International Journal of Soft Computing and Artificial Intelligence, ISSN: 2321-404X, Volume-2, Issue-1, May-2014 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 Email: [email protected], [email protected] 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. Keywords— Constriction factor, DNA sequence assembly, Inertia weight, Particle swarm optimization I. 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 is a program for assembling shotgun DNA sequence data. Ting Chen and Steven Skiena 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 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. Eugene Myers 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 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 fragment assembly. EULER, in contrast to the Celera 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. analyzed various genetic algorithm operators for one permutation problem related with the Human Genome Project. Parsons et al. 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. Overcomes several major obstacles in assembling Solving DNA Sequence Assembly Using Particle Swarm Optimization With Inertia Weight And Constriction Factor 88 International Journal of Soft Computing and Artificial Intelligence, ISSN: 2321-404X, assembler, does not mask such repeats but uses them instead as a powerful fragment assembly tool. Meksangsouy proposed an asymmetric ordering representation where a path, co-operatively generated by all ants in the colony represents the search solution. Kim and Mohan presents a fragment assembler using a new parallel hierarchical adaptive variation of evolutionary algorithms. Fang et al. Approach maximizes the similarity (overlaps) between given fragments and a candidate sequence. Luque and Alba 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 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. Proposed local search method (PALS) to obtain optimal solutions for large instances of this problem. Nebro et al. Proposed a grid based genetic algorithm in solving the DNA fragment assembly problem. Enrique and Gabriel solved the DNA fragment assembly problem by using a new hybrid genetic algorithm. Zerbino et al. 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. Proposed improved sequence alignment method based on the ant colony algorithm. Zuwairie et al. 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. proposed a solution for DNA sequence assembly problem using Particle Swarm Optimization (PSO) with Shortest Position Value (SPV) rule. Kikuchi and Chakraborty 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. Volume-2, Issue-1, May-2014 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 DNA SEQUENCE ASSEMBLY PROBLEM 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]: 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 size of the human genome consists of 23 chromosome pairs, which is about 3.2 billion nucleotides in length Solving DNA Sequence Assembly Using Particle Swarm Optimization With Inertia Weight And Constriction Factor 89 International Journal of Soft Computing and Artificial Intelligence, ISSN: 2321-404X, n Length of the Fragment i Coverage i0 (1) Target Sequence Length 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. C1 and C2 are positive constants called “cognitive” and “social” parameter weighing the influence of the 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 individual particle ‘i’ is Vi 1 w.Vi C1. R1 pBestid Xid C2. R2 gBestid Xid (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: W i 1 W Max W Max W *i Min (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): search area. Its velocity is given by the vector, v i v i1, v i 2,..., v iD . The best previous position visited each (3) x i 1 x id v i 1 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 by Volume-2, Issue-1, May-2014 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 i1 V i C1.R1 pBestid X id C2.R2 gBestid X id (2) Solving DNA Sequence Assembly Using Particle Swarm Optimization With Inertia Weight And Constriction Factor 90 International Journal of Soft Computing and Artificial Intelligence, ISSN: 2321-404X, K and 2 2 2 4 on the SPV rule, the continuous position vector can be transformed a dispersed value permutation. Table 1 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. (7) 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. Volume-2, Issue-1, May-2014 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. F I 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 n2 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 Solving DNA Sequence Assembly Using Particle Swarm Optimization With Inertia Weight And Constriction Factor 91 International Journal of Soft Computing and Artificial Intelligence, ISSN: 2321-404X, individual would get the highest score value between the population. Volume-2, Issue-1, May-2014 given by the user. The two major conditions are mean 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. 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. Table 2. The Genfrag Benchmarks for DNA Fragment Assembly Problem. 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. 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. Table 3. Optimized Parameter Values for Particle Swarm Optimization and its variants (10) VI. 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 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 Solving DNA Sequence Assembly Using Particle Swarm Optimization With Inertia Weight And Constriction Factor 92 International Journal of Soft Computing and Artificial Intelligence, ISSN: 2321-404X, 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 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. Volume-2, Issue-1, May-2014 the PSO has been examined and conclusions are derived to obtain the optimal fitness score. The performance of the proposed CPSO with SPV rule based PSO has been validated on the different GenFrag benchmark data instances. It has been shown 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. REFERENCES Table 4. Experimental Results of the CPSO against Standard PSO Method for Swarm Size =100 [1] Burks C, “DNA sequence assembly, Engineering in Medicine and Biology Magazine,” IEEE, Vol. 13, pp. 771- 773, 1994. [2] Parsons, R.J., Forrest, S. and Burks C, “Genetic algorithms, operators, and DNA fragment assembly,” Machine Learning, Vol. 21, pp. 11- 33, 1995. 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Solving DNA Sequence Assembly Using Particle Swarm Optimization With Inertia Weight And Constriction Factor 94
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