costwindtour

PartIAFrameworkforVisualizationandOptimization17Thefivechaptersofthispartprovideawhirlwindtourofsomebasictheories,frameworks,andideasfromavarietyoffieldsincludingcogni-tivepsychology,human-computerinteraction,computergraphics,com-puterscience,artanddesign.
Clearlythosefieldsarefartoobroadtobecoveredinthreechapters,letaloneasinglebook.
Thefocusisonsomeofthemoreimportantideasandresults.
Inthesecondpartofthebook,webuildonthebasicspresentedhere,emphasizingtheirapplicationtovisualizationandoptimization.
Inordertoorganizeourdiscussionofvisualizationandoptimization,wepresentasimpleframework(Figure1.
4).
Theframeworkis:Thesuccessofvisualizationforaproblem-solvingprojectdependsonthetaskstobeaccomplished,thepeopleinvolved,andtherepresentationsformatsusedforthetaskandthepeo-ple.
TaskPeopleFonnatFigure1.
4:Aframeworkforvisualizationandoptimization.
Inotherwords,differentpeoplemaybenefitfromdifferentrepresen-tationformatsfordifferenttasks.
Althoughthisframeworkmayseemobvious,ithasnotalwaysbeenapparenttomany.
Forexample,researchcomparingtheeffectivenessoftraditionaltwo-dimensionalplotstotabularrepresentations(knownasthe18"graphs-vs-tables"question)iswidelyacknowledgedtobe"amess"[1].
Theresearchresultstodatehavebeenalmostcompletelyequivocal.
Somestudiesfoundnodifferenceinperformance,othershavefoundthattablesproducedbetterperformance,andothersfoundthatgraphsproducedbet-terperformance.
Theexplanation,intheabstractatleast,isquitesimple.
Mostofthestudiesuseddifferenttasks,representations,andsubjects.
Withineachstudy,onlyvariationsinrepresentationformatweremade.
Eachindivid-ualexperimentthereforewasvalidonlyfortheparticulartaskandsub-jectpopulationstudied.
Therealquestionisnotgraphsversustables,butrather,whatcharacteristicsoftasksandsubjectsfavorgraphsovertables(andviCeversa)Anotherexampleontheimportanceofrepresentationtoproblemsolv-ingcomesfromLarkinandSimon[2].
Considerthefollowinggame:Eachofthedigits1through9iswrittenonaseparatepieceofpaper.
Twoplayersdrawdigitsalternately.
Assoonaseitherplayergetsanythreedigitsthatsumto15,thatplayerwins.
Ifallninedigitsaredrawnwithoutawin,thenthegameisadraw.
Onemightbesurprisedtolearnthatthisgameisequivalenttotic-tac-toe(sometimescalled"noughtsandcrosses").
Ifoneplacesthedigits1through9inthefollowingtable,however,thecorrespondenceisclear.
618753294Anywinintic-tac-toecorrespondstoaselectionofdigits,threeofwhichsumto15.
Inthiscase,avisualrepresentationseemsparamount.
However,anotherexample,fromAdams(viaGlassandHolyoak[3])showstheimportanceoftextualrepresentationsovervisualrepresenta-tions:Considerasheetofpaper1I100thofaninchthick.
Foldthepaperinhalf,andtheninhalfagain.
Repeatthisprocess50timesintotal.
Ofcourse,itisnotphysicallypossibletoper-formthistask,butimagineifyoucan.
Howthickisthere-sultingfoldedpaperInthiscase,thevisualrepresentationgivesfewclues,butusingstandardmathematicalnotation-text-theanswercaneasilybefound,1/100x250inches.
19Theimportanceofmatchingthecharacteristicsofthetask,theviewerandtheformathasbeencalledcognitivefitbyVessey[4],[5].
Vessey[4]definescognitivefitasacost-benefitcharacteristicthatsuggeststhat,formosteffectiveandefficientproblemsolvingtooccur,theprob-lemrepresentationandanytoolsoraidsemployedshouldallsupportthestrategies(methodsorprocesses)requiredtoper-formthattask.
