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Abstract

This paper presents a review on glowworm swarm optimization (GSO) algorithm based methods. GSO is a current nature-inspired optimization algorithm that simulates the behavior of the lighting worms. GSO algorithm is suitable for a concurrent search of several solutions and dissimilar or equal objective function values. A number of reviews are provided that describe applications of GSO algorithms in different domains, such as clustering and various optimization problems.
International Journal of Information Technology (IJIT) Volume 3 Issue 2, Mar - Apr 2017
ISSN: 2454-5414 www.ijitjournal.org Page 49
A Review on Glowworm Swarm Optimization
T. Kalaiselvi [1], P. Nagaraja [2], Z. Abdul Basith [3]
Department of Computer Science and Applications,
The Gandhigram Rural Institute-Deemed University, Gandhigram, Dindigul.
Tamil Nadu India
ABSTRACT
This paper presents a review on glowworm swarm optimization (GSO) algorithm based methods. GSO is a current nature-
inspired optimization algorithm that simulates the behavior of the lighting worms. GSO algorithm is suitable for a concurrent
search of several solutions and dissimilar or equal objective function values. A number of reviews are provided that describe
applications of GSO algorithms in different domains, such as clustering and various optimization problems.
Keywords Clustering, Optimization, Swarm Intelligence, Glowworm Swarm Optimization.
I. INTRODUCTION
The behaviour of a solitary ant, bee, termite and wasp
often is too simple, but their combined and social actions are
of paramount consequence. The collective and social
behaviour of living creatures are motivated the researchers to
undertake the lessons of today what is known as Swarm
Intelligence (SI). Historically, the phrase SI was coined by
Beny and Wang in the context of cellular robotics [1]. A
group of researchers in different parts of the world currently
works almost at the same time to study the versatile behavior
of different living creatures and in particular the social insects.
The efforts to mimic such behaviors through computer
imitation finally resulted into the fascinating field of SI. SI
systems are typically made up of a population of simple
agents interacting locally with one another and with their
environment. Although there is normally no centralized
control structure dictating how individual agents must behave,
limited interactions between such agents often lead to the
emergence of global behavior. A lot of biological creatures
such as fish schools and bird flocks clearly display structural
order, with the behavior of the organisms so integrated that
even though they may change shape and direction, they appear
to move as a single coherent entity [2]. The main properties of
the collective behavior can be pointed out as follows and is
summarized in Figure 1.
The homogeneity is every bird in flock has the same
behavioral model. The flock moves without a leader, even
though temporary leaders seem to appear. The locality is
nearest flock-mates just influence the motion of each bird.
Vision is considered to be the most important senses for flock
organization. The collision avoidance is used to avoid
colliding with nearby flock mates. The velocity matching is
attempted to match velocity with nearby flock mates. The
flock centring is attempt to stay close to nearby flock mates
Individuals attempt to maintain a minimum distance between
themselves and others at all times. This rule is given the
highest priority and corresponds to a frequently observed
behavior of animals in nature [3]. If individuals are not
performing an avoidance maneuver they tend to be attracted
towards other individuals (to avoid being isolated) and to
align themselves with neighbors [4], [5].
II. GLOWWORM SWARM OPTIMIZATION
The Glowworm Swarm Optimization (GSO) is a original
swarm intelligence algorithm for optimization developed by
Krishnanand and Ghose which imitate the flashing behaviour
of glowworms [6]. Each glowworm carries a luminescence
amount called luciferin, which is decided by the function
value of glowworm’s current location. All through the course
of movement, glowworm identifies its neighbors based on
local-decision area and selects a neighbor which has a
luciferin value higher than its own using a probabilistic
mechanism and moves on the way to it [712]. The GSO
approach has been compared to the complete search algorithm,
Fig. 1 Major character of collective behaviour
RESEARCH ARTICLE OPEN ACCESS
International Journal of Information Technology (IJIT) Volume 3 Issue 2, Mar - Apr 2017
ISSN: 2454-5414 www.ijitjournal.org Page 50
the honey bee mating optimization, the firefly algorithm, the
Ant Bee Colony Optimization algorithm, and the Particle
Swarm Optimization algorithm. The experiments were passed
out using five level images and the experimental results
showed that the proposed GSO approach efficiently identifies
up to five thresholds that are very close to the optimal
thresholds identified by the complete search method.
