Hybrid Approach with Improved Genetic Algorithm and Simulated Annealing for Thesis Sampling

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future internet
Article
Hybrid Approach with Improved Genetic Algorithm
and Simulated Annealing for Thesis Sampling
ShardromJohnson1,2,3,*,JinwuHan2,YuanchenLiu4,LiChen1andXinlinWu5
1 XianDaCollegeofEconomicsandHumanities,ShanghaiInternationalStudiesUniversity,
EastTiyuhuiRoad390,Shanghai200083,China;[email protected]
2 SchoolofComputerEngineeringandScience,ShanghaiUniversity,ShangdaRoad99,
Shanghai200444,China;[email protected]
3 InformationCentre,ShanghaiMunicipalEducationCommission,DaguRoad100,Shanghai200003,China
4 FacultyofForeignLanguages,NingboUniversity,FenghuaRoad818,Ningbo315211,China;
[email protected]
5 DepartmentofEducationEvaluationResearch,ShanghaiEducationEvaluationInstitute,
SouthShaanxiRoad202,Shanghai200031,China;[email protected]
* Correspondence:[email protected];Tel.:[phone]
Received:11July2018;Accepted:27July2018;Published:30July2018
Abstract: Sampling inspection uses the sample characteristics to estimate that of the population,
anditisanimportantmethodtodescribethepopulation,whichhasthefeaturesoflowcost,strong
applicability and high scientificity. This paper aims at the sampling inspection of the master’s
degreethesistoensuretheirquality,whichiscommonlyestimatedbyrandomsampling. Sincethere
are disadvantages in random sampling, a hybrid algorithm combined with an improved genetic
algorithm and a simulated annealing algorithm is proposed in this paper. Furthermore, a novel
mutationstrategyisintroducedaccordingtothespecialtyofShanghai’sthesissamplingtoimprove
theefficiencyofsamplinginspection;theaccelerationofconvergenceofthealgorithmcanalsotake
advantageofthis. Thenewalgorithmfeaturesthetraditionalgeneticalgorithm,anditcanobtain
theglobaloptimumintheoptimizationprocessandprovidethefairestsamplingplanunderthe
constraintofmultiplesamplingindexes. Theexperimentalresultsonthemaster’sthesisdatasetof
Shanghaishowthattheproposedalgorithmwellmeetstherequirementsofthesamplinginspection
inShanghaiwithalowertime-complexity.
Keywords: sampling; genetic algorithm; simulated annealing algorithm; thesis and dissertation
sampling;mutationstrategy
1. Introduction
Thethesisisoneoftheessentialprerequisitesforthegraduationofpostgraduates. Accordingly,
thesissamplinginspectionhasbeenregardedasasignificanttaskforanalyzingandcontrollingthe
quality. Such a quality inspection ensures the high-quality standards of postgraduate education.
Mostoftheexistingresearchstillisfocusedonthedouble-blindedreviewprocessofthedegreetheses.
Moreover,thereexistsnoappliedresearchoftheproblemthatPh.D.dissertationsandmaster’sdegree
thesesofthepreviousacademicyearmustbesampledforinspectionafter[1]wasissued.
In this paper, theses of the postgraduates who have achieved their degrees are used to carry
out sampling inspection under the requirements of the Shanghai Academic Degrees Committee.
The Shanghai Academic Degrees Committee builds the platform for provincial degree and
postgraduateeducation,andthesystemispracticallyusedintheShanghaiPostgraduateEducation
QualityInformatizationEvaluationSystem[2].
Tothisend,thispaperfocusesonthesamplingmethodthatmeetstheactualneedforquality
inspection. Thehybridapproachwiththecombinationofthegeneticalgorithmandthesimulated
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annealingalgorithmautomaticallysamplesmaster’sthesesfromShanghaiinthepreviousyearunder
the requirements of national sampling inspection of the Shanghai Academic Degree Committee.
Developmenttoolsareusedtoimplementthemethodtoreboundthetheoreticalresearchandpractical
applicationsfromtheaspectofspecificoperations.
