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Evolutionary DNA Computing Algorithm for JobScheduling Problem

Gudar J. Ibrahim, Tarik A. Rashid & Ahmed T. Sadiq

To cite this article: Gudar J. Ibrahim, Tarik A. Rashid & Ahmed T. Sadiq (2018): EvolutionaryDNA Computing Algorithm for Job Scheduling Problem, IETE Journal of Research, DOI:10.1080/03772063.2017.1362964

To link to this article: https://doi.org/10.1080/03772063.2017.1362964

Published online: 03 May 2018.

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Evolutionary DNA Computing Algorithm for Job Scheduling Problem

Gudar J. Ibrahim 1, Tarik A. Rashid 2 and Ahmed T. Sadiq 1

1Department of Software and Informatics Engineering, Salahaddin University-Erbil, Erbil, Iraq; 2Department of Computer Science andEngineering, University of Kurdistan Hewler, Erbil, Iraq

ABSTRACTDNA computing techniques have interesting properties such as vast parallel computationattainment, organic edges, and tiny parts. These properties have attracted researchers from variousfields (Bioinformatics, Biochemistry, and others). These techniques mainly rest on biochemicalresponses of molecules of DNA. Nonetheless, these biochemical responses might anneal inunsystematic fashion and conceivably generate inappropriate computations. This motivatesprospects to utilize evolutionary computation as it lays importance on probabilistic andoptimization search approaches. In this research study, the ability of DNA computing isdemonstrated and verified by selecting the job scheduling problem (JSP). JSP can be easily tackledby a human or by using standard computers. A proposed evolutionary DNA algorithm is presentedin this paper to solve the JSP; the proposed technique produces promising and better results thanthe standard DNA computing algorithm. Through adding supportive operations to the evolutionaryoperations, the performance becomes better; in addition, it has more solutions at the end, andtherefore, the possibility of having an optimum or near optimum solution is increased, and theaverage number of solutions is improved.

KEYWORDSDNA computation algorithm;Evolutionary DNA algorithm;Job scheduling problem;Metaheuristics; Parallelcomputation

1. INTRODUCTION

DNA computing was initially used for computation pur-poses in laboratories independently from using standardcomputers. The idea was demonstrated by LeonardAdleman. He used the Hamiltonian path problem(HPP) or widely called Travelling Salesperson Problemas an example to obtain solutions through investiga-tional DNA experiments [1]. It can be easily said that ifAdelman had chosen an easier task to tackle, then addi-tional advancement would have been accomplished.Afterwards, Adelman carefully chose the nondeterminis-tic polynomial time (NP)-complete and the HPP prob-lem depending on regular computer procedures [2].Selecting this foot path by Adelman paved more inspir-ing paths and enabled other scientists and scholars toreflect and put more efforts on working with DNA com-puting. With undertaking this task, he carefully believedthat the influence of DNA approach was abundant. Healso elaborated considerable views meant for the conceptof parallel computing, which is very realizable throughmethods using DNA [3,4].

Basically, DNA computing is regarded as a group of pre-ferred stands of DNA. Amalgamating these strands ofDNA can suggest explanations for a specified problemwhich needs solutions or a solution. Thus, the possibilityof parallel computing in this case is very significant. It is

of importance to state that DNA computing for hugeproblems needs substantial parallel computation pro-cesses, assuming an abundant DNA and primary proce-dure. DNA computing can tackle these difficult taskssuccessfully. On the contrary, regular computer devicesneed considerable hardware components and parallelprocessing [2].

A genetic procedure in the field of computer science isregarded as a metaheuristic stimulated through the natu-ral selection process that falls into the greater category ofevolutionary algorithms. The genetic procedure orgeneric algorithm is widely utilized for producing first-class solutions to search issues and optimization viadepending on bio-inspired operators such as selection,mutation, and crossover [5].

Also, metaheuristics are soft computing-basedapproaches. They are considered tolerated and can alsoexploit the reality of those solutions that are inaccurateand inexact for the problem as well as redevelop them toaccurate and exact solutions that fulfil the needs of prac-tical applications and their objectives. Furthermore, theyare capable of handling fuzziness, vagueness, and miscal-culations in the application data. They likewise handlepartial information intelligently to generate precise solu-tions for machine learning problems, searching algo-rithms, and optimization issues [6,7].

© 2018 IETE

IETE JOURNAL OF RESEARCH, 2018https://doi.org/10.1080/03772063.2017.1362964

Metaheuristics are normally regarded as methods thatoutline structures to develop a collection of techniquesthat can provide approximate solutions for machinelearning techniques, optimization problems, and search-ing methods. They represent soft computing approachesthat can be guided in the direction of various problemsof optimization through constructing the common planfor different problems and in each instance, a smallnumber of modifications is needed to be conducted[6,7]. Practically speaking, there are numerous optimiza-tion issues which are related to searching and machinelearning techniques. These optimization issues can bedescribed as follows: they are extremely difficult as theyrequire numerous computation due to large searchingspace, they might hold hard constraints, they are multi-objective, they encompass complex mathematical mod-els, or they might need to accomplish big data. Most ofthese issues are practical applications from differenttechnological playing field. There are some conventionalsolutions as branch and bound approaches, enumerativesearching algorithms, backtracking techniques, integerand linear programming approaches, and so forth. Thesesorts of solutions can find optimal solutions for theabove optimization issues. Yet, they are practically inad-equate and unreasonable as they are exceedingly timeconsuming. Alternatively, metaheuristic approaches useprobabilistic approximation schemes to precisely tackleoptimization issues. Like all the above conventionalapproaches, metaheuristic approaches do not producethe optimal solutions; however, they generally producegood-quality solutions and sub optimal solutions withina realistic implementation time for various optimizationproblems, including those that cannot be solved throughconventional methods [6,7].