Furthermore, compared to the new thresholding techniques,
the computational time of GSO is competitive taking the
second or third place behind the firefly algorithm and the
artificial bee colony algorithm.
III. GSO ALGORITHM
GSO is one of the popular modern swarm intelligence
method introduced by Krishnanand and Ghose [6]. GSO was
first used for optimizing multimodal functions with equivalent
or uneven plan function values. In GSO, glowworm swarm
S
,
which consists of
m
glowworms, is distributed in the
objective function search space. Each glowworm
)...1( mjgj
is assigned a random position
j
p
inside the
given function search space. Glowworm
carry its own
luciferin level
j
L
, and has the vision range called local
decision range
j
rd
. The luciferin level depends on the
objective function value and glowworm position. The
glowworm with a improved position is brighter than others,
and therefore, has a higher luciferin level value and is very
close to one of the optimal solutions. All glowworms seek the
neighborhood set within their restricted decision range, and
then move towards the brighter one within the neighborhood
set. Finally, most of the glowworms gather to make compact
groups in the function search space at multiple optimal
locations of the objective function. At first, all the glowworms
carry an equal luciferin level
)( 0
L
. The
rd
, radial sensor
range
s
r
are initialized with the same value
)( 0
r
. After that,
the iterative process consists of several luciferin updates and
glowworm movements are executed to find the optimal
solutions. Throughout the luciferin level update, the objective
function is evaluated at the current glowworm position
)( j
p
and then the luciferin level for all glowworms is used to
the new objective function values. The luciferin level
j
L
is
updated using the following equation:
(t))
j
γF(p)(t
j
ρ)L((t)
j
L11
(1)
where
)1( tLj
is the previous luciferin level for
glowworm
j
;
is the luciferin decay constant
))1,0((
;
is the luciferin enhancement fraction, and
))(( tpF j
represents the objective function value for
glowworm
j
at current glowworm position
)( j
p
;
t
is the
current iteration. After that, each glowworm
j
explores its
own neighbourhood region to extract the neighbors that have
the highest luciferin level by applying the following rule:
)()()()( tLtLandtrddifftNz jzjjzj
(2)
Where
d
is the distance and
z
is one of the closer
glowworms to glowworm
j
,
)(tNj
is the neighbourhood set,
jz
d
is the Euclidean distance between glowworm
j
and
glowworm
z
,
)(trdj
is the local decision range for
glowworm
j
, and
)(tLz
and
)(tLj
are the luciferin levels
for glowworm
z
and
j
, respectively. After that, to select the
best neighbor from the neighbourhood set, the probabilities
for all neighbors are calculated using the following equation:
)( )()(
)()(
tNk jk
jz
jz
jtLtL
tLtL
prob
(3)
Where
z
is one of the neighborhood set
)(tN j
of
glowworm
j
. After that, each glowworm selects the
movement direction using the roulette wheel method whereby
the glowworm with the higher probability has a higher chance
to be selected from the neighborhood set. Then, the
glowworm position
)( j
p
is adjusted based on the selected
neighbor position
)( z
p
using the following equation:
jz
jz
jj ceDis
tptp
stptp tan
)()(
)1()(
(4)
Constant, and
jz
d
is the Euclidean Distance between
glowworms
j
and
z
. At the end of the GSO iteration, the
local decision range
j
rd
is adjusted by the following
equation:
|)]})1(|()1(,0max[,min{)( tNnttrdrstrd jjj
(5)
)1( trd j
is the previous
j
rd
,
s
r
is the radial sensor
range constant,
is a model constant,
nt
is a constant
parameter used to restrict the neighborhood set size, and
|)(| tN j
is the actual neighborhood set size. In our proposed
algorithm, we relaxed the local decision range update step and
fixed the value of the
j
rd
to be the same value as the
s
r
International Journal of Information Technology (IJIT) Volume 3 Issue 2, Mar - Apr 2017
ISSN: 2454-5414 www.ijitjournal.org Page 51
STEP 1: Parameters initialize
pj: Glowworm individual
d: Number of Decision variables
n: Population size
S: Step size
iter_max: Number of iteration
l0: The initial value of luciferin
r0: The initial value of the radial range
Set γ, β, p and n: Values
STEP 2: Initialize solutions
Set t=0;
for i=1 to np do
Randomly generate the initialize solutions Pj,
Lj(t)=l0; rdi(t)=r0;
Calculate the value of objective function Fj(t)
STEP 3: Iteration Procedure
For i=1 to iter_max do
1) Luciferin update phase:
For i=1 to N do
Calculate lj(t) for each glowworm using (1)
2) Movement phase:
For i=1 to N do
Calculate Nj(t) for each glowworm
by using(3)
For z € Nj(t) do
Calculate Pi(t) for each I in the
neighborhood of glowworm i.