Withthecombinationofthetraditionalgeneticalgorithmandthesimulatedannealingalgorithm,
anewmutationoperationisalsodeveloped,leadingtoefficientandeffectiveoptimizationforthe
sampling inspection of master’s degree theses. Under the process of the method, the sampling
inspection of the master’s theses of provincial degree committees will be more standardized
andinstitutionalized.
The rest of the paper is organized as follows: Section 2 introduces the background of paper
quality sampling, sampling rules and related algorithms. The details of the hybrid algorithms
withtheimprovedgeneticalgorithmandthesimulatedannealingalgorithmaregiveninSection3.
Experimental settings and dataset preprocessing are provided in Section 4. Section 5 presents the
experimentalresultswiththeanalysis. Section6drawstheconclusion.
2. Background
2.1. ThesisInspectionviaSampling
Nearly40,000postgraduatesgraduatefromShanghai’suniversitieseachyear. Becauseofthe
importance of the thesis to the graduation mentioned above, the quality of their theses needs to
be controlled. For this reason, the Academic Degrees Committee of the State Council and the
MinistryofEducationformallypromulgated[1]on29January2014,whichstipulatesthatthestate
will sample the doctoral dissertations and master’s degree theses in the previous academic year
nationwide. Thesamplingresultswouldbeusedasanimportantindicatorfortheevaluationofdegree
authorizationpoints. Ratherthanevaluatingallitems,samplinginspectionaimstorandomlyselecta
smallnumberofsamplesfromabatchofindividualsoraprocessaccordingtoanestablishedsampling
planandjudgewhetherthebatchofindividualsortheprocessmeetsthequalityrequirements[3]. Itis
animportantmethodtodescribethepopulation,whichhasthefeaturesoflowcost,strongapplicability
andhighscientificity.
Compared o the national sampling after degree-granting, the Shanghai Academic Degree
Commissionhasspent300,000to400,000RMBsince1997fortherandomsamplingand“double-blind”
reviewofdoctoraldissertationsandmaster’sthesesbeforedegreegranting. Ithasdirectlypromoted
the overall attention of graduate students and their supervisors to the quality of their theses or
dissertations[4]. Jiangsu,Hunan,Shandongandotherprovincesandcitieshavealsofollowedsuit
andthushavesomeachievements. Toacertainextent,theyhavealltogetherexertedapositiveeffect
onrectifyingacademicplagiarismandotherunhealthyacademictendencies,justasthesayinggoes,
“Ifyouwantpeopletothinkcorrectly,thefirstthingistoeliminateacademicmisconducts. Whenfaults
occur,thenrightorwrongisreversed“[5].
The primary purpose of this national sampling after degree-granting is not to influence
the normal learning and employment of the applicants for degrees and the degree-granting of
degree-cultivationunits,buttopromotetheconstructionofprofessionaldisciplinesandthetraining
oftalents. Emphasisislaidupontheperformanceofsupervisorsandthetrainingqualityofdegree
authorization institutions [6]. Moreover, [1] further clarified as the method for the sampling of
master’sdissertationsis determinedbyprovincialdegree committeesand thePeople’sLiberation
ArmyAcademicDegreeCommittee.
Therefore, the correct understanding of the spirit of the national sampling method and how
to implement it in the administrative area of Shanghai have become some of the critical tasks at
themoment.
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2.2. SamplingRules
IntheShanghaisamplingmethod,thesamplingrulesarelistedasbelow.
(1) Thesamplingrateofmasters’thesesfromeachmasterdegreeconferringinstitutionisabout5%.
(2) About10%offoreignmasters’thesesneedtobeextractedforsamplinginspection.
(3) Thesamplingrateofthesesofmasterswhosetutorguidedtenormorepostgraduatesinthesame
yearisabout10%.
2.3. GeneticAlgorithm
Thegeneticalgorithm(GA)[7]isanevolutionaryalgorithminspiredbytheprincipleprocessof
naturalselectionandsurvivalofthefittest. GAiscommonlyusedtogeneratehigh-qualitysolutionsto
optimizationandsearchproblemsbyrelyingonbio-inspiredoperationssuchasmutation,crossover
andselection[8]. AsshowninFigure1.
Figure1.Schematicdiagramofthegeneticalgorithm.
