SOLVING DNA SEQUENCE ASSEMBLY USING PARTICLE SWARM
OPTIMIZATION WITH INERTIA WEIGHT AND CONSTRICTION
FACTOR
1
R. INDUMATHY, 2S. UMA MAHESWARI
1
Research Scholar, Department of ECE, Coimbatore Institute of Technology, Coimbatore, India
Associate Professor, Department of ECE, Coimbatore Institute of Technology, Coimbatore, India
2
Abstract— This paper introduces an effectual technique to solve the DNA sequence assembly problem using a variance of the
standard Particle Swarm Optimization (PSO) called the Constriction factor Particle Swarm Optimization (CPSO).The
problem of sequence assembly is one of the primary problems in computational molecular biology that requires optimization
methodologies to rebuild the original DNA sequence. This paper implements the particle swarm optimization using an inertia
weight and a constriction factor with Smallest Position Value (SPV) rule to solve the DNA sequence assembly problem. The
constriction factors proposed in this work ensures the accuracy of convergence of the particle swarm algorithm and helps to
fine tune the search. The proposed approach maximizes the overlapping score between the fragments. The performances of the
proposed CPSO algorithm were compared with the variants of particle swarm optimization algorithms and other known
methodologies. The experimental results show that the proposed approach produces better overlap score than the other
techniques when tested with different sized benchmark instances.
Index Terms— Constriction factor, DNA sequence assembly, Inertia weight, Particle swarm optimization
I.
obstacles in assembling projects such as: the large
number of pair wise comparisons required for the
presence of repeat regions, chimeras introduced in the
cloning process and sequencing errors. A number of
fragment assembly packages have been developed
which were used to sequence different organisms. The
widely used popular package PHRAP was developed
by Green[5] is a program for assembling shotgun
DNA sequence data. Ting Chen and Steven Skiena [6]
implemented two different applications for trie based
data structures. The first application is the fragment
assembly for DNA sequences that helps in fast
fragment assembly and another application is the
unification factoring for optimizing logic programs.
Huang and Madan [7] developed CAP3 program,
which includes a number of improvements and new
features to improve DNA sequence assembly. CAP3
uses base quality values in computation of overlaps of
reads, creation of multiple sequence alignments and
generation of consensus sequences. One of the
optimization algorithms for the fragment assembly
problem is the greedy algorithm, based on the best set
of maximum weight contigs approach developed by
Elloumi and Kaabi [8]. Eugene Myers [9] developed
Celera assembler for de novo whole-genome shotgun
DNA sequence assembler. Celera is the first whole
genome shotgun sequence of a multi-cellular
organism and the first diploid sequence of an
individual human. Pevzner [10] developed a novel
approach to fragment assembly that abandons the
classical "overlap - layout - consensus" pattern
available in all currently available assembly tools.
EULER algorithm resolves the repeat problem in
INTRODUCTION
The invention of state-of-art technology in the field of
soft computing offer solutions to solve many
challenging problems in bioinformatics. Genome
sequencing using computational approaches is an
extremely prominent research problem. The genome
sequences are exceedingly long ranging from few
thousand nucleotides to more than three giga
nucleotides. The aim of genome sequencing is to find
out the accurate order of nucleotides within a DNA
molecule. DNA sequence assembly problem is
NP-hard, and extremely complex to attain precise
solutions. A novel method is needed to determine the
letters of the genetic code. This task is accomplished
by huge datasets using the combination of heuristic
techniques and mathematical formulations.
Christian Burks suggested that DNA sequencing
throughput would be increased by orders of magnitude
to complete the task in a period of 15 years that was
laid out for the Human Genome Project. Many
heuristic approaches are applied in DNA Sequence
Assembly to improve the process of DNA Sequence
Assembly. One of them is Genetic Algorithm.
Parsons et al.[2] analyzed various genetic algorithm
operators for one permutation problem related with
the Human Genome Project. Parsons et al.[3]
discussed the modifications in the previous genetic
algorithm used, the experimental design process by
which new results were obtained and have also made
preliminary attempts to explain the results and to
obtain proper solution. The TIGR assembler
developed by Sutton et al. [4] overcomes several major
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Solving Dna Sequence Assembly Using Particle Swarm Optimization With Inertia Weight And Constriction Factor
fragment assembly. EULER, in contrast to the Celera
assembler, does not mask such repeats but uses them
instead as a powerful fragment assembly tool.