Select i according j
Calculate Lj(t+1) for each
glowworm j by using (4)
3) Decision range update:
For i=1 to N do
Calculate rid(t) for each glowworm by using(5)
STEP 4: End Algorithm, return the best solution
constant. However, the parameters
nt
and
are also
relaxed. Fig.1 showed the flowchart of GSO algorithm in
terms of computational procedure.
IV. GSO CLUSTERING ALGORITHM
The proposed GSO clustering algorithm is described as
follows:
Input cluster data object;
Set maximum iteration number =iter_max;
Let s be the step size;
Let r be the local space radius;
Let li (0) be the initial luciferin;
Let (0) be the initial dynamic decision domain radius
Set t =1
While (t <= iter_max) do:
{
for i = 1 to n do
for each glowworm i do: % Movement-phase
{
where is the norm of for each glowworm
do:
j= select glowworm where is the maximal element
of p
;
}
}
Algorithm symbolic description:
)(txi
is the glowworm i in t
iteration location;
)(tli
is the luciferin of the glowworm i in t
iteration;
)(tNi
is the neighborhood set of glowworm i in t
iteration;
)(tri
d
is the dynamic decision domain radius of
glowworm i in t iteration; is the upper bound of the
)(tri
d
;
)(tpij
is the probability of glowworm i selects neighbor j.
V. LITERATURE SURVEY
Deng-xu et al., proposed a connected glowworm swarm
enhancement to fathom the Multi-Constrained Multicast
Routing (MQMR) issue utilizing an enhanced encoding
strategy. With the fast improvement of Internet, more business
demand the nature of administration of the system is Quality
of Service (QoS) is required. This is the reason multi-
compelled QoS multicast directing is proposed. Previously,
there are numerous approaches to fathom the unconstrained
QoS multicast steering issue by a few scientists, for example,
dijkstra calculation, Steiner tree, and so on. Be that as it may,
these conventional techniques are powerless to settle the
multi-obliged QoS multicast steering issue.
International Journal of Information Technology (IJIT) Volume 3 Issue 2, Mar - Apr 2017
ISSN: 2454-5414 www.ijitjournal.org Page 52
Fig.2 Flowchart of GSO
The recreation comes about substantiate that GSO beats ACO
and GA execution for MQMR issue [13].
Zhang Yuli et al. propose a multi-robot collaboration
methodology for scent sources limitation in view of an
adjusted GSO calculation (M-GSO). The applications for
utilizing independent robots to perform tuft following and
smell source limitation are far reaching. A multi-robot
collaboration methodology in view of changed glowworm
swarm advancement system has been proposed to accomplish
limitation for various smell sources. This system can
guarantee robots to begin hunting down the following smell
source after the disclosure of a scent source and guarantee that
different robots would not re-find this scent source.
Recreation comes about affirms that the proposed M-GSO can
successfully empower the robot framework to inquiry and
discover all the scent sources existed in the indoor
environment rapidly and precisely [14].