GA mainly borrows the principle of the survival of the fittest in biological evolution.
First,thesolution to the optimization problem is encoded. Here, the encoded solution is called a
chromosome,andtheelementsthatmakeuptheencodingarecalledgenes. Then,accordingtothe
objective function of the optimization problem, the corresponding fitness function is constructed,
andthechromosomeisselectedbytheprobabilitydistributiondeterminedbythesizeofthefitness
function. Thesurvivedchromosomesconstituteapopulation,andatthesametime,theparentsare
randomly generated according to the probability distribution. Then, the parents create offspring
throughmatingbetweenthecodes,andconsequently,theoffspringmutatewithacertainprobability
toformanewpopulation. Atthistime,thedecodingturnsbacktothesolutiontotheoptimization
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problem. Finally, the termination rule is applied. Through the above cycle, the solution of the
optimizationproblemisobtained.
Common iterative methods tend to fall into a local minimum trap, and thus, a dead loop
phenomenon emerges, which makes the iteration process unable to continue. To overcome this
shortcoming,GAadoptsaglobaloptimizationapproach[8]. Comparedwithtraditionaloptimization
methods(likeenumeration,heuristics,etc.),GAhasgoodconvergenceduetotheadaptationofthe
biologicalevolutionmodel[9]. GAalsohasseveraladvantagesasfollows.
• Ithasnobiasforspecificproblemareas.
• Ithasthecapacitytoperformafastandrandomsearch.
• Itusesasimplesearchprocesswiththeevaluationfunction.
• Itfeaturesrandomnessastheprobabilisticmechanismusedfortheiteration.
• Itisextensibleandeasytointegratewithotheralgorithms.
ManyvariantsofGAanditsapplicationswerethoroughlystudiedby[10]. Recently,GAhasbeen
oneofthewidely-usedalgorithmsinsolvingoptimizationproblemssuchasforimageprocessing
andcommunications. Inthispaper,weuseittomakeasamplinginspectionof40,000masters’theses
accordingtothethreerulesforthesissamplinginShanghaimentionedinSection2.2.
2.4. SimulatedAnnealing
Simulatedannealing(SA)isalearningmethodthatsimulatesthephysicalquenchingprocess
in thermodynamics. Its starting point is based on the similarity between the annealing process of
solidmaterialsinphysicsandgeneralcombinatorialoptimization[11]. Itisagreedyalgorithm,butits
searchprocessintroducesrandomfactors. Wheniteratingtoupdatethefeasiblesolution,asolution
worse than the current solution is accepted with a certain probability, so it is possible to get the
optimalglobalsolutionbyjumpingoutofthelocaloptimalsolution[12]. In[13–15],thesimulated
annealingalgorithmwasimprovedorcombinedwithotheralgorithmstoachieveabetterperformance
inexperiments.
Figure2isanexample. Assumingthattheinitialsolutionistheleftbluepoint A,thesimulated
annealingalgorithmwillquicklysearchfortheoptimallocalsolutionB,butaftersearchingforthe
optimal local solution, it does not end there, but will move to the left with a certain probability.
Maybeafterafewofthesenon-locallyoptimalmoves,theglobaloptimumDisreached,andthelocal
minimumjumpsout.
Figure2.Simulatedannealingalgorithm.
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Accordingtotheprincipleofthermodynamics,whenthetemperatureisT,theprobabilityofthe
temperaturedropwiththeenergydifferenceofdEis p(dE),whichisexpressedas:
dE
p(dE) =exp( ), (1)
kT
wherekistheBoltzmannconstant;thevalueis1.3806488×10−23,anddE <0. ThereforedE/kT <0,
sothevaluerangeofthe p(dE)functionis(0,1). Infact,themoreintuitivemeaningofthisformula
is: thehigherthetemperature,thegreatertheprobabilitythattheenergydifferenceis p(dE),andthe
lowerthetemperature,thelowertheprobabilityoftemperaturedrop.