In general, the job scheduling problem (JSP) is known asan NP-hard and a difficult task and it is also defined as acombinatorial complexity task [8,9]. It illustrates a vitaljudgement practice in modern engineering and indus-trial systems. Thus, we can find considerable researchworks which have dedicated for the JSP [8]. In the mean-time, this problem has excessive difficulty. Thus, somelatest research works are concentrated on metaheuristicmethods such as genetic algorithms [10–12], Tau Search[13], particle swarm optimization (PSO) [14], ant colonyoptimization [15,16], and a different evolution algorithm[17].

Other research works have focused on the uncertaintyfactor via fuzzy set theory or stochastic theory [18–24].Additionally, the stochastic theory is used to determinethe probability distribution and fuzzy set theory is usedto determine the required membership function.

Nevertheless, to construct these functions, a largeamount of data is required. This will be very expensiveor impossible in real engineering and industrial system[25,26]. Hamed Rafiei, Masoud Rabbani, Hassan Gholi-zadeha, and, Hossein Dashti dealt with the cell forma-tion and job scheduling problems at the same time. Theysuggested a mixer integer nonlinear program to solveproblems linked to job scheduling and cell formation ina job-shop arrangement. Their suggested techniquereduced the costs of operations [25,26].

The key contributions of this research work are as follows:(1) Recommending an improved evolutionary DNA tech-nique depending on conventional DNA technique. (2)Using the suggested evolutionary DNA technique totackle job scheduling problem via providing extra sup-portive operations to the evolutionary operations. Thus,the number of solutions at the end will be increased andthis will lead to increase the possibility of devising the bestsolution and intensifying the average number of solution.(3) The suggested technique can be adapted to otherproblems such the shortest path problem.

The objective of this paper is to present an improvedDNA computing approach by means of evolutionaryalgorithms to generate additional solutions and guaran-tee the best solution.

2. LITERATURE REVIEW

In 1994, Leonard Ademan primarily perceived andestablished the principle of DNA computing to challengethe problem of HPP [1]. Thus, various Turing machineprocedures, innovations, and progress were formed rightafter early tests that were conducted by Adleman. It is ofinterest to say that even though the main determinationwas to take advantage of this new approach, compositedifficulties are revealed in terms of computations. Onthe other hand, it was promptly and decisively exposedthat the procedures were obviously not suitable to beused for this sort of algorithm [1,3,4,27,28].

Boolean circuit’s investigation is described and suggestedin [29], noticeably, Nand Boolean circuits can includeNand gates only. They indicated that the link betweenthe runtime slow down and the Boolean circuit’ssupreme fan out logarithm is relative, likewise, they pre-sented that the link is also relative among the space com-plexity, the product size and the supreme fan out[27–29,30–32].

A computer device depending on molecular program-design was established in [33]. Enzymes and DNA

2 G. J. IBRAHIM ET AL.: EVOLUTIONARY DNA COMPUTING ALGORITHM FOR JOB SCHEDULING PROBLEM

molecules are used to construct a computing deviceinstead of the integrated circuits and microchips madefrom silicon materials. A deoxyribonucleic acidcomputer is used which was capable of discoveringtumor-associated objects inside a cell. They managed togenerate medication conversed cancer confrontation atwhatever time the disease was detected [33,34].

In [35], a research work is carried out to control thesensitivity of single strand conformation polymorphism(SSCP) to identify factor IX. This work was conductedin Iran to examine the haemophilia B blood in patients.The element of phenol chloroform along with other ele-ments are used for extracting DNA. Both PCR andPrimer are used to enlarge the regions of gene. In [36],diffident models for different applications of DNA com-puting; for instance, DNA Turing machines, aqueouscomputing, molecular computing, and nascent field ofsynthetic biology are described and explained [34].Another research study in [36] was conducted to pro-duce better effectiveness and tractability. Basically, aheuristic search is inserted in a DNA computing tech-nique. They enriched the DNA technique throughdecreasing the time of running, reducing capacity ofmemory, and increasing the number of solutions.

In [2], a progressive and effective approach technique fortackling the minimum vertex cover issue via a suggestedDNA computing algorithm to solve problems that canbe inflexible for silicon computers was introduced. Con-versely, they suggested that DNA approach is not verysuitable to tackle simple tasks, simply because it involvesparallelism with high degree of computation [2].

A good number of researchers have been fascinated byfuzzy and stochastic scheduling techniques and severalapproaches have been recorded in the literature such asthe one in [10] aimed at the fuzzy job-shop schedulingand recommended a genetic algorithm (GA) to tacklethe fuzzy processing time and due date. Ip, Hui, Lau,and Chan [20] adapted a system which is called the toolmonitoring system to distribute a machine schedulethrough fuzzy techniques that rely on the facts from thetools and part relationships. Niu, Jiao, and Gu in [37]recommended a PSO by way of genetic operators so thatto moderate the fuzzy make span. Lei in [23] developeda system which is called the decomposition integrationgenetic algorithm intended for a problem with a flexiblejob-shop scheduling with fuzzy processing time.