J. Senthilnath et al utilized GSO bunching calculation for
progressive part and converging of programmed multi-
phantom satellite picture order. To make best utilization of
land and its regular asset, there is a need decent genuine data
of the land and its elements. The satellite picture is one of the
sources which can catch the transient way of this information
for land usage. Arrive cover mapping data can be utilized to
review arrive utilization, with regards to city arranging and
land-use. For a given satellite picture, if there is an absence of
ground truth data then unsupervised procedure can be
connected for naturally arranging a satellite picture into
particular land cover areas. This paper epitomizes the
utilization of GSO grouping calculation for various levelled
part and converging of programmed multi-unearthly satellite
picture arrangement. Multi-unearthly picture, for example,
Landsite 7 topical mapped picture gained from southern area
of India are utilized as contributions to the various levelled
classifier display. The progressive method receives GSO and
Mean Shift Clustering (MSC) for part the information set by
fulfilling Bayesian Information Criterion (BIC) and k-implies
calculation is utilized to combine the information set. The
results of the paper authenticate that the, progressive classifier
show GSO execution is unrivalled than the MSC unsupervised
strategy [15].
Min li et al., recommended a technique to utilize the oil
chromatographic disconnected information to accommodate
the oil chromatographic on-line information utilizing GSO
upgraded SVM. GSO has been utilized to streamline the SVM
parameters, including mistake punishment consider, unfeeling
parameter and part parameter. The oil chromatographic on-
line observing of the transformer can immediately get a
handle on the working status of the transformer, recognize and
track potential blame, and give assurance to solid operation of
the transformer. The test comes about demonstrate that the
GSO streamlined can get littler fitting mistake, accomplish
more steady and precise outcome, and more reasonable for
field compromise of oil chromatographic on-line information
when contrasted with execution of Neural Network prepared
utilizing back engendering strategy[16].
Gao et al. Proposed a multilevel thresholding technique
which was based on the optimization based algorithm
(CQPSO). The quantum-behaved PSO employing the
cooperative method (CQPSO) was proposed to save
computation time and to overcome the profanity of
dimensionality. This method maintains the fast convergence
rate of PSO. OTSU method was used to evaluate the
performance of proposed method and result showed the
effectiveness in terms of less computational time of the
traditional OTSU method [17].
Apurba et al., proposed a hue preserving color image
enhancement technique which was based on PSO to find
optimized solution for image enhancement. In proposed
method the quality of the intensity image is improved by a
parameterized transformation function which was similar
quiet to propose. In addition gamut problem is also solved by
rescaling method was then compared with other techniques
like hue-preserving color image enhancement without gamut
problem (HPCIE) and a genetic algorithm based approach to
color image enhancement (GACIE). The proposed algorithm
was very efficient and provided better results compared to
other two methods [18].
Barrera and Coello [19] proposed a multimodal functions
have many peaks (local maximum) with the equal or various
objective values of GSO. They optimized the multimodal
functions to set all maxima according to definite constraints.
Spaces of high measurement increase the calculation of peaks
and this cause the evaluation of each function to call for
lengthier execution times in finding the greatest target peaks.
Classify to solve multimodal functions, the swarm has to be
able to divide itself into dissimilar groups for the sake of
giving out extra local information for result more peaks, the
amount of individuals has to be improved [20].
GSO is slow regarding union. Thus, Zhou et al., [21]
introduce an artificial GSO algorithm stuck on cloud model.
This paper is discussed about the cloud based GSO for
function optimization. In the meantime, a spontaneous version
of GSO algorithm was introduced by Tang et al, [22]. This
paper proposes the mutation usage in the optimal process in
global solution. This version is known as the parallel hybrid
mutation Glowworm Swarm Optimization.
Jayakumar and Venkatesh [23] was proposed a GSO
algorithm identifying the finest solution for the problem of
multiple-objective ecological economic dispatch. This paper
proposes the usage of mutation in the exploration process of
GSO. This will increase the range of the swarm and assist the
swarm in discover the global optimum solutions. The
mutation operation’s change increases the population’s range
by the mutation of preferred solution.
Atheer and Nordin [24] in this paper proposes the usage
of mutation in the exploration process of GSO, it will increase
the range of the swarm and aid the swarm in discover the
global best solutions. The mutation operation’s modify
increases the population’s range by the mutation of preferred
solution. The operation of mutation allows individuals
solutions to be better. By way of mutation operation, some
point of diffusion the solutions in space of search is retained.