Inpracticalproblems,thecalculationof“certainprobability”herereferstotheannealingprocess
of metal smelting. Assuming that the currently feasible solution is x and the iteratively-updated
solutionisx ,thenthecorresponding“energydifference”isdefinedas:
new
∆f = f(x )− f(x), (2)
new
anditscorresponding“certainprobability”is:
1, if ∆f >0

p(∆f) = ∆f (3)
exp( ), if ∆f ≤0
kT
Here,letk=1. Thesimulatedannealingalgorithmcanbedescribedasbelow,
Step1: Initialization: initialtemperatureT(sufficientlylarge),originalbestsolutionxobtainedafter
GAapplied;solutionobtainedfromthepreviousiterationx .
new
Step2: Calculate theincrement ∆f = f(x )− f(x), where f(x) is theoptimization target. Here,
new
itisthefunctionthatminimizesthemeanabsoluteerror(cid:101)calculatedaccordingtothesampling
rulesafterthesamplingresultisobtainedbydecodingthesolution. Weusetheresultofone
minus(cid:101)torepresentthefitnessfunctionvalue;seeSection3.4.
Step3: If∆f >0,x isacceptedasthenewcurrentsolution,otherwisex isacceptedasthenew
new new
currentsolutionwiththeprobabilityexp(∆f).
kT
Step4: Iftheterminationconditionissatisfied,thecurrentsolutionisoutputastheoptimalsolution
toterminatetheprogram. Otherwise,waitforanewx togotoStep2.
new
3. TheProposedAlgorithm
3.1. TheMainIdea
Themajorstepsoftheproposedalgorithmare:
Step1: Initialize the variables of GA and SA; determine the initial temperature of annealing T ,
0
temperature reduction parameter k, size of population s, crossover probability pcross and
mutationprobability pmutationbytheresultobtainedfromtheexperimentinSection4.2;
Step2: Randomlygenerateinitialpopulation p ,andencodeeachchromosome;thesizeof p is10;
0 0
Step3: Calculatethemeanabsoluteerror(cid:101)ofthesamplingschemecorrespondingtoeachchromosome
according to the sampling rules, then the fitness of each chromosome is denoted as f;
let f =1−(cid:101).Determinethefitnessfunctionofeachchromosomeinthepopulation(f =1−(cid:101));
seeSection3.4;
Step4: Roulettewheelmethodisusedtoselectschromosomesfrom p toconstitutenewpopulation
0
p,theprobabilityofchoosinganindividualdependsdirectlyonitsfitnessvalue f;
Step5: Randomlychoosetwochromosomesfrom p,andapplythecrossoveroperatortothem;
Step6: ApplythemutationoperatordescribedinSection3.3tothenewpopulation;
Step7: Letthecurrentpopulationbethenewpopulation;
Step8: Ifthemeanabsoluteerror(cid:101)islessthan0.2%,thentheconvergencecriterionissatisfied;stop.
Otherwise,gotoStep4.
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3.2. CodingandInitializationMethods
According to [16], the floating point representation is faster, more consistent and provides
higherprecisionespeciallywithlargedomainswherebinarycodingwouldrequireprohibitivelylong
representation. Comparedwithbinarycoding,thefloatingpointcodinghasobviousadvantages[17]
asfollows.
1. Thefloatingpointcodingdoesnotrequireadecodingprocess.
2. It represents a larger range of numbers in the genetic algorithm, which is convenient in
largerspaces.
3. Italsosimplifiesthetraditionalgeneticalgorithmandimprovesthecomputationalefficiency.
4. Furthermore,thefloatingpointencodingpreventstheprecisionerrorscausedbythehexadecimal
conversion.
5. Itiseasytomixitwithclassicaloptimizationmethods.
Thus,thefloatingpointrepresentationisusedinthispaper. Afterthemaster’sthesisdatasetis
preprocessed,thethesisnumberwillparticipateinthecodingoperation.
Figure3showsthechromosomecodingschemeinthispaper. nisthetotalnumberofthesisto
besampled. p_ij(1≤ i ≤k,1≤ j ≤m)isthesequencenumberofthethesistakenfromthethesis
samplepopulationrandomlytogeneratethepopulationinGA.Then,letω_ij= p_ij/ntoindicatethe
encodedvalueofthegenesinchromosomes.
Figure3.Initializationandencoding.
