Efficient Encoding Scheme in Genetic Algorithm for Requirement Optimization

(1)International Journal of Innovative Technology and Exploring Engineering (IJITEE) ISSN: 2278-3075, Volume-8 Issue-8S3, June 2019. Efficient Encoding Scheme in Genetic Algorithm for Requirement Optimization Rajesh Kumar, Rakesh Kumar . Abstract:T RequirementsT analysisT isT theT initialT stepT ofT theT softwareT developmentT process.T RequirementT selectionT isT anT engineeringT processT toT selectT aT bestT setT ofT systemT requirementsT forT implementation.T InT thisT paper,T GeneticT algorithmT isT usedT asT anT optimizationT techniqueT toT optimizeT theT requirements.T EveryT searchT andT optimizationT algorithmT needsT aT techniqueT toT representT theT probableT solutionsT toT aT particularT problem.T InT orderT toT makeT theT useT ofT geneticT algorithm,T oneT shouldT beT ableT toT representT theT solutionsT inT theT formT ofT chromosomesT so that crossover, mutation etc. operators can be applied to generate the new solutions. In this paper, limitations of a number of Encoding scheme has been identified and a Encoding scheme is proposed for chromosome for identifying optimum requirements. Index Terms: Chromosome, Encoding, Genetic Algorithm Requirement, Optimization.. I. INTRODUCTION RequirementsT analysisT isT theT firstT phaseT ofT theT softwareT developmentT lifeT cycleT andT it’sT oneT ofT theT mainT concernT ofT softwareT engineering.T SystemT requirementT selectionT isT theT engineeringT processT toT findT aT minimumT setT ofT systemT requirementT forT implementation.T Additionally,T inT realT lifeT problems,T theT requirementsT selectionT suffersT fromT complication due to varying interest of heterogeneous users. To find theT optimalT setT ofT requirements,T thereT isT aT strongT needT ofT optimizationT techniques.T Meta-heuristicT algorithms,T suchT asT tabuT search,T simulatedT annealingT andT geneticT algorithmT haveT beenT appliedT toT aT wideT rangeT ofT optimizationT orT searchT problems.T InT thisT paper,T theT useT ofT geneticT algorithmT hasT beenT discussedT inT requirementT engineeringT . II.. GENETIC ALGORITHM. GeneticT algorithmT (GA)T isT categorizedT underT evolutionaryT algorithms.T TheyT areT primarilyT usedT forT solvingT optimizationT problems.T InT bigT problem,T stateT spaceT representationT isT characterizedT byT aT setT ofT objects;T eachT ofT themT hasT distinctT parameters.T TheT objectiveT ofT optimizationT problem,T workingT onT aboveT mentionedT . parametersT andT optimizeT them.T AllT optimizationT techniqueT needsT aT representationT methodT whichT depictionsT theT solutionsT toT aT specificT problem.T Likewise,T GAT workT onT codingT spaceT andT solutionT spaceT alternatively.T GeneticT algorithmsT areT inspiredT fromT biology,T soT havingT twoT spacesT isT supportedT byT naturalT evidence.T InT nature,T codingT spaceT refersT toT theT genotypicT spaceT andT phenotypicT spaceT isT referredT byT solutionT space.T ThisT hadT beenT clearlyT investigatedT byT MendelT inT 1866[1].T AT transformationT existsT betweenT genotypeT andT phenotype,T alsoT calledT mapping,T whichT usesT theT genotypicT informationT toT designT theT phenotypicT trait.T AT chromosomeT specifyT toT aT stringT ofT positiveT lengthT whereT allT theT geneticT dataT ofT anT individualT isT stored.T AllT chromosomesT consistT ofT manyT allelomorph.T AllelesT areT theT littlestT dataT itemsT inT aT chromosomeT [2].T IfT aT phenotypicT