Meksangsouy [11] proposed an asymmetric ordering
representation where a path, co-operatively generated
by all ants in the colony represents the search solution.
Kim and Mohan [12] presents a fragment assembler
using a new parallel hierarchical adaptive variation of
evolutionary algorithms. Fang et al.[13] approach
maximizes the similarity (overlaps) between given
fragments and a candidate sequence. Luque and Alba
[14] presented several methods: a canonical genetic
algorithm, a cross generational elitist selection
method, a scatter search algorithm, and a simulated
annealing, to solve the problem accurately which has
got instances that are 77K base pairs long. Kikuchi
and Chakraborty [15] added two heuristic ideas with
genetic algorithm to make it more efficient. The first
step is Chromosome Reduction (CRed) step and the
second step is Chromosome Refinement (CRef) step.
Alba et al. [16] proposed local search method (PALS)
to obtain optimal solutions for large instances of this
problem. Nebro et al. [17] proposed a grid based
genetic algorithm in solving the DNA fragment
assembly problem. Enrique and Gabriel [18] solved
the DNA fragment assembly problem by using a new
hybrid genetic algorithm. Zerbino et al. [19]
developed a set of algorithms called “Velvet” which
used de Bruijn graphs for genome sequence assembly.
A new approach to assembly that can control short
reads in grouping with read pairs to construct
assemblies. Zhao et al.[20] proposed improved
sequence alignment method based on the ant colony
algorithm. Zuwairie et al. [21] in their approach
model represented the DNA sequence design as a
path-finding problem, which consists of four nodes, to
enable the implementation of the ant colony system
and compared their results with other methods such as
the genetic algorithm. Ravi et al.[22] proposed a
solution for DNA sequence assembly problem using
Particle Swarm Optimization (PSO) with Shortest
Position Value (SPV) rule. Kikuchi and Chakraborty
[23] proposed a modified genetic algorithm; the
length of the chromosome has been reduced with
advancing generations to improve the search
efficiency. Greedy mutation has been introduced by
swapping nearby fragments using some heuristics to
get better fitness of chromosomes.
II.
size of the human genome consists of 23 chromosome
pairs, which is about 3.2 billion nucleotides in length
and cannot be read at once. Sophisticated sequence
assembly algorithms are needed to efficiently perform
the assembling process. The DNA sequence assembly
for shotgun sequencing is performed by cloning the
DNA sequence into several copies, splitting each copy
into millions of random fragments, reading the
individual fragments and then assembling those
fragments. The process of assembling huge sequences
can be divided into two major steps. The first step is to
rebuild the longer sequence from the short fragments
by using heuristic algorithms. The second step is to
align the sequence obtained from the assembling
process through sequence alignment algorithms. One
of the genome sequence assembly technique is the
Overlap-Layout Consensus approach.
Overlap Stage - Finding the overlapping fragments. In
this stage, the comparison of all possible pairs of
fragments is done using semi global alignment
algorithm to determine the similarity score.
Layout Stage - Finding the exact order of fragments
based on computed similarity scores. This stage is
complicated because it is tough to decide accurate
overlaps.
Consensus Stage - Deriving the DNA sequence from
the layout stage. The common technique used in this
stage is to apply the majority rule in building the
consensus.
An example of genome sequence assembly technique
is shown in Figure 1. a) Given a set of four fragments
b) To find the overlap c) To find the layout and d) To
assemble the four fragments into the consensus
sequence.
Fig. 1 Example of the genome sequence assembly technique
Since finding the exact order takes a huge amount of
time, a heuristic technique can be applied in this step.
The quality of a consensus sequence is normally
measured by the term coverage. It is defined as the
total number of base reads from fragments as a ratio of
the length of the source DNA. [24]:
n
 Length of the Fragment i
Coverage  i 0
(1)
T arget Sequence Length
DNA SEQUENCE ASSEMBLY PROBLEM
Deoxyribonucleic acid (DNA) is a nucleic acid that
contains the genetic information used in the
development and functioning of all known living
organisms and some viruses. DNA sequence is made
of four elements, Adenine (A), Thymine (T), Guanine
(G) and Cytosine (C).The letters A, T, C, and G
represent molecules called nucleotides or bases. The
Proceedings of 4th IRF International Conference, Pune, 16th March-2014, ISBN: 978-93-82702-66-5
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Solving Dna Sequence Assembly Using Particle Swarm Optimization With Inertia Weight And Constriction Factor
where n is the total number of fragments. If coverage
is high, the probability of covering original genome is
higher and the correctness of the assembled parts has
been enhanced. Coverage is evaluated according to
equation (1).