International Journal of Information Technology (IJIT) Volume 3 Issue 2, Mar - Apr 2017
ISSN: 2454-5414 www.ijitjournal.org Page 53
This is to reduce the speed of meeting and to find new regions
in search space. But, in some problems of optimization, some
solutions turn into infeasible following the operation of
mutation and migration. If such condition occurs, it is
important that the solutions’ possibility is verified via the
addition of other method to attach the solutions. Further, in the
iteration method, it does not get into account the suitability
history of each individual, as well as GSO algorithm also has
poor movement strength [25, 26].
Clustering with swarm-based algorithms is emerging as
an alternative to more conventional clustering methods [27-
30]. Yu Zeng et al, [31] combined heuristic strategy with GSO
for the problem of rectangle layout optimization with
equilibrium constraint. Layout optimization of satellite
module concerns the best way to place a number of objects
with different shapes, sizes and quality. Placement of objects
cannot exceed the satellite round bottom and squeeze each
other. With the direct use of heuristic algorithms to search, not
only the search time is longer, the accuracy is also low
standard. With the background of satellite module layout
heuristic strategy can be combined with the glowworm swarm
optimization for the problem of rectangle layout optimization
with equilibrium constraint. On the basis of the heuristic
strategy, glowworm swarm optimization algorithm is applied
to search for the optimal placing order, and finally the optimal
layout is obtained. Simulation’s numerical results have shown
that proposed approach is more effective than the existing
algorithms like PSO and ACO algorithm with least maximum,
minimum and average enveloping circle radius, least
computational time and maximum space utilization.
Yang et al., [32] proposed a big data clustering method
based on the Map Reduce framework. They used the ant
colony approach to decompose the big data into several data
partitions to be used in parallel clustering. This method used
map reduces with the ACO algorithm lead to the automation
of the semantic clustering to improve the data analysis. The
proposed algorithm was developed and tested on data sets
with large number of records and showed acceptable accuracy
with good efficiency.
Ibrahim et al., [33] has presented GSO algorithm, for
formulating the clustering problem as a multimodal
optimization problem to extract the optimal cancroids based
on glowworm’s movement. Proposed GSO algorithm for
clustering can discover the numbers of clusters without
needing to provide the number in advance. Experimental
results of GSO based clustering on several real datasets
namely iris, Ecoli, glass, Balance, seed and two artificial data
sets namely: mouse and vary density has proved to be efficient
compared to well-known clustering methods that have been
used in the literature such as K-Means clustering, average
linkage agglomerative Hierarchical Clustering (HC), Furthest
First (FF), and Learning Vector Quantization (LVQ).
Yongquan et al., [34] for clustering several benchmark
images namely Lena, Mandrill and Peppers. Image
classification is an image processing method of distinguishing
between dissimilar categories of objects according to the
different features contained in their image information. K-
means works through several iterations, and updates every
cluster center gradually until getting the best clustering results.
However, there are two downsides for this algorithm. It
depends on the initial condition, which may cause the
algorithm to converge to suboptimal solutions and it falls into
local optimum easily. To overcome this K-means image
clustering algorithm based on glowworm swarm optimization
(ICGSO) is proposed by combining GSO with K-means
algorithm. Experimentation results have exposed that ICGSO
algorithm performed very well when compared to the both K-
means algorithm and fuzzy k-means clustering algorithm.
GSO algorithm has been applied for numerous complex
optimization problems. Qifang et al., [35] and Horng [36]
used GSO algorithm based on Otsu’s method and minimum
cross entropy for multilevel threshold image segmentation and
the experimental results show that the method has better
performance for gray images. In order to improve the
performance of the standard GSO algorithm and search the
global optimal value efficiently and accurately, the improved
glowworm swarm optimization (IGSO) is presented in this
paper. Step size 𝑠 is an important parameter in determining the
convergence of GSO algorithm, so a new update method of
step size is proposed. Furthermore the sensor range is
extended to the whole search space and the random movement
of the brightest glowworms of firefly algorithm is also
introduced.