Inareviewofthegraphsversustablesliterature[5],basedonthecog-nitivefithypothesis,Vesseywasabletoofferacogentexplanationastowhysomestudiesfoundgraphssuperiortotablesandothersfoundtablessuperiortographs.
Eachstudyconsidereddifferenttasksanddifferentrepresentationformats.
Whateverformatwasbestmatchedtothetaskyieldedsuperiorperformance.
Thecognitivefithypothesisimpliesthatrepresentationformatmat-ters;itaffectshumanperformanceinsolvingproblems.
Bycarefullymatch-ingtherepresentationformattothetaskathand,performancecanbeen-hanced.
Oneofthegoalsofthisbookistoexploreappropriaterepresen-tationformatsforthemanytasksinvolvedinoptimizationmodeling.
1.
6TasksNumerousauthorshaveproposedframeworksforclassifyingthetasksin-volvedinanoptimizationproject.
Theseframeworksassumethatopti-mizationprojectsinvolveaseriesofstagesorsteps,thatis,amodelinglife-cycle.
1.
6.
1TheModelingLifeCycleThelife-cycleideaisembodiedinSimonandNewell's[6],[7]modelofdecisionmaking,Intelligence-Design-Choice.
Accordingtohisframe-work,intheIntelligencephaseofproblemsolving,informationisgath-eredinanattempttounderstandthenatureoftheproblem-thebound-ariesoftheproblem,thoseaffectedbytheproblem,thecostsandbenefitsoftheproblem.
IntheDesignphase,alternativesolutionstotheproblemareconstructed.
IntheChoicephase,oneormoreofthealternativesareselected.
Manyproblemsconcentratemoreononeofthesephasesthanonanother.
Foroptimizationmodeling,manydifferentauthorshavedescribedthestagesinthemodelinglife-cycle,withvaryinglevelsofdetail.
Table1.
1201.
6.
TASKSAuthorsSimonandChurchman,Ack-ThisBookNewell[6],[7]offandArnoff[8]IntelligenceFormulatingtheModelproblemDevelopmentDesignConstructingaAlgorithmmathematicalDevelopmentmodeltorepre-sentthesystemunderstudyDerivingaso-lutionfromthemodelTestingthemodelSolutionAnalysisandthesolutionderivedfromitChoiceEstablishingResultscontrolsoverthePresentationsolutionImplementationPuttingtheso-Implementationlutiontowork:implementationTable1.
1:Comparisonofdifferentversionsofthemodelinglife-cycle.
21liststhreeofthedifferentframeworks,attemptingtomatchstepsfromoneframeworkwiththosefromanother.
Forpurposesofthistext,weshallsimplifythemodelinglife-cycleintofivestages:1.
ModelDevelopment.
Thisincludesidentifyingtheunderlyingprob-ilem,collectingandanalyzingdata,formulatingamathematicalmodel.
2.
AlgorithmDevelopment.
Dependingontheproblemidentifiedinthepreviousstage,algorithmdevelopmentmaybetrivial,ifanex-istingpieceofsoftwarecanbeusedtoanalyzethemodel.
How-ever,formanyoptimizationproblems,thealgorithmmustbecare-fullyconstructed.
3.
SolutionAnalysis.
The"solutions"producedbyalgorithmsmustbetested,probedanddebugged.
Thedatacould(will)haveer-rors,themodelcouldhaveproblems,orthealgorithmcouldfailtoconverge.
Furthermore,evenwithadebuggedmodel,dataandal-gorithm,onemustthenattempttounderstandtheirbehavior.
Whenthepriceofasetofinputsrises,howdoesthataffectthesolutionIfonerelaxessomeconstraints,howdoesthesolutionchangeInotherwords,inthisphase,onealsoattemptstorelatetheinforma-tionprovidedbythealgorithmbacktotherealproblembeingat-tacked.
4.
ResultsPresentation.
Theresultsgeneratedbythepreviousphasemustbepresentedtothepeopleincharge,thepeoplepayingforthestudy,thepeopleactuallyresponsibleforsolvingtheproblem