Rajkumar introduced a greedy randomized adaptivesearch procedure to deal with the flexible job schedulingproblem through restricted source [38]. Amiri

implemented a variable neighbourhood search algo-rithm. A few neighbourhood structures connected withassignment and sequencing problems were utilized togenerate neighbouring solutions [19]. A new scheme isintroduced by Xiaoge to handle the problems of uncer-tain processing times. They developed a dynamic GA viacommutation of the fitness value, crossover, mutation,and others where an operation-based demonstration isutilized to code in the chromosome [8]. In [39], an evo-lutionary-based membrane approach is used to solveoptimization tasks of DNA sequence. This approachsounded so simple for designing of DNA sequence, veryfast converging, and theoretically appealing. In addition,they managed to generate better and great quality ofDNA sequences. Finally, they concluded that their novelapproach needs further investigation and adjustment tohandle hard optimization problems. In [40], a multi-objective evolutionary approach was utilized for thedesign of DNA sequence, this is different from previousevolutionary algorithms. They used an approach ofmatrix-based chromosome for their strategy of encod-ing. They established that using the matrix-based GAaccompanied by its genetic operators might enhanceDNA sequence optimization performance.

This work integrates an evolution approach into DNAcomputing by means of the strategy parameter and thecrossover operator to expand the final solutions in termsof quality. The best solutions are accomplished when thefinal solutions’ size is amplified and the most correct sol-utions are evolved and obtained. The construction of thisresearch can be summarized as follows: the JSP usingDNA computing approach is described in Section 3,then, in Section 4, the suggested evolutionary algorithmbased on DNA computing is introduced. After that, inSection 5, detailed descriptions of the investigational out-comes are demonstrated, and to end, the conclusions aresummarized in detail. Table 1, shows a list of glossary.

3. DNA COMPUTING APPROACH FOR JSP

Information in Biology can be kept in DNA. In addition,letter strings can be related to amalgamations of fourmain bases; Adenine (A), Thymine (T), Guanine (G)and Cytosine (C). The information can be transformedthrough these letter strings by complex processes oneach item cell. It is undoubtedly true that DNA polymer-ase is regarded as the key enzyme with which an indi-cated DNA stands under appropriate environmentswhich can produce the complementary strand (a differ-ent DNA sequence of Watson–Crick within which, Cwill oppose G, G will oppose C, A will oppose T, and Twill oppose A). Consequently, a fresh AGTACAGGG

G. J. IBRAHIM ET AL.: EVOLUTIONARY DNA COMPUTING ALGORITHM FOR JOB SCHEDULING PROBLEM 3

molecular sequence will be formed via DNA polymerasesimply from the TCATGTCCC molecular sequence.Thus, the DNA can be reproduced by DNA polymerase.This is called a process of DNA replication throughDNA polymerase which is tremendously significant inlife in general. Principally speaking, DNA polymerasesare regarded as Nano machines which link strands ofDNA. They can read and pass each base as well as writethe complementary information like a new expandedDNA strand [34,41].

It is of interest to mention that there is a great deal ofsimilarity between the DNA polymerase and Turingmachine. Ultimately, Turing developed a Turingmachine which was a device that simulates a computermodel. In the beginning, the Turing machine was pro-posed for theoretical purposes and was suitable to han-dle mathematical analyses. It was in Allan Turing’sintention to make it simple. Overall, it was explained asa control machine which was limited and consisted ofcouples of tapes. Information can be read and writtenwhen the machine control travels sideward using theinput and output of the tape, respectively. It is worthnoticing that the control machine can be programmedusing basic instructions in which strings such as A, T, C,and G can be encoded on the tape input for reading andgenerating the tape output in the form of Watson–Crickcomplementary string.

For that reason, a Watson–Crick complementary stringcan be produced via a Turing machine which can codevarious programs to emulate games such as chess, etc.The basic DNA computing operations that are widelyused can be described as follows [23,34,36,38,41–49]:

(1) Pairing of Watson–Crick: this prevalent, clearly,strands of DNA can have their Watson–Crickstring complements. If a DNA molecule comesacross Watson–Crick original complementarystrand, the process of pairing will take place.Therefore, both DNA strands can get joined andannealed to yield the double helix.

(2) Polymerases: DNA polymerases can generateDNA complementary strands to Watson–CrickDNA original string. Thus, information can becopied from a specific molecule to another one viapolymerases.

(3) Ligases: these are very useful for connecting mac-ules. The process of ligase would use two strandsof DNA to generate one.

(4) Nucleases: collapse and thus suppress DNA andRNA.

(5) Gel electrophoresis: they are used to examine andset apart protein macromolecules, DNA, andRNA.

(6) Synthesis: basically, the DNA sequences are writ-ten on a piece of paper and sent to the facility ofsynthesis. Then, over 1000 of molecules of DNAcontained in a tube are returned by the facility ofsynthesis within a couple of days.

For simplicity, a set of jobs with the corresponding run-ning time is defined. The first come, first served policy isused to schedule these jobs; so, the first job comes, it isserved first. The key operational steps of the standardDNA algorithm are as follows (see Figure 1): DNA prob-lem representation (coding); building of random solu-tions (construction); DNA random solutionsintensification via PCR (amplification); dismissal ofrepetitive jobs via SSCP (elimination), sequencing ofDNA strands via gel electrophoresis (arranging,) andfinally find the best job schedule (get the best solution).For encoding the problem in DNA, each job is associatedwith a designed palindrome 10-mer sequence of DNAand an oligonucleotide 3 0 5-mer complementarysequence of the current job followed by 5 0 5-mer com-plimentary sequence of the next job is synthesized. InPCR, amplification of DNA solutions that are having thecorrect number of jobs are performed. Each line in theinput file is having a job name and running time ofthe job, so the job name is coded in the DNA strand willbe used in joining with the next job to make the edge