propertyT ofT anT individual,T likeT itsT eyeT colorT isT determinedT byT oneT orT moreT allelomorphs,T thenT theseT allelomorphsT togetherT areT denotedT asT geneT asT shownT inT FigureT 1.. FigureT 1.T RepresentationT ofT Gene-AlleleT inT chromosome.. A gene is a location on a chromosome, which is responsible for a particular character state property [3]. ProblemT representationT inT GAT needsT someT EncodingT scheme.T DesirableT traitT ofT EncodingT areT (i)T itT shouldT beT ableT toT representT allT possibleT phenotypes,T (ii)T itT shouldT encodeT noT infeasibleT solutions,T (iii)T itT shouldT beT unbiased,T (iv)T decodingT fromT phenotypicT traitT toT genotypeT shouldT beT easy,T andT (v)T problemT shouldT beT representedT atT theT correctT levelT ofT abstraction. III. TYPES OF ENCODING A. Binary Encoding It is most familiar representation of chromosome in GA. A BinaryT stringT isT describedT byT usingT aT binaryT alphabetT {o,T 1}.T EachT functionalT variableT isT encodedT inT aT binaryT alphabetT ofT aT certainT lengthT li,T describedT byT theT userT [4,5,6].T Thereafter,T aT completeT 1-bitT stringT isT formedT byT connectingT allT substringsT together.T Thus,T theT lengthT LT ofT stringT inT GAT has: N. Revised Manuscript Received on Date. Rajesh Kumar, Dept. of Computer Science & Applications, K.U., Kurukshetra, Haryana, INDIA. Prof. Rakesh Kumar, Dept. of Computer Science & Applications, , K.U., Kurukshetra, Haryana, INDIA.. Retrieval Number: H11120688S319/19©BEIESP. S = å Si. (1). i=1. suchT thatT NT representT theT numberT ofT objectT variables.T. 489. Published By: Blue Eyes Intelligence Engineering & Sciences Publication.

(2) Efficient Encoding Scheme in Genetic Algorithm for Requirement Optimization. BinaryT EncodingT allowsT forT aT higherT degreeT ofT parallelism.T ItT containsT moreT schemasT thanT decimalT coding.T InT spiteT ofT theseT benefits,T theyT areT abnormalT andT clumsyT forT manyT problems.T TheyT areT proneT toT arbitraryT orderingsT [7,8].T BinaryT EncodingT doesT notT supplyT theT collectionT ofT optionsT requiredT toT dealT withT theT varietyT ofT problemsT endureT inT business,T scienceT andT engineering.T InT thisT encoding,T distinctT bitsT haveT disparateT significanceT andT hammingT distanceT betweenT twoT successiveT integersT isT generallyT notT equivalentT toT oneT [9,10].T B. Gray Encoding NormalT binaryT EncodingT representationT ofT theT objectT mayT gradualT convergenceT ofT aT GA.T ExpendingT theT numberT ofT bitsT inT theT binaryT representationT amplifyT theT problemT [10,11].T GrayT CodeT canT preventT thisT problemT byT redefiningT theT binaryT stringsT soT thatT consecutiveT numbersT haveT aT HammingT distanceT ofT oneT [12].T GrayT codesT accelerateT convergenceT timeT byT keepingT theT algorithmsT attentionT onT convergingT towardT aT solutionT [13]. C. Floating Point Encoding Floating-pointT EncodingT (FPE)T schemeT wasT designedT byT DebT forT continuousT variablesT [14].T InT FPET scheme,T distinctT genesT namedT asT MT representT mantissaT andT ET representT exponentT ofT aT Floating-pointT parameter.T ForT aT multi--parameterT optimizationT problem,T aT commonT geneT hasT threeT elements,T asT opposedT toT twoT inT earlierT EncodingT schemes.T TheT threeT elementsT areT (i)T parameterT IDT number,T (ii)T mantissaT orT exponentT declaration,T andT (iii)T itsT value.T VariousT experimentsT haveT shownT thatT theT floatingT pointT EncodingT isT simpleT toT implement,T