotic L´evy flight bat
algorithm to estimate parameters in nonlinear dynamic
biological systems, which proved the effectiveness of the
proposed algorithm.
5.4 Classifications, Clustering and Data Mining
Komarasamy and Wahi (2012) studied K-means
clustering using bat algorithm and they concluded that
the combination of both K-means and BA can achieve
higher efficiency and thus performs better than other
algorithms.
Khan et al. (2011) presented a study of a clustering
problem for office workplaces using a fuzzy bat
algorithm. Khan and Sahari (2012a) also presented a
comparison study of bat algorithm with PSO, GA,
and other algorithms in the context for e-learning, and
thus suggested that bat algorithm has clearly some
advantages over other algorithms. Then, Khan and
Sahari (2012b) also presented a study of clustering
problems using bat algorithm and its extension as a bi-
sonar optimization variant with good results.
On the other hand, Mishra et al. (2012) used bat
algorithm to classify microarray data, while Natarajan
et al. (2012) presented a comparison study of cuckoo
search and bat algorithm for Bloom filter optimization.
Damodaram and Valarmathi (2012) studied phishing
website detection using modified bat algorithm and
achieved very good results.
Marichelvam and Prabaharan (2012) used bat
algorithm to study hybrid flow shop scheduling problems
so as to minimize the makespan and mean flow time.
Their results suggested that BA is an efficient approach
for solving hybrid flow shop scheduling problems. Faritha
Banu and Chandrasekar (2013) used a modified bat
algorithm to record deduplication as an optimisation
approach and data compression technique. Their study
suggest that the modified bat algorithm can perform
better than genetic programming.
5.5 Image Processing
Abdel-Rahman et al. (2012) presented a study for full
body human pose estimation using bat algorithm, and
they concluded that BA performs better than particle
swarm optimization (PSO), particle filter (PF) and
annealed particle filter (APF).
Du and Liu (2012) presented a variant of bat
algorithm with mutation for image matching, and they
indicated that their bat-based model is more effective
and feasible in imagine matching than other models such
as differential evolution and genetic algorithms.
5.6 Fuzzy Logic and Other Applications
Reddy and Manoj (2012) presented a study of optimal
capacitor placement for loss reduction in distribution
systems using bat algorithm. It combined with fuzzy
logic to find optimal capacitor sizes so as to minimize

X. S. Yang 7
the losses. Their results suggested that the real power
loss can be reduced significantly.
Furthermore, Lemma et al. (2011) used fuzzy systems
and bat algorithm for exergy modelling, and later
Tamiru and Hashim (2013) applied bat algorithm to
study fuzzy systems and to model exergy changes in a
gas turbine.
At the time of writing when we searched the Google
scholar and other databases, we found other papers
on bat algorithm that were either just accepted or
conference presentations. However, these papers do not
yet have enough details to be included in this review.
In fact, as the literature is expanding, more and more
papers on bat algorithm are emerging, a further timely
review will be needed within the next two years.
6 Discussions and Conclusions
Likely many metaheuristic algorithms, bat algorithm has
the advantage of simplicity and flexibility. BA is easy
to implement, and such a simple algorithm can be very
flexible to solve a wide range of problems, as we have
seen in the above review.
6.1 Why Bat Algorithm is Efficient
A natural question is: why bat algorithm is so efficient?
There are many reasons for the success of bat-based
algorithms. By analysing the key features and updating
equations, we can summarize the following three key
points/features:
• Frequency tuning: BA uses echolocation and
frequency tuning to solve problems. Though
echolocation is not directly used to mimic the true
function in reality, frequency variations are used.
This capability can provide some functionality
that may be similar to the key feature used in
particle swarm optimization and harmony search.
Therefore, BA may possess the advantages of other
swarm-intelligence-based algorithms.
• Automatic zooming: BA has a distinct advantage
over other metaheuristic algorithms. That is,
BA has a capability of automatically zooming
into a region where promising solutions have
been found. This zooming is accompanied by the
automatic switch from explorative moves to local
intensive exploitation. As a result, BA has a quick
convergence rate, at least at early stages of the
iterations, compared with other algorithms.
• Parameter control: Many metaheuristic algorithms
used fixed parameters by using some, pre-tuned
algorithm-dependent parameters. In contrast, BA
uses parameter control, which can vary the
values of parameters (A and r) as the iterations
proceed. This provides a way to automatically
switch from exploration to exploitation when
the optimal solution is approaching. This gives
another advantages of BA over other metaheuristic
algorithms.
In addition, preliminary theoretical analysis by Huang
et al. (2013) suggested that BA has guaranteed global
convergence properties under the right condition, and
BA can also solve large-scale problems effectively.
6.2 Further Research Topics
However, there are still some important issues that
require more research. These key issues are: parameter-
tuning, parameter control and speedup of convergence.
Firstly, parameter-tuning is important for any
metaheuristic algorithm to work properly. In almost
all cases, the performance of an algorithm is largely
dependent on the parameters of the algorithm. To find
the best parameter settings, detailed parametric studies
have to be carried out. It is not known yet if there
is a method to automatically tune parameters for an
algorithm to achieve the optimal performance for a given
set of problems. This should be an important topic for
further research.
Secondly, associated with the parameter tuning, there
is an important issue of parameter control. In many
algorithms, the parameter settings are fixed, and these
settings will not vary during the iterations. It could be
advantageous and sometime necessary to vary the values
of algorithm-dependent parameters during the iterative
search process. How to vary or control these parameters
is another, higher level, optimisation problem, which
needs further studies. For the bat algorithm, we have
introduced the basic parameter control strategy, there is
still room for improvement. An open question is that:
what is the best control strategy so as to switch from
exploration to exploitation at the right time?
Finally, even though the bat algorithm and other
algorithms are efficient, it is still possible to improve
and enhance their performance further. However, how
to speed up the convergence of an algorithm is still a
very challenging question. It is hoped this this paper
can inspire more research in the near future. Future
research should focus on the theoretical understanding
of metaheuristic algorithms and large-scale problems in
real-world applications (Yang, 2005; Koziel and Yang,
2011; Yang and Koziel, 2011; Yang et al., 2012b).
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