Table 1: List of glossaryAbbreviation Description

AP Represents the average pathDNA Deoxyribonucleic aciddrpPCR Represents the number of dropped PCR solutionsdrpSSCP Represents the number of dropped SSCP solutionsE Represents the number of network edgesEA Evolutionary algorithmevolSSCPcross Represents the number of evolutionary SSCP crossover

operationsGRS Generate random solutionsHDNA Heuristic deoxyribonucleic acidsscpGen Represents the number of SSCP solutions generated by

crossover operationsSP Represents the shortest pathSPP Shortest path problemPCR Polymerase chain reactionpcrGen Represents the number of PCR solutions generated by

crossover operationPCRP Represents the number of PCR solutionseDNA Evolutionary DNAEvol AP Represents the average SSCP evolutionary pathEvol SP Represents the shortest SSCP evolutionary pathGELP Represents the number of gel electrophoresis solutionsMER The length of the oligonucleotide is usually denoted by

“mer” (from Greek meros, “part”)SSCP Single strand conformation polymorphism, represents

the number of SSCP solutionssscpCross Represents the number of SSCP crossover operationsLIG Represents the number of DNA ligationspcrCross Represents the number of PCR crossover operationsRNA Ribonucleic acidRepAdd Replace/add start/end at PCR operation

4 G. J. IBRAHIM ET AL.: EVOLUTIONARY DNA COMPUTING ALGORITHM FOR JOB SCHEDULING PROBLEM

and coded in DNA strand, then, put all the strands intothe initial test tube for annealing. The PCR operation inJSP explores the strand if it is having all the jobs or not.

Assuming there is a set of job (see Table 2), along withthe running time of each job. The key operations of thestandard DNA algorithm are as follows:

(1) DNA problem representation (coding)

For encoding the problem in DNA, each job is associatedwith a designed palindrome 10-mer sequence of DNA andan oligonucleotide 3 0 5-mer complementary sequence ofcurrent job followed by 5 0 5-mer complimentary sequenceof next job is synthesized. For each job, synthesize a ran-dom 10-based palindrome DNA as following:

Jobs (10)

A ! 5 0CTGATTATTC3 0 Comp: 3 0GACTAATAAG5 0OR 5 0GAATAATCAG3 0

B ! 5 0CTTGAACGGA3 0 Comp: 3 0GAACTTGCCT5 0OR 5 0TCCGTTCAAG3 0

C ! 5 0CTATCTTTAA3 0 Comp: 3 0GATAGAAATT5 0OR 5 0TTAAAGATAG3 0

D ! 5 0CAGGCTTAAA3 0 Comp: 3 0GTCCGAATTT5 0OR 5 0TTTAAGCCTG3 0

E ! 5 0CAAGCGACGC3 0 Comp: 3 0GTTCGCTGCG5 0OR 5 0GCGTCGCTTG3 0

F ! 5 0CTCGAAACGG3 0 Comp: 3 0GAGCTTTGCC5 0OR 5 0CCGTTTCGAG3 0

G ! 5 0CACTGTCACT3 0 Comp: 3 0GTGACAGTGA5 0OR 5 0AGTGACAGTG3 0

H ! 5 0CACCTTGTAG3 0 Comp: 3 0GTGGAACATC5 0OR 5 0CTACAAGGTG3 0

I ! 5 0CCCCCGTGTA3 0 Comp: 3 0GGGGGCACAT5 0OR 5 0TACACGGGGG3 0

J ! 5 0CAGGAATGTC3 0 Comp: 3 0GTCCTTACAG5 0OR 5 0GACATTCCTG3 0

Encoding the edges: for each job and the job next to itsynthesize a 10-based DNA strand consisting comple-mentary of 3 0 5-mer sequence of first job and comple-mentary of 5 0 5-mer sequence of second job.

Edges (10):

A–B! 5 0ATAAGGAACT3 0

B–C! 5 0TGCCTGATAG3 0

C–D! 5 0AAATTGTCCG3 0

D–E! 5 0AATTTGTTCG3 0

E–F! 5 0CTGCGGAGCT3 0

F–G! 5 0TTGCCGTGAC3 0

G–H! 5 0AGTGAGTGGA3 0

H–I! 5 0ACATCGGGGG3 0

I–J! 5 0CACATGTCCT3 0

J–A! 5 0TACAGGACTA3 0

Figure 1: Standard DNA algorithm for job scheduling problem

Table 2: Example of a set of jobs with their corresponding run-ning timesJob name A B C D E F G H I J

Running time 4 101 9 24 7 19 3 9 61 5

G. J. IBRAHIM ET AL.: EVOLUTIONARY DNA COMPUTING ALGORITHM FOR JOB SCHEDULING PROBLEM 5

(2) Building of random solutions (construction)

The DNA sequence corresponding to a job and the DNAcomplimentary sequence corresponding to another jobor edge might meet by chance so they will stick/annealtogether.