TABLE 1
An overview of GA, ACO, PSO and GSO and their behaviour
International Journal of Information Technology (IJIT) Volume 3 Issue 2, Mar - Apr 2017
ISSN: 2454-5414 www.ijitjournal.org Page 54
Subsequently the IGSO algorithm using different objective
functions is used for multilevel color image thresholding
problem, such as between-class variance and minimum cross
entropy (MCE). The performance of IGSO algorithm for
multilevel color image thresholding is measured in terms of
the optimal threshold values, objective values, the peak signal
ITEMS
ALGORITHM
GA
ACO
PSO
GSO
YEAR
1975
1992
1995
2005
AUTHOR
John Holland
Marco Dorigo
James Kennedy &
Russell Eberhart
K.N.Krishnanand
and Debasish Ghose
OPTIMIZATION
Discrete Optimization
Meta heuristic
Optimization
Stochastic
Optimization
Meta heuristic
Optimization
PARAMETERS
Reproduction,
Crossover,
Mutation.
Construct Ant
Solutions,
Daemon Actions
(optional),
Update Pheromones.
Current velocity,
Personal Best,
Neighbourhood Best.
Initialization,
Updating Luciferin,
Movement,
Updating the Local-
Decision Range.
PURPOSE
Find the best among
others.
Find the shortest path.
Reach target with
minimal duration.
Find the local finest
solution.
ADVANTAGES
1) Efficient means of
investigating large
combinatorial problems
and can solve them,
2) Many orders of
magnitude faster than
exhaustive ‘brute force’
searches.
1) Inherent parallelism.
2) Positive feedback
accounts for rapid
discovery of good
solutions.
3) Efficient for
Travelling Salesman
Problem and similar
problems.
4) Can be used in
dynamic application
(adapts to changes such
as new distances, etc)
1) PSO can be applied
into both scientific
research and
engineering use,
2) It has no
overlapping and
mutation calculation.
3) The search can be
carried out by the
speed of the particle.
4) PSO adopts the real
number code, and it is
decided directly by the
solution.
1) GSO can deal with
highly non- linear,
multi-modal
optimization problems
naturally and
efficiently.
2) GSO does not use
velocities, and there is
no problem as that
associated with
velocity in PSO.
3) The speed of
convergence of GSO
is very high in
probability of finding
the global optimized
answer.
DISADVANTAGES
1) Computationally
expensive
2) Some problems
require many days or
weeks to run.
3) However often still
faster than force.
4) Blind, to direct a GA
towards optimal
solution area if know.
1) Theoretical analysis
is difficult.
2) Sequences of
random decisions (not
independent).
3) Probability
distribution changes by
iteration.
4) Research is
experimental rather
than theoretical.
1) Tendency to a fast
and premature
convergence in mid
optimum points.
2) The method cannot
work out the problems
of scattering and
optimization.
3) Slow convergence
in refined search step.
1) GSO is poor in high
dimensional problems.
2) In GSO, the
dynamic change of
decision domains in
the method of
glowworms moving,
the algorithm slows
convention speed and
has poor local search
ability delayed in the
iteration.
MEDICAL FIELD
Genetic Algorithm
outperformed optimizes
the artificial neural
networks among others.
ACO also optimizes
the artificial neural
networks for
applications in medical
image processing.
1) Detection of Brain
tumor using Image
segmentation(MRI)
2) PSO used for
optimize the artificial
neural networks for
applications in medical
Image processing.
GSO will present new
methods for future
selection problems.
International Journal of Information Technology (IJIT) Volume 3 Issue 2, Mar - Apr 2017
ISSN: 2454-5414 www.ijitjournal.org Page 55
to noise ratio (PSNR), and structural similarity index (SSIM)
and then compared with other swarm intelligence algorithms
such as adaptive particle swarm optimization (APSO) [37] and
self-adaptive differential evolution (SADE) algorithm [38].
The extensive review of GA, PSO, ACO and GSO is shown in
Table 1.
VI. CONCLUSIONS
This paper describes the algorithm of GSO and attempts to
review on GSO based on the several field like clustering,
optimization problem, multicast routing problem (MQMR)
problem and multi-robot based problems. The literature
survey confirms that the outcomes of GSO are better when
compared to the other optimization methods namely, PSO,
ACO and GA.
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... Attraction draws glowworms towards brighter neighbors within their sensing range. Repulsion avoids clustering and ensures a minimum distance from other glowworms 13,14 . The bioluminescence displayed by glowworms is a dynamic phenomenon that is intricately influenced by both their individual fitness and the fitness of their neighboring glowworms. ...
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