asT itT doesT notT requireT anyT conversionT mechanismT thatT convertsT bitT stringT toT realT value.T VariousT experimentsT haveT shownT thatT theT geneticT algorithmT withT floatingT pointT EncodingT isT simplerT forT implementationT andT fasterT thanT geneticT algorithmT withT binaryT representation.T ThisT isT becauseT inT caseT ofT binaryT implementation,T theT algorithmT mustT haveT conversionT mechanismT thatT convertsT bitT stringT toT realT value.T SuchT mechanismT isT notT requiredT inT caseT ofT floatingT pointT Encoding.T ItT hasT beenT foundT thatT algorithmT withT floatingT pointT EncodingT givesT betterT resultsT thanT algorithmT withT binaryT EncodingT asT itT canT easilyT incorporateT variousT constraints. D. Permutation Encoding Permutation Encoding (PE) is used in Ordering problems, such as traveling salesman problem etc. Given N rare objects, N! permutations of the object exist. In Permutation scheme,T everyT chromosomeT isT aT stringT ofT numbersT thatT representT aT positionT (number)T inT aT sequence.T InT certainT casesT randomT generatedT numbersT betweenT oT andT 1T areT alsoT usedT toT codeT theT problem.T ThenT toT decodeT theT solutionT theseT generatedT valuesT areT usedT asT sortT keys.T SampleT representationT forT twoT chromosomesT is. Retrieval Number: H11120688S319/19©BEIESP. Figure 2. Representation of chromosome in PE. Permutation issues can not be handled using the same generic recombination and mutation operators that are enforced to parameter optimization problems. Permutations are also substantial for scheduling applications, variants of which are also often Non Deterministic time Polynomial (NP) complete. This Encoding is likewise known as path representation [15]. E. Value Encoding ValueT codingT schemeT canT beT usedT inT problemsT whereT someT moreT arduousT valuesT suchT asT realT numbersT areT usedT [16].T UseT ofT simpleT BinaryT EncodingT forT suchT typeT ofT problemsT wouldT beT veryT difficult.T InT thisT EncodingT scheme,T allT chromosomesT isT aT arrayT ofT someT valuesT thatT canT beT anythingT connectedT toT theT problem,T suchT asT realT numbers,T charactersT orT anyT objects.T ItT isT oftenT necessaryT toT developT someT specificT crossoverT andT mutationT techniquesT forT theseT chromosomesT [17].T SampleT representationT is:. FigureT 3.T RepresentationT ofT chromosomeT inT ValveT encoding. F. Tree Encoding ItT isT usedT generallyT forT geneticT programming.T InT thisT treeT EncodingT schemeT allT chromosomeT isT aT TreeT ofT anyT objects,T suchT asT behaviorT orT commandsT inT programmingT languageT [18].T TheT representationT spaceT isT describedT byT characterizingT theT setT ofT behaviorT andT terminalsT toT labelT theT veritiesT inT theT tree.T TreesT supportT richT representationT thatT isT adequateT toT representT computer-programs,T analyticT functions,T andT dynamicT lengthT structure,T evenT computer-hardware.T ParseT treeT isT aT well-knownT representationT forT emergingT executableT structuresT [4].T ParseT treeT includeT naturalT recursiveT definition,T whichT allowsT forT variableT sized structures. In this representation, the elements of the parse T. Figure 4. Tree Encoding Representation. treeT determineT theT powerT andT fitnessT ofT theT representation.T AsT aT resultT ofT cyclicT natureT ofT parseT trees,T iterativeT computationsT areT notT easilyT characterized.T T. 490. Published By: Blue Eyes Intelligence Engineering & Sciences Publication.

(3) International Journal of Innovative Technology and Exploring Engineering (IJITEE) ISSN: 2278-3075, Volume-8 Issue-8S3, June 2019. ToT classifyT theT stoppingT criteriaT forT suchT problemsT isT veryT difficult.T So,T theT derivedT functionT isT evaluatedT withinT aT hiddenT loopT thatT re-executesT theT evolvedT functionT untilT someT predefinedT stoppingT criteriaT isT reached.T G. Grammar based Encoding GrammarT basedT EncodingT isT usedT inT problemsT dealingT withT optimizationT ofT networksT [19].T TheT globalT motionsT ofT automataT networksT (suchT asT artificialT neuralT networks)T areT aT functionT ofT itsT topologyT andT theT choiceT ofT automataT used.T EvolutionaryT computationT canT beT enforcedT toT theT optimizationT ofT theT parameters,T butT theirT computingT costT isT restrictiveT unlessT theyT operateT onT aT solidT representation.T EarlierT directT codingT wasT usedT asT itT wasT simple.T ThisT EncodingT schemesT useT constructionT forT genes,T theT verbalizationT ofT whichT formsT theT phenotypeT [6].T TheT circumlocutionT ofT thisT EncodingT admitT forT aT many-to-oneT mappingT withT aT correspondingT richnessT inT possibleT genotypicT representations.T GraphT grammarsT provideT suchT aT representationT byT allowingT networkT regularitiesT toT beT efficientlyT capturedT andT reused.. IV. NEED OF NEW ENCODING SCHEMES TheT effectivenessT ofT softwareT system,T itT totallyT dependsT onT theT measurementT inT whatT wayT bothT theT demandsT ofT itsT usersT andT itsT operationalT environmentT wereT beingT metT andT thoseT needsT wereT includedT inT theT systemT requirements.T InT thisT view,T theT requirementsT engineeringT (RE)T couldT beT describedT asT aT processT byT whichT theT requirementsT areT drivenT thus,T successfulT RET includedT theT followingT aspects:  UnderstandingT theT variousT needsT ofT users,T customersT andT otherT stakeholders  T UnderstandingT theT approachT inT whichT theT systemT wouldT beT developedT  MakingT sureT thatT theT documentedT requirementsT wereT consistent. T InT theT contextT ofT aT bigT software,T theT earlyT stageT ofT theT requirementT engineeringT isT veryT demanding,T asT itsT resultedT decisionsT areT bothT crucialT andT difficult;T andT thatT isT dueT toT theT differentT typesT ofT usersT andT theirT varyingT interestT ofT systemT interaction. Moreover,T theseT decisionsT haveT aT abidingT impactT onT theT softwareT system.T Thus,T selectionT ofT requirementsT fromT heterogeneousT requirementsT isT aT decision-makingT processT thatT empoweredT systemT managersT toT focusT onT theT deliverableT softwareT thatT addedT mostT valueT toT aT system'sT outcome.T ToT findT theT optimalT setT ofT requirements,T justifyT thatT theirT isT aT needT ofT optimization.T AsT discussedT earlier,T inT thisT paperT geneticT algorithmT isT usedT toT optimizeT theT requirementT selectionT process.T InT orderT toT useT theT geneticT algorithm,T anT EncodingT schemeT isT usedT toT representT theT solutionT inT theT formT ofT chromosome.. Retrieval Number: H11120688S319/19©BEIESP. A. Design principle of Encoding Scheme InT orderT toT designT aT newT EncodingT scheme,T designerT mustT understandT theT basicT principalT ofT buildingT blocks(BB).T AccordingT toT GoldbergT [2o],T designT ofT encodingT schemeT hasT aT strongT impactT onT theT performanceT ofT GeneticT algorithmT andT shouldT beT chosenT carefully.T GoldbergT purposeT twoT basicT designT principalT namely: 1. The principle of meaningful building blocks 2. The principle of minimal alphabets TheT firstT principleT statesT thatT userT shouldT preferredT anT encodingT codingT schemeT suchT thatT theT buildingT blocksT ofT aT primaryT problemT areT limitedT andT analogouslyT unrelatedT toT buildingT blocksT atT otherT locations.T TheT principleT ofT significantT buildingT blocksT isT directlyT inspiredT byT theT \dT schemaT theoremT [2].T IfT schemataT areT deeplyT fit,T preciseT andT ofT lowT order,T thenT theirT numbersT rapidlyT increaseT overT theT generations. TheT otherT principleT statesT thatT theT userT shouldT selectT theT minimalT elementT thatT authorizesT anT expressionT ofT theT problemT soT thatT theT numberT ofT exploitableT schemasT isT maximizedT [21].T TheT principleT ofT minimalT elementsT tellsT usT toT maximizeT theT promisingT numberT ofT schemaT byT compressingT theT cardinalityT ofT theT elements.T WhenT usingT minimalT elementsT theT numberT ofT possibleT schemataT isT maximal.T ThisT isT theT reasonT whyT GoldbergT advisesT toT useT bitT stringT representations,T becauseT deepT qualityT schemataT areT moreT hardT toT findT whenT usingT elementsT ofT biggerT cardinality.T V. ANALYSIS OF EXISTING ENCODING SCHEMES DependingT onT theT designT ofT EncodingT scheme,T itT canT beT divideT intoT twoT class,T knownT as,T 1-dimensionalT andT 2-dimensional.T Binary,T Value,T RealT valueT andT PermutationT EncodingT areT 1-dimensionalT andT TreeT EncodingT isT 2-dimensionalT EncodingT techniquesT [3].T AnalyzingT theseT EncodingT schemes,T everyoneT canT concludeT thatT charactersT representedT byT permutationT EncodingT areT positionT reliant.T InT theT BinaryT EncodingT schemeT andT realT valueT EncodingT scheme,T theT charactersT areT valueT dependent.T T TheT twoT differentT aspectT classifiedT byT studyingT unlikeT EncodingT schemesT areT valueT andT locusT inT theT chromosome.T Thus,T factorsT likeT valueT andT locusT shouldT beT keptT inT mindT whileT EncodingT aT solutionT forT aT certainT problem.T BinaryT EncodingT isT theT familiarT arrangementT andT backingsT variousT typesT ofT crossoverT activities.T IntegerT andT FPRT haveT definedT applicationT relyT uponT theT problem.T PermutationT encodingT schemeT isT usedT toT showT certainT orderT inT chromosomes.T ItT allowsT inversionT operatorT butT doesT notT supportT simpleT crossoverT operatorT likeT oneT pointT crossover,T NT pointT crossover.T SpecialT crossoverT operatorsT likeT Partially-mappedT crossoverT (PMX),T OrderT crossoverT (OX)T orT CycleT crossoverT (CX)T isT usedT forT thisT representationT makingT itsT useT absolutelyT complex.T. 491. 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(4) Efficient Encoding Scheme in Genetic Algorithm for Requirement Optimization. VI. GOLDBERG CATEGORIZATION OF ENCODING GoldbergT hasT concludedT inT hisT workT thatT fitnessT functionT forT aT particularT EncodingT techniqueT isT dependentT onT twoT factors--T valueT andT orderT [22].T ThreeT differentT categoriesT ofT EncodingT canT beT groupedT dependingT onT fitnessT evaluationT factorsT suchT as:  Encoding schemes where fitness depends on only value: f(V). Eg: Value Encoding  Encoding schemes where fitness depends on order and value: f(V,o). Eg: Binary Encoding  Encoding schemes where fitness depends on only order: f(o). Eg: Permutation Encoding.. Figure 5. Representation of the requirements in the form of a chromosome. VIII. IX. CHALLENGES FOR NEW ENCODING SCHEME. VII. RESULTS AND PROPOSED ENCODING SCHEME So,T theT extantT EncodingT schemesT belongT theseT threeT classesT andT accordinglyT fitnessT functionT canT beT devised.T InT theT existingT EncodingT schemesT discussedT inT theT previousT sections,T theT lengthT ofT theT chromosomeT isT fixed,T andT suchT EncodingT schemesT areT notT suitableT forT theT representationT ofT theT requirementsT becauseT differentT usersT viewT theT problemT fromT differentT dimensions.T Consequently,T ifT theT requirementsT ofT aT userT areT representedT usingT chromosomeT whereinT genesT indicateT theT requirementsT onT aT threadT thenT theT sizeT ofT chromosomeT willT notT beT fixedT itT willT varyingT fromT oneT userT toT another.T TheirT requirementsT areT varying,T someT areT commonT andT someT areT altogetherT different.T ItT isT aT bigT challengeT forT softwareT engineersT toT representT theT requirementsT (gatheredT fromT theT differentT users),T inT theT formT ofT aT chromosomeT becauseT theT heterogeneityT ofT theT requirements.T Consequently,T thereT arisesT aT needT toT bringT toT lightT aT newT EncodingT schemeT thatT isT independentT ofT aboveT saidT twoT factorsT i.eT valueT andT order.T InT thisT newT EncodingT scheme,T RequirementsT areT storedT inT theT formT ofT aT SETT toT maintainT theT uniquenessT andT aT numberT isT assignedT toT everyT uniqueT requirement. A. Prerequisites for new Encoding scheme ItT isT assumedT thatT thereT areT NT usersT andT MT possibleT systemT requirementsT areT gatheredT fromT users,T outT ofT theseT MT requirementsT someT areT commonT andT someT areT altogetherT different.T EveryT requirementT isT assignT aT uniqueT numberT onT theT basicT ofT theirT uniqueness.T It is assumed that there is a SET of users, N={N1,N2,……….Nn} and a SET of possible system requirements, R = {{R1,R2 ,………………….Rm} In this new Encoding scheme all the requirements gathered from a user are represented as a chromosomes in raw form. In figure 3, chromosome 1 represents the requirements gathered from user 1 and so on.. A. Fitness function for new Encoding scheme TheT nextT challengeT isT toT findT theT fitnessT functionT forT proposedT EncodingT schemeT becauseT noT mathematicalT functionT isT availableT toT calculateT theT fitnessT valveT ofT aT chromosome.T AsT aT consequence,T humanT basedT oracleT [23]T canT beT usedT asT aT fitnessT function.T Therefore,T humanT basedT computationT isT anT alternateT fitnessT function.T B. Crossover Operators for Different Representations BinaryT EncodingT isT theT simplestT methodT ofT representingT chromosome.T InT crossoverT operation,T itT takesT twoT chromosomesT asT parentT andT generatesT twoT offspringT chromosomes.T ThreeT distinctT formsT ofT crossoverT suitableT forT binaryT EncodingT areT oneT pointT crossover,T NT pointT crossoverT andT UniformT crossover.T TheT sizeT ofT chromosomeT inT newT EncodingT schemeT isT notT fixed.T Consequently,T differentT crossoverT operatorsT usedT inT fixT lengthT binaryT EncodingT schemeT canT notT beT usedT inT thisT newT EncodingT scheme.T ChromosomesT havingT RealT valueT orT FPRT endureT ArithmeticT crossover.T ThisT crossoverT buildsT aT newT alleleT atT eachT geneT locationT inT theT offspring.T TheT valueT ofT newT alleleT goesT betweenT theT valuesT ofT theT ancestorT alleles. TheT crossoverT operatorT usedT inT valveT EncodingT canT notT beT usedT inT newT EncodingT scheme.T InT theT valueT Encoding,T everyT geneT representsT someT valueT butT inT theT proposedT Encoding,T everyT geneT representsT aT requirement. Encoding scheme acquiring integer values in their representation also execute the same set of crossover operations as executed by Binary Encoding such as One point crossover, N point crossover, Uniform crossover. InT permutationT Encoding,T theT fitnessT valueT ofT aT chromosomeT dependsT onT theT orderT ofT genesT butT newT EncodingT schemeT isT independentT ofT thisT factor.T InT viewT ofT theT aboveT facts,T itT isT concludedT thatT selectionT ofT crossoverT operatorT isT aT bigT challenge for this proposed Encoding. C. Mutation Operators for Different Representations InversionT ofT bitT isT veryT elementaryT mutationT usedT forT binaryT Encoding.T InT this,T bitT 1T invertedT byT 0T andT viceversa.T TheT numberT ofT bitsT thatT invertT relyT uponT theT mutationT rate.T ForT RealT. Retrieval Number: H11120688S319/19©BEIESP. 492. Published By: Blue Eyes Intelligence Engineering & Sciences Publication.

(5) International Journal of Innovative Technology and Exploring Engineering (IJITEE) ISSN: 2278-3075, Volume-8 Issue-8S3, June 2019. valueT orT FPR,T thereT existsT uniformT mutati0n,T GaussianT mutationT andT BoundaryT mutati0n.T ForT permutationT representation,T thereT areT collectionT ofT mutationT operatorsT likeT Swap,T ScrambleT andT InversionT [23].T SelectionT ofT mutationT operationT isT anotherT challengeT forT newT novelT EncodingT scheme.. 15.. X. CONCLUSION AND FUTURE WORK TheT intentionT ofT theT currentT researchT paperT wasT toT optimizeT theT requirementT engineeringT processT usingT metaheuristic.T InT orderT toT useT meta-heuristicT suchT asT GA,T firstT stepT isT toT representT allT theT possibleT solutionsT ofT aT problemT inT theT formT ofT aT chromosome.T InT thisT currentT paper,T itT hasT beenT identifiedT thatT theT existingT EncodingT schemesT areT notT suitableT toT optimizeT theT requirements.T AT newT EncodingT schemeT forT requirementT 0ptimizationT hasT beenT proposedT whichT canT dealT withT theT chromosomesT ofT varyingT lengths.T ItT isT hopedT thatT theT setT ofT challengesT discussedT inT theT previousT sectionT wouldT serveT toT stimulateT furtherT researchT inT thisT area.. 16.. 17.. 18.. 19. 20. 21.. REFERENCES. 22.. 1. GregorT Mendel.T VersucheT überT pflanzenhybriden.T VerhandlungenT desT naturforschendenT VereinesT inT Brunn4:T 3,T 44,T 1866. 2. 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DavidT ET Goldberg.T GeneticT algorithms.T PearsonT Education,T India,T 2006. DavidT ET Goldberg.T MessyT geneticT algorithms:T MotivationT analysis,T andT firstT results.T ComplexT systems,T 4:415–444,T 1989. DavidT ET GoldbergT andT JohnT HT Holland.T GeneticT algorithmsT andT machineT learning.T MachineT learning,T 3(2):95–99,T 1988. AET EibenT andT JET Smith.T IntroductionT toT evolutionaryT computingT (naturalT computingT series).T 2008. Yuen,T M.-C.,T Chen,T L.-J.,T andT King,T I.T (2009).T AT surveyT ofT humanT computationT systems.T 2009T InternationalT ConferenceT onT ComputationalT ScienceT andT Engineering,T 4:723–728. AUTHORS PROFILE RajeshT KumarT obtainedT hisT B.Sc.T Degree,T Master'sT DegreeT (MasterT ofT ComputerT Applications)T fromT KurukshetraT University,T Kurukshetra.T Currently,T HeT isT anT AssistantT ProfessorT inT theT DepartmentT ofT ComputerT ScienceT andT Application's,T inT ChhajuT RamT MemorialT JatT College,T Hisar,T Haryana,T INDIA.T HisT researchT interestsT areT inT GeneticT Algorithm,T TheoryT ofT Automata,T SoftwareT Engineering,T ArtificialT Intelligence,T DesignT andT AnalysisT ofT AlgorithmT andT Linux.T T. RakeshT KumarT obtainedT hisT B.Sc.T Degree,T Master'sT DegreeT --T GoldT MedalistT (MasterT ofT ComputerT Applications)T andT PhDT (ComputerT ScienceT \&T Applications)T fromT KurukshetraT University,T Kurukshetra.T Currently,T HeT isT ProfessorT &T ChairpersonT inT theT DepartmentT ofT ComputerT ScienceT andT Applications,T Kurukshetra,T University,T Kurukshetra,T Haryana,T INDIA.T HisT researchT interestsT areT inT GeneticT Algorithm,T SoftwareT Testing,T ArtificialT Intelligence,T andT Networking.T HeT isT aT seniorT memberT ofT InternationalT AssociationT ofT ComputerT ScienceT andT InformationT TechnologyT (IACSIT).. 493. T. Published By: Blue Eyes Intelligence Engineering & Sciences Publication.


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