(1)- CTGATTATTCCTTGAACGGA: A!B

(22)- CCCCCGTGTACAGGAATGTCCTGATTATTCCTTGAACGGACTATCTTTAA: I!J!A!B!C

(36)- CACCTTGTAGCCCCCGTGTACAGGAATGTCCTGATTATTCCTTGAACGGA: H!I!J!A!B

(53)- CTTGAACGGACTATCTTTAACAGGCTTAAA-CAAGCGACGCCTCGAAACGGCACTGTCACTCACCTTGTAG: B!C!D!E!F!G!H

(54)- CAAGCGACGCCTCGAAACGGCACTGTCACTCACCTTGTAGCCCCCGTGTACAGGAATGTCCTGATTATTCCTTGAACGGACTATCTTTAACAGGCTTAAACAAGCGACGC: E!F!G!H!I!J!A!B!C!D!E

(72)- CTGATTATTCCTTGAACGGACTATCTTTAA-CAGGCTTAAACAAGCGACGCCTCGAAACGG: A!B!C!D!E!F

(97)- CTATCTTTAACAGGCTTAAACAAGCGACGCCTCGAAACGGCACTGTCACT: C!D!E!F!G

(101)- CTGATTATTCCTTGAACGGACTATCTTTAACAGGCTTAAACAAGCGACGCCTCGAAACGGCACTGTCACTCACCTTGTAGCCCCCGTGTACAGGAATGTC: A!B!C!D!E!F!G!H!I!J!

(165)- CACTGTCACTCACCTTGTAGCCCCCGTGTACAGGAATGTCCTGATTATTCCTTGAACGGACTATCTTTAACAGGCTTAAACAAGCGACGCCTCGAAACGGCACTGTCACTCACCTTGTAGCCCCCGTGTACAGGAATGTCCTGATTATTC: G!H!I!J!A!B!C!D!E!F!G!H!I! J!A

(166)- CTATCTTTAACAGGCTTAAACAAGCGACGCCTCGAAACGGCACTGTCACTCACCTTGTAGCCCCCGTGTA: C!D!E!F!G!H!I

(3) Intensification of DNA solution using PCR(amplification)

It is the result of filtering all the strands which containsall the jobs.

PCR Solutions (88):

(1)- CAGGCTTAAACAAGCGACGCCTCGAAACGG-CACTGTCACTCACCTTG TAGCCCCCGTGTACAG-GAATGTCCTGATTATTCCTTGAACGGACTATCTTTAA

(2)- CTCGAAACGGCACTGTCACTCACCTTGTAGCCCCCGTGTACAGGAATGTCCTGATTATTCCTTGAA CGGACTATCTTTAACAGGCTTAAACAAGCGACGC

(3)- CTATCTTTAACAGGCTTAAACAAGCGACGCCTCGAAACGGCACTGTCACTCACCTTGTAGCCCCCGTGTACAGGAATGTCCTGATTATTCCTTGAACGGA

(12)- CCCCCGTGTACAGGAATGTCCTGATTATTCCTTGAACGGACTATCTTTAACAGGCTTAAACAAGCGACGCCTCGAAACGGCACTGTCACTCACCTTGTAG

(13)- CAAGCGACGCCTCGAAACGGCACTGTCACTCACCTTGTAGCCCCCGTGTACAGGAATGTCCTGATTATTCCTTGAACGGA CTATCTTTAACAGGCT-TAAACAAGCGACGCCTCGAAACGGCACTGTCACTCACCTTGTAGCCCCCGTGTACAGGAATGTCCTGATTATTCCTTGAACGGACTATCTTTAA

(18)- CTTGAACGGACTATCTTTAACAGGCTTAAA-CAAGCGACGCCTCGAAACGGCACTGTCACTCACCTTGTAGCCCCCGTGTACAGGAATGTCCTGATTATTCC TTGAACGGACTATCTTTAACAGGCTTAAA-CAAGCGACGCCTCGAAACGGCACTGTCACTCACCTTGTAGCCCCCGTGTACAGGAATGTCCTGATTATTCCTTGAACGGACTATCTTTAACAGGCTTAAACAAGCGACGCCTCGAAACGG

(20)- CAAGCGACGCCTCGAAACGGCACTGTCACTCACCTTGTAGCCCCCGTGTACAGGAATGTCCTGATTATTCCTTGAACGGACTATCTTTAACAGGCT-TAAACAAGC GACGC

(24)- CAGGCTTAAACAAGCGACGCCTCGAAACGGCACTGTCACTCAC CTTGTAGCCCCCGTGTACAG-GAATGTCCTGATTATTCCTTGAACGGACTATCTTTAACAGGCTTAAACAAGCGACGCCTCGAAACGGCACTGTCACTCACCTTGTAGCCCCCGTGTA-CAGGAATGTCCTGAT TATTCCTTGAACGGA

(43)- CAGGCTTAAACAAGCGACGCCTCGAAACGGCACTGTCACTCACCTTGTAGCCCCCGTGTACAG-GAATGTCCTGATTATTCCTTGAACGGACTATCTTTAACAGGCTTAAACAAGCGACGCCTCGAAACGGCACTGTCACTCACCTTGTAGCCCCCGTGTACAGGAATGTCCTGATTATTCCTTGAACGGACTATCTT

6 G. J. IBRAHIM ET AL.: EVOLUTIONARY DNA COMPUTING ALGORITHM FOR JOB SCHEDULING PROBLEM

TAACAGGCTTAAACAAGCGA CGCCTCGAAACGGCACTGTCACTCACCTTGTAGCCCCCGTGTACAGGAATGTCCTGATTATTCCTTGAACGGA

(4) Dismissal of repetitive jobs (elimination)

This is the result of filtering all the strands which doesnot have repeated jobs.

SSCP Solutions (85):

(1)- (I- J- A- B- C- D- E- F- G- H) - (W = 172) -(T = 181)

CCCCCGTGTACAGGAATGTCCTGATTATTCCTTGAACGGACTATCTTTAACAGGCTTAAACAAGCGACGCCTCGAAA CGGCACTGTCACTCACCTTGTAG

(2)- (D- E- F- G- H- I- J- A- B- C) (W = 209) - (T = 218)

CAGGCTTAAACAAGCGACGCCTCGAAACGG CACTGTCACTCACCTT GTAGCCCCCGTGTACAGGAATGTCCTGATTATTCCTT GAACGGACTATCTTTAA

(3)- (C- D- E- F- G- H- I- J- A- B) - (W = 132) - (T = 233)

CTATCTTTAACAGGCTTAAACAAGCGACGCCTCGAAACGGCACTGTCACTCACCTTGTAGCCCCCGTGTACAGGAATGTCCTGATTATTCCTTGAACGGA

(4)- (A- B- C- D- E- F- G- H- I- J) - (W = 233) -(T = 238)

CTGATTATTCCTTGAACGGACTATCTTTAACAGGCTTAAACAAGCGACGCCTCGAAACGGCACTGTCACTCACCTTGT AGCCCCCGTGTA CAGGAATGTC

(5)- (F- G- H- I- J- A- B- C- D- E) (W = 216) - (T = 223)

CTCGAAACGGCACTGTCACTCACCTTGTAGCCCCCGTGTACAGGAATGTCCTGATTATTCCTTGAACGGACTATCTTTAACAGGCTTAAACAAGCGACGC

4. EVOLUTIONARY DNA COMPUTINGAPPROACH

The simulation of the standard DNA computing to solvethe problem of the job scheduling is done in this paperusing Java programming. The standard DNA algorithmused the following sifting tactics; a random set of solu-tions is generated and a solution to the problem isobtained by filtering out all the generated solutions that

are not considered to be the answers to the problem. Onthe one hand, the best job scheduling is found. On theother hand, there can be few limitations that might behighlighted as follows: (1) apparently, the DNA approachwould produce solutions randomly. These solutions areruled accidentally in accordance with the strands ofDNA for meeting one another or they might not meetat all; therefore, the standard DNA approach may notguarantee to generate altogether the potential solutions.(2) recognizing the best solution cannot be guaranteedwhen the DNA approach is not able to generate all thepossible solutions. (3) when the range of solution isintensified, accordingly, the number of possible solu-tions might, respectively, be intensified. In this way,additional final solutions might be achieved. On theother hand, longer time and extra memory capacity areneeded for searching process. Yet, the best solution can-not be guaranteed.

Therefore, based on the above-mentioned reasons,there must be different methods to improve the DNAcomputing approach to achieve further variety withinthe range of obtained solutions so that to generatenew and accurate solutions, and in the long run,achieve the most favourable solution. To do so, a tech-nique is recommended to integrate DNA computingapproach into an evolutionary DNA approach. Themain purpose of using evolutionary algorithm is toyield solutions via evolutionary processes within con-siderable sequence populaces rising from the DNA.Thus, in the evolutionary approach, the system dimen-sion is increased via substituting the standard filteringwith an evolutionary approach. Eventually, the mostfavourable solutions may possibly have achieved viaiterative amplification, re-merging populaces ofstrands, removing unsuitable solutions containedwithin the populace, and finally, gel electrophoresis isused to choose the most favourable solutions asopposed to extracting them from the initial populace.There are three modifications which are ordered in1,2,3 boxes in the suggested improvement of thisapproach (see Figure 2). Each operation has its influ-ence on the approach, while they all share the samerepresentation of the knowledge.

The modification operations in [50] are adapted to jobscheduling problem:

4.1 Crossovering Dropped PCR Solutions

The algorithm in [50] is modified through an update viawhich receiving the dropped PCR solutions and two

G. J. IBRAHIM ET AL.: EVOLUTIONARY DNA COMPUTING ALGORITHM FOR JOB SCHEDULING PROBLEM 7

nodes within the solution strand can be chosen ran-domly as well as substituted via choosing two nodesobtained from the original nodes within a set. Thisoperation is very like the operation of a semi-crossoverand it is used to intensify the likelihood of receivingadditional solutions. The outcome of this operationcan be directed to PCR operation to obtain the rightPCR solutions and then direct them to subsequentSSCP operation. This modification is described by thefollowing program.

PCR Semi Cross Over:Input: Dropped PCR Solutions, Original NodesOutput: Added Modified PCR Solution to PCRsolutions

For each dnaStrand in PCRDropped SolutionsWhile no termination do // two crossovers or breakGet random nodeS from dnaStrandGet random NodeS from Original NodesReplace nodeS with NodeS

OdIf isPCR (dnaStrand) // isPCR function already avail-able

Add dnaStrand to PCR SolutionsEnd If

End For

4.2 Crossovering Dropped SCCP Solutions

This is like PCR semi-crossover in [50], yet, it is used todrop SSCP solutions. The change in this situation is tosemi-crossover two random nodes (this does not includethe start or the end of the node, as these nodes arealready considered to be the right solutions amongthe strands of solution). It is of interest to mention thatthe outcome from this task can be directed to SSCPoperation to obtain the right SSCP solution in the site.This modification is described by the following program.

SSCP Semi Cross Over:Input: Dropped SSCP Solutions, Original NodesOutput: Added Modified SSCP Solution to SCCPSolutions

For each dnaStrand in SSCP Dropped SolutionsWhile no termination do // two crossovers or breakGet random nodeS from dnaStrand but not start/end nodeGet random NodeS from Original NodesReplace nodeS with NodeSOd

If isSSCP (dnaStrand) // isSSCP function alreadyavailableAdd dnaStrand to SSCP Solutions

End IfEnd For

4.3 Evolutionary SSCP

This modification in [50] is the actual evolutionarydevelopment on DNA computing approach. In thisstage, the algorithm selects the following solutions fromthe list of SSCP solution: (1) the ten percentage of theother SSCP solutions (which are not considered to bethe best solutions) and (2) the best SSCP solution. Inthis way, a fresh generation can be formed out of thesechosen solutions. This is done through crossing over asolution node randomly and proving the conditionwhether a lower-cost solution is generated in this case.This solution is considered when there is no good or bet-ter solution can be generated. Apparently, two nodes areused for crossing over rather than using one node onlyand the tuning is done for the strategy parameter. Then,the development of algorithm is assessed. New popula-tions are continuously generated from the original set ofpopulation until an improved solution can be obtained,if not, then, the halt condition is encountered. This mod-ification is described by the following program.

Figure 2: Proposed evolutionary DNA computing for job sched-uling problem

8 G. J. IBRAHIM ET AL.: EVOLUTIONARY DNA COMPUTING ALGORITHM FOR JOB SCHEDULING PROBLEM

SSCP Evolution Strategy:Input: SSCP Solutions, Original NodesOutput: Added Evolved SSCP Solution to SCCP Solu-tionsWhile no termination do // two crossovers or breakGet best solution and 10% random solutions fromSCCP SolutionsFor i = 0 to n // number of generationsIf (new generation is worse than previous one)Set crossinOverNodes = 2 // strategy parame-ter setting

ElseSet crossinOverNodes = 1

End IfmakeNewGeneration()Get best solution and 10% random solutionsfrom new generation

End ForAdd best solution from new generation to SCCPSolutionsEnd WhilemakeNewGeneration()While no termination doSSCP Semi Cross Over (currentStrand,OriginalNodes)// function is already definedadd crossedOver strand to new populationEnd While

5. RESULTS AND DISCUSSION

The DNA algorithm is used to solve the job schedulingproblem. After getting all the results of the normal DNAalgorithm, the improved DNA algorithm is used to solvethe same problem with the same properties. The sug-gested evolutionary DNA algorithm takes the advantagesof the evolutionary strategies to be embedded in the nor-mal DNA algorithm to optimize it [50]; hence, gettingbetter results. By optimizing, it means that the numberof solutions is increased so the possibility of getting opti-mum solutions is increased as well. Also, since the evolu-tionary technique is used, the initial resulted solutionsare being evolved; hence, the average quality of the solu-tion is increased generation after generation. It is consid-erable that in job scheduling problem, usingevolutionary DNA algorithm for getting the optimumsolution is guaranteed.

By implementing the evolutionary DNA algorithm, sev-eral conclusions are reached in general or specific to theproblem, which represents the advantages and

disadvantages of the new proposed algorithm upon thenormal DNA algorithm. The following items are theimportant conclusions:

(1) In evolutionary DNA, the running time and mem-ory capacity of the DNA algorithm were increasedby average 198% and 27%, respectively.

(2) In evolutionary DNA, the number of final solu-tions was increased by 8.75% and the average costof the final solutions was optimized by 18.13%.

(3) The optimum solution was optimized by 11%.

Evolutionary DNA is always generating the optimumsolution.

The following variables are defined and are used in theresults of the job scheduling problem (see Table 3). Thedata in Tables 4 and 5 are the results of standard DNAapproach and evolutionary DNA approach for solvingjob scheduling problem. Figure 3 shows the average no.of SSCP solutions for both DNA algorithm, and evolu-tionary SSCP. The average no. of SSCP solutions for theproposed evolutionary SSCP was performed better thanDNA algorithm.

Figure 4 shows the average no. of final solutions; DNAalgorithm, evolutionary SSCP. The results for eDNAwere better than the standard DNA algorithm.

Figure 5 shows the average waiting time for both thestandard DNA algorithm, and the proposed evolution-ary SSCP.

Figure 6 shows the shortest waiting time for both thestandard DNA algorithm, and proposed evolutionarySSCP.

Figure 7 shows the average turning around time for boththe standard DNA algorithm, and the proposed evolu-tionary SSCP.

Table 3: Variables and their representativeVariables Representative

JN Represents the number of jobsLIG Represents the number of DNA ligationsRSG Represents the number of random solution generationPCRP Represents the number of PCR solutionsSSCP Represents the number of SSCP solutionsALLS Represents the number of final solutionsAWT Represents the average waiting timeSWT Represents shortest wait timeATT Represents the average turning around timeSTT Represents the shortest turning around timeRT Represents the run time of the DNA algorithmMC Represents the memory capacity of the DNA algorithm

G. J. IBRAHIM ET AL.: EVOLUTIONARY DNA COMPUTING ALGORITHM FOR JOB SCHEDULING PROBLEM 9

Figure 8 shows the shortest turning around time for boththe standard DNA algorithm, and proposed evolution-ary SSCP. It can be seen from the Figure that the differ-ence is very little.

Figure 9 shows the average running time for the stan-dard DNA algorithm and the proposed evolutionarySSCP.

Figure 10 displays the average memory capacity for boththe DNA algorithm and the proposed evolutionary SSCP.

In Table 5, summarized results were indicating that themodified DNA computing algorithm was generating bet-ter results than the standard DNA computing algorithm.

Table 4: Standard DNA algorithmAlgorithm JN LIG RSG PCRP SSCP AllS AWT SWT ATT STT RT MC

DNA 10 16,223 175 77 7 4 165 132 195 141 0.053 93,42515 79,023 390 117 4 3 385 351 406 360 0.102 193,41220 289,782 685 299 11 7 522 488 570 553 0.267 1,247,36225 686,253 948 412 11 7 638 591 683 656 0.630 634,54230 5,066,140 5030 2957 8 5 857 800 905 865 7.097 1,021,468

Table 5: Improved DNA algorithm using evolutionary SSCPAlgorithm JN LIG RSG PCRP SSCP AllS AWT SWT ATT STT RT MC

Evol SSCP 10 16,362 175 80 28 4 80 80 153 141 0.954 1,207,34815 86,309 390 89 29 3 250 250 352 351 1.769 275,348.220 287,639 685 288 44 8 452 452 553 553 3.096 1,060,12725 800,879 1065 358 46 7 555 555 661 656 4.912 297,317.330 5,502,555 5030 2502 50 6 764 764 868 865 13.540 1,208,716

Figure 3: Average no. of SSCP solutions; DNA algorithm, evolu-tionary SSCP

Figure 4: Average no. of final solutions; DNA algorithm, evolu-tionary SSCP

Figure 5: Average waiting time; DNA algorithm, evolutionarySSCP

Figure 6: Shortest waiting time; DNA algorithm, evolutionarySSCP

10 G. J. IBRAHIM ET AL.: EVOLUTIONARY DNA COMPUTING ALGORITHM FOR JOB SCHEDULING PROBLEM

In evolutionary DNA, the running time and memorycapacity of the DNA algorithm were increased by aver-age 198% and 27%, respectively, for JSP (see Table 6). Inevolutionary DNA, the number of the final solutions

was increased by 8.75% and the average cost of the finalsolutions was optimized by 18.13% for JSP. The opti-mum solution was optimized by 11%. EvolutionaryDNA was always generating the optimum solution forJSP, because in JSP, all the nodes were already involvedin the final solutions, so the evolutionary function wastreating with all the possible solutions. Although theincreases in running time and memory capacity werenoticeable, the focus of the improvement was to getmore results; hence, increasing the possibility of gettingthe optimum result at the end.

Both the standard DNA computing and the modifiedevolutionary DNA computing approaches were alsoapplied on the shortest path problem for the evaluationpurposes. This is known as the shortest path problem[50]. It is regarded as an organization of numerousnodes and edges. Edges are used to connect the nodes.Thus, each edge load along this normal path can beadded to compute the length of the path. The goal ofthis task was to determine the shortest solution or pathwhich could have the minimum cost of load within allthe other solutions or paths contained in the connectedgraph taking into consideration moving from a definitesource to an explicit end. Simulations for both DNAcomputing approach and the modified evolutionaryDNA computing approach are implemented and testedin this work. Numerous experimental tests are con-ducted for evaluation purposes. In addition, percentageof improving the evolutionary DNA approach over stan-dard DNA approach for the shortest path problem wasoutlined (see Table 7).

Figure 7: Average turning around time; DNA algorithm, evolu-tionary SSCP

Figure 9: Average running time; DNA algorithm, evolutionarySSCP

Figure 10: Average memory capacity; DNA algorithm, evolution-ary SSCP

Figure 8: Shortest turning around time; DNA algorithm, evolu-tionary SSCP

Table 6: Percentage of improving DNA algorithm over standard DNA algorithmAlgorithm RSG PCRP SSCP AllS AWT SWT ATT STT RT MC

Evol SSCP 1.62 14.13 395.25 8.75 18.13 11.05 6.25 0.35 197.88 26.92

G. J. IBRAHIM ET AL.: EVOLUTIONARY DNA COMPUTING ALGORITHM FOR JOB SCHEDULING PROBLEM 11

6. CONCLUSION

In this paper, we presented the basic concepts of theDNA computing and evolutionary DNA computingapproaches. We also explained the practice of the stan-dard DNA computing. Then, the DNA algorithm forsolving the job scheduling problem was explained andafter that, the evolutionary DNA algorithm for solvingthe same problem was designed and presented. Evolu-tionary DNA algorithm outperformed the standardDNA algorithm for job scheduling problem. The algo-rithm did not only show if a solution exists, but also pro-vided additional possible solutions, therefore, theopportunity of obtaining the best solution wasimproved. The proposed algorithm might be extendedto solve other optimization problems.

ACKNOWLEDGEMENTS

Authors would like to thank both Salahaddin University-Erbil andUniversity of Kurdistan-Hawler for their continuous support.

DISCLOSURE STATEMENT

No potential conflict of interest was reported by the authors.

FUNDING

University of Kurdistan Hewler [UKH-G5].

ORCID

Gudar J. Ibrahim http://orcid.org/0000-0001-8123-3348Tarik A. Rashid http://orcid.org/0000-0002-8661-258XAhmed T. Sadiq http://orcid.org/0000-0002-4217-1321

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AuthorsGudar J. Ibrahim obtained his MScdegree in software engineering from Col-lege of Engineering, Salahaddin Univer-sity-Erbil, in 2012. He is an assistantlecturer at Salahaddin University-Erbil,Kurdistan.

E-mail: gudar.ibrahim@su.edu.krd

Tarik A. Rashid received his PhD degreefrom University College Dublin, in 2006.He is a professor at the department ofComputer Science and Engineering, Uni-versity of Kurdistan Hewler, Kurdistan.

Corresponding author. E-mail: tarik.ahmed@ukh.edu.krd

Ahmed T. Sadiq is a professor of artifi-cial intelligence in postgraduate studiesat five Iraqi universities. He has super-vised 14 PhD and 45 MSc theses.

E-mail: drahmaed_tark@yahoo.com

14 G. J. IBRAHIM ET AL.: EVOLUTIONARY DNA COMPUTING ALGORITHM FOR JOB SCHEDULING PROBLEM