Forexample,forthefirstchromosomeinFigure3,assumenequals10andmequals5: thetheses
withSerialNumbers1,3,5,7,8areselected. Accordingly,afterencoding,thegenecodesare0.1,0.3,
0.5,0.7,0.8.
3.3. Selection,CrossoverandMutation
Theselectionoperatorchoosessomegoodindividualsfromthecurrentpopulationandtransfers
them to the next generation [18]. Methods used as the selection operator can be classified into
two categories: proportional and elitist. The former category employs the probability of selection
proportional to the fitness value of each individual. These methods allow maintaining a genetic
diversitywithinthepopulationofcandidatesolutionsthroughoutthegenerations,whichprevents
GAfromfallingintolocaloptima. However, thesemethodsincreasethetimeofconvergence[19].
Thispaperusestheroulettewheelmethodmakingindividualswithhigh-fittingvaluesgetahigher
probabilityofsurvival. Thebasicideaunderthismethodisthattheprobabilityofeachindividual
beingselectedisproportionaltoitsfitnessvalue. Theproportionalselectionmethodhasenormous
randomnessandthusmightbetrappedinlocalextrema. Theintegrationofsimulatedannealingfactor
intothegeneticalgorithmleadstoavoidslowconvergencerateandlocalextremaproblem.
Thecrossoveroperatornewlyproducessomebetterindividualpatterns[20],whichisthemain
elementofthesearchprocessinoptimization. TheencodingtypeusedinGAisthemajorcriteriafor
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selectingthecrossover. Theglobalconvergenceandsearchspacemustbeconsideredforselectingthe
crossoveroperators. theeffectofcrossoveroperatorsinGAisdependentontheapplication,aswellas
encoding[21]. Here,thetwo-pointarithmeticcrossoverisused.
ω (t) = (ω ,ω ,...,ω ) (4)
1 11 21 n1
ω (t) = (ω ,ω ,...,ω ) (5)
2 12 22 n2
whereω (t)andω (t)aretwochromosomesattimet. Lettworandomnumbersgeneratedattime
1 2
tbei(1 ≤ i ≤ n)and j(0 < j < 1). Then,thetwo-pointarithmeticcrossoveratthei-thlocusofthe
(cid:48) (cid:48)
abovetwochromosomes,respectively,asω (t)andω (t),isdefinedasfollows:
1 2
(cid:48)
ω = j∗ω +(1−j)∗ω (6)
i1 i2 i1
(cid:48)
ω = j∗ω +(1−j)∗ω (7)
i2 i1 i2
Thefollowingdescendantsarepropagated:
(cid:48)
ω (t+1) = (ω ,ω ,...,ω ,...,ω ) (8)
1 11 21 i1 n1
(cid:48)
ω (t+1) = (ω ,ω ,...,ω ,...,ω ) (9)
2 12 22 i2 n2
where,iisthelocusinvolvedinthecrossoveroperationonthechromosome. nisthelengthofthe
chromosomes,thatis,thenumberofgenes. Inthispaper,itisthenumberofselectedtheses.
The mutation operator is employed to avoid establishing a uniform population unable to
evolve [22]. According to [23], the NP-complete problems are intractable, i.e., they can be solved
theoretically,butinpractice,theytaketoolongfortheirsolutionstobeuseful.
Onceanewgenerationiscreatedafterthecrossoveroperation,thegeneticprocessisperformed
iterativelyuntilanoptimalresultisfound. Wehaveusedthetraditionalgeneticalgorithmtosolvethe
thesissamplingproblem. Morethan30,000iterationswerecarriedout,whichtooknearly3.5h,and
thesamplingeffectwasnotideal. Byanalyzingthetraditionalgeneticalgorithm,wefoundthatthe
wholealgorithmwastimeconsuming. Sincethemutationoperatorisdirectionless,webelievethat
somemodificationscouldbemadetothemutationoperatorbasedonthetraditionalgeneticalgorithm
tospeeduptheconvergenceofthealgorithm. Thus,animprovedmutationstrategyisintroducedas
Algorithm1.
Figure4,providedbelow,isforeasierunderstandingoftheproposedmutationoperation.
Figure4.Schematicdiagramoftheimprovedmutationoperation.