III.
two different swarm memories, and R1 and R2 are
random numbers uniformly distributed between 0 and
1. The equation (2) and (3) defines the standard
version of PSO algorithm. A constant, Vmax,
introduced to arbitrarily limit the velocities of the
particles and improve the resolution of the search. The
maximum velocity Vmax, serves as a constraint to
control the global exploration ability of particle
swarm. A particle inertia weight is introduced to
increase the ability for the particle to jump out of the
local best value and equation (2) is changed as follows:
OVERVIEW OF PARTICLE SWARM
OPTIMIZATION
Particle Swarm Optimization (PSO) is an evolutionary
optimization technique introduced by Kennedy and
Eberhart [25]. PSO is a population based stochastic
optimization technique for the solution of continuous
optimization problems. Kennedy and Eberhart [26]
have first used PSO for presenting discrete problem.
PSO was based on swarm intelligence, simulates the
social behaviors of bird flocking and fish schooling. In
PSO, each single solution is a “bird” in the search
space, called the “particle.” The concept of PSO is to
have a swarm of particles flying through a
multidimensional solution space, seeking for the
global optimum. All the particles will have a fitness
value, which are evaluated by the fitness function to be
optimized, and have velocities, directing the particles
to fly in the search space. A swarm of particles is
initialized with a group of random particles
(solutions) and then searches for optima by updating
generations. In every generation, each particle is
updated by following two “best” values. The first one
is the best solution (fitness), it has achieved so far.
This fitness value is stored, called the particle Best
(pBest). Another “best” value that is tracked by the
particle swarm optimizer is the best value, obtained so
far by any particle in the population. This best value is
called global Best (gBest). In PSO, each particle not
only reads from its own best history record, but also
reads from the current global optimum record. After
finding the two best values, the particles update its
velocity and positions. The movement of the particles
is influenced by two factors using information from
generation to generation as well as particle to particle.
For a multidimensional search space, the vector gives
the
position
of
the
i-th
particle,
x i  x i1, x i 2, ..., x iD where ‘D’ is the dimension of the

each
individual
particle
‘i’
is
W i 1  W Max 

W
Max
W
Min
 *i
(5)
N iter
In equation (5) Niter is the maximum number of
iterations and i is the current iteration. In this paper,
WMax and WMin values were set to 0.9 and 0.1
respectively.
IV.
THE PROPOSED CONSTRICTION
FACTOR PARTICLE SWARM
OPTIMIZATION (CPSO) APPROACH
The constriction factor approach is a variation of the
basic particle swarm optimization (PSO), which has
relatively enhanced convergent rate. For insuring
convergence, an analysis of the algorithm from
mathematical aspects was given by Clerc [31] using
constriction factor. The constriction factor, velocity
constraint, and population size all have major impact
on the performance of CPSO. The constriction factor
and velocity constraint have optimal values in
practical application, and improper choice of these
factors will lead to bad results. Increasing population
size can improve the solution quality, although the
computing time will be longer. In CPSO the velocity
vector is calculated according to equation (6).
V i 1  K . V i  N 1. R1 pBest id  X id  N 2.R 2 gBest id  X id 
(6)
with the constriction factor K as defined in equation
(7):
denoted
as p  p , p , ..., p . Mathematically, given a
i
i1
i2
iD
multidimensional search space, the i-th particle
updates its velocity and positions according to the
following equations: [27,28]
V i1  V i  C1.R1 pBestid X id   C2.R2  gBestid X id 
(2)
x i 1  x id  v i 1

(4)
In equation (4), w is the inertia weight, a weighing
factor for the velocity that is employed to control the
impact of the previous history of velocities on the
current velocity. [29] The inclusion of an inertia
weight in the particle swarm optimization algorithm
has been first reported by Ratnawera et al. [30]. The
inertia weight can be constant inertia weight or
varying inertia weight. The mathematical expression
for the varying is given as follows:
search area. Its velocity is given by the vector,
v i  v i1, v i 2,..., v iD . The best previous position visited
by

V i  1  w. V i  C1 . R1 pBestid  X id  C 2 . R 2 gBestid  X id
(3)
K
C1 and C2 are positive constants called “cognitive”
and “social” parameter weighing the influence of the
2
2   2  4
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Solving Dna Sequence Assembly Using Particle Swarm Optimization With Inertia Weight And Constriction Factor
(7)
and
shows an example of position values generated from
the permutation results using SPV rule. Here the
dimension value is 5, which is equal to the number of
fragments. Generated random numbers in the interval
of [-5, +5] could be considered as the continuous
position value. Now using SPV rule the fragments had
been rearranged based on the assigned discrete
position value.
