Efficient Encoding Scheme in Genetic Algorithm for Requirement Optimization



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 complica-

tion 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

 _{Revised Manuscript Received on Date}

Rajesh Kumar, Dept. ofComputer Science & Applications, K.U., Kurukshetra, Haryana, INDIA.

Prof. Rakesh Kumar, Dept. ofComputer Science & Applications, , K.U., Kurukshetra, Haryana, INDIA.

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 l_i,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:

S

=

S

i=1 N

å

i

suchT thatT NT representT theT numberT ofT objectT variables.T

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

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

T 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

Figure 4. Tree Encoding Representation

T treeT determineT theT powerT andT fitnessT ofT theT

representation.T AsT aT resultT ofT cyclicT natureT ofT parseT

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.

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

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.

VII.RESULTSANDPROPOSEDENCODING

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.

Figure 5. Representation of the requirements in the form of a chromosome.

VIII.

IX. CHALLENGES FOR NEW ENCODING SCHEME

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

off-spring.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

vice-versa.T TheT numberT ofT bitsT thatT invertT relyT uponT theT

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.

X.CONCLUSION AND FUTURE WORK

TheT intentionT ofT theT currentT researchT paperT wasT toT

optimizeT theT requirementT engineeringT processT usingT

meta-heuristic.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.

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AUTHORSPROFILE

T 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