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Algorithm1:Mutationstrategy.
1. Input:Thesisdata,mutationprobability,chromosomelength,numberofchromosomesandthefitness
2. valueofeachchromosome.
3. Output:Mutatedchromosomes
4. Initializeparameter:(cid:101)
5. fori=1tothesizeofthepopulation
5. do
6. fork=1tothelengthofthechromosome
7. do
8. Denotetheextractedthesisset(chromosome)asS,thencalculatetheerroroftheuniquesubset
9. ofSdeterminedbythesamplingsrulesaccordingtothevalueofthegenes.
10. endfor
11. Assume that the subset a of set S has the maximum error, and subset b of set S has the
minimumerror.
12. Onthecurrentchromosome,amutationoperationisperformedbyrandomlyreplacingagene
13. correspondingtoanelementofsetawithagenethatsatisfiessetb.
14. Checkwhetherthechromosomeafterthemutationmeetstherequirementthatthesametwogenes
15. donotexistonthechromosome.
16. ifthemutatedchromosomemeetstherequirements
17. ThemutatedchromosomesareacceptedaccordingtoEquation(3);
18. else
19. Undothemutationoperation.
20. endif
21. endfor
3.4. TheDefinitionofFitnessFunction
AccordingtothesamplingrulesintroducedinSection2.2,thefitnessfunctionisdefinedasfollows:
1 ∑n (cid:113)
f =1− (P −E)2, (10)
i i
n
i=1
itisequivalentto:
f =1−(cid:101), (11)
where n denotes the number of constrained conditions (sampling rules) and P and E indicate,
i i
respectively,theactualsamplingrateandtheexpectedsamplingrateofthesubsetthatsatisfiesthei-th
samplingrule. (cid:101)isthemeanabsoluteerror. Then,theobjectivefunctionofourproposedalgorithmis,
1 ∑n (cid:113)
g = min( (P −E)2), (12)
i i
n
i=1
whichisequivalenttothefollowingequation,
1 ∑n (cid:113)
h = max(1− (P −E)2). (13)
i i
n
i=1
4. ExperimentalSetup
This section describes the experimental setup for evaluating the proposed algorithm.
Theparametersusedforthealgorithmarealsoprovided.
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4.1. ExperimentalSetup
TheimprovedGAwasimplementedinMATLABandevaluatedinthetaskforthesamplingof
Shanghaipapers. Forafaircomparison,thetraditionalGAandothercomparisonalgorithmswerealso
implementedinMATLAB.TheevaluationswereexecutedonaMacBook-Prowith8GBmemoryona
2.7-GHzIntelCorei5processor. TheprocessedinformationofShanghaimunicipalmaster’sdegree
thesessubmittedfromShanghaiin2014wasusedasinputdata. Intotal, 39,779theseswereused
fortheevaluation. Thenumberofsampledthesesanderrorrateswereanalyzedandprovidedin
Section5.
4.2. Parameters
Figures5–7showtheanalysisaccordingtovaryingparameters. Basedontheanalysisandother
information,theparametersweresetasTable1.
Table1.Experimentparameters.
Sizeofinitialpopulationis10
Sizeofpopulationsizepop=4
Probabilityofcrossoverpcross=0.97
Probabilityofmutationpmutation=0.3
Modeofselection fselect=‘roulette’
Methodofcoding fcode=‘float’
Modeofcrossover fcross=‘float’
TemperatureofannealingT =100
0
Temperaturereductionparameterk=0.98
Figure5.Effectofchromosomenumberontheobjectivefunctionvalue.
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Figure6.Effectofcrossoverprobabilitiesontheobjectivefunctionvalue.
Figure7.Effectofmutationprobabilitiesontheobjectivefunctionvalue.
4.3. RedundancyReductioninData
ThesourcedatashownasFigure8ahavetoomuchredundantinformationrelativetothedata
requiredfortheexperiment,sotheyneedtobeprocessed.Theprocessmainlyincludes:addingmissing
dataitems,numberingthethesesfrom1to39,779andaddingattributesrelatedtothesamplingrules.
Toremoveirrelevantdataitems,theprocesseddataareasshownbelow.