is computed as in equation (8):
  N  N ,  4
1
2
(8)
The constriction factor K controls the magnitude of
the particle velocity and can be seen as a dampening
factor. It provides the algorithm with two significant
features by Eberhart and Shi [32]. First, it usually
leads to a quicker convergence than standard PSO.
Second, the swarm keeps the ability to perform broad
movements in search space even if convergence is
already highly developed but a new optimum is found.
Hence the CPSO has a potential ability to keep away
from being trapped into local optima while possessing
a quick convergence capability and is shown to have
superior performance than the standard PSO.
V.
Table 1. Position Information and Rearrangement of
Permutation Using SPV Rule.
IMPLEMENTATION OF CPSO
ALGORITHM FOR DNA SEQUENCE
ASSEMBLY PROBLEM
B. Fitness Evaluation
A fitness function is calculated after solution
representation. Parsons et al. [2] proposed the fitness
function as shown in Equation (9). The fitness
function, F (I), sums the overlap score for adjacent
fragments f [ i ] and f [ i + 1 ] in a given solution. The
objective function is a maximization function that
involves maximizing the score. It means that the best
individual will have the highest score.
The proposed method in this paper is a solution for
DNA sequence assembly problem using Constriction
Factor Particle Swarm Optimization with SPV rule.
The aspects of the problem formulation, fitness
evaluation and the implementation procedure of the
DNA sequence assembly problem have been explained
in the following sections.

A. Problem Formulation
To solve the DNA sequence assembly problem, a set of
fragments are given as input. The aim is to assemble
and build a consensus sequence, which should not
have any repeated patterns. A permutation of integers
represented a sequence of fragment numbers where
successive fragments overlap. An exclusive integer ID
has been assigned to the lists of fragments to represent
a solution. For example, if there are 5 fragments their
IDs are represented as 0, 1, 2, 3 and 4. Special
operators have been used to maintain a feasible
solution. Generally, to get a feasible solution two
conditions must be satisfied. They are (i) all fragments
must be presented in the ordering, and (ii) no
duplicate fragments are allowed in the ordering. For
DNA sequence assembly problem, each solution or
individual of PSO represents the fragment. Every
solution has certain position (dimension) value equal
to the number of fragments taken for assembly. This
paper uses a heuristic approach known as Smallest
Position Value (SPV) rule that converts the
continuous values into discrete values. The SPV rule is
used to find a permutation corresponding to the
continuous position Xi. The position vector has a
continuous set of values where k represents the
particle and n represents the dimension index. Based
on the SPV rule, the continuous position vector can be
transformed a dispersed value permutation . Table 1
F I 
n2

    
W F i ,F i 1
(9)
i 0
where i is the individual and W ( F [ i ] , F [ i + 1 ] ) is
the pair wise overlap strength of fragments F [ i ] and
F [ i + 1 ]. The overlap score (W) in F is computed
using the semi global alignment algorithm, a classical
dynamic programming technique to calculate the pair
wise alignments. Dynamic programming technique
can be applied to produce global alignments using the
Needleman –Wunsch algorithm, and local alignments
using the Smith-Waterman algorithm. Semi-global
alignment- Needleman-Wunsch algorithm with two
modifications:
i) Penalize end gaps i
n the pattern, but not in the long sequence; ii) Trace
back from the highest scoring node along the long
edge of the path graph. The example of Semi-Global
alignment is shown in Figure 2. For the input DNA
Sequence S1: ATCG and S2: ATTCG, the match
score is defined by 2, a mismatch score is defined by 0,
and a penalty of gap defined by - 2. Finally, the overlap
score between S1 and S2 was calculated to be 6, and
the new S1 is modified in AT-CG, the symbol”-”
means gap in a DNA sequence. However, the best
individual would get the highest score value between
the population.
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Solving Dna Sequence Assembly Using Particle Swarm Optimization With Inertia Weight And Constriction Factor
fragment length and coverage of parent sequence. To
test the performance of the proposed method three
sequences have been chosen from the National Center
for Biotechnology Information. Table 2 presents
information about the specific fragment sets used to
evaluate the proposed method.
Table 2. The Genfrag Benchmarks for DNA Fragment Assembly
Problem.
Fig. 2 Examples of the Semi-Global Alignment Algorithm
C. Implementation
CPSO algorithm with SPV rule is the proposed
technique used to solve the DNA sequence assembly
problem. In the problem of DNA sequence assembly
the inputs are different lengths of fragments and the
output is the consensus sequence which should not
have any repeated patterns. Solution representation is
the initial step of the CPSO algorithm. The next
process begins by generating the initial fragments
randomly. SPV rule has been applied to find the
permutation of the fragment order that has been
generated. The initial swarm is computed using the
fitness function given in equation (9). The personal
best of each fragment and the global best of the entire
sequence is predicted. The velocity and position of all
the fragments are randomly set within a range. In each
iteration, the velocities of every fragment are updated
according to the equation (4), a weighting factor for
velocity update is used to control the impact of the
preceding history of velocities on the present velocity.
In this paper, a constriction factor is used in the
velocity update equation (6) to enhance the convergent
rate. Moreover, the position of every fragment is
updated according to the equation (3). Using SPV rule
a new fragment order is generated. The fitness of the
updated sequences is calculated. The pBestid and
gBestid are updated according to the equation (10).
Finally, the consensus DNA sequence is computed.
This process is terminated by specifying the maximum
number of generations reached or when the solution is
no longer improving.
The experiments have been executed on a Dell XPS
L502X with Intel (R) Core(TM) i7 -2670 QM CPU @
2.20 GHz with 8GB of RAM running on Microsoft
Windows 7 platform. The proposed algorithm is
implemented using C# programming language on the
.NET platform and the database used is MySQL. The
parameter settings for PSO and its variants were
selected as shown in Table 3. The methods
implemented were simulated 30 times with different
random seeds and their average fitness scores were
recorded.
Table 3. Optimized Parameter Values for Particle Swarm
Optimization and its variants
(10)
VI.
To test and investigate the performance of the
proposed algorithm the overlap score of the
nucleotides are calculated. The fitness function is used
to calculate the overlapping score of adjacent
fragments. The major objective is to maximize this
total score. This paper discusses the evaluation of
overlapping score in Particle Swarm Optimization
(PSO) variants and other methodologies. Table 4
shows the comparison between the existing techniques
and variants of particle swarm optimization method. It
is noticed that the maximum overlap score is produced
EXPERIMENTAL RESULTS AND
DISCUSSION
In this section, the experimental setup and the
performance of the proposed method are analyzed.
The problem instances that have been generated by
Engle and Burks [33]. GenFrag are used in this
assessment. GenFrag takes a known sequence and
uses it as a parent strand from which random
fragments are generated according to the criteria
given by the user. The two major conditions are mean
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Solving Dna Sequence Assembly Using Particle Swarm Optimization With Inertia Weight And Constriction Factor
by the proposed constriction type CPSO method when
compared to the existing methods. This emphasizes
the better quality solution for the proposed methods.
The summary of the experimental results presented in
Table 4 shows the best overlap score achieved by
different PSO algorithms for swarm size equal to
hundred. The methods achieved the global maximum
solution but comparatively, the CPSO has better
consistency and also achieved global maximum.
through different trials that the CPSO method
outperforms the other known techniques and PSO
based method in terms of high quality solution,
consistency, faster convergence and accuracy.
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CONCLUSION
This paper presents a Constriction Factor Particle
Swarm Optimization with Smallest Position Value
rule based Particle Swarm Optimization technique to
tackle the complicated DNA sequence assembly
problem.
Computational techniques have been
applied to obtain an optimum solution. The
application of nature-inspired algorithms such as
Particle Swarm Optimization algorithm to solve
complex optimization problems have increased due to
its simplicity, ease of implementation, robustness and
the convergence rate. The Smallest Position Value
rule has been employed to enable the continuous
version of PSO in to discrete version of PSO. The
DNA sequence assembly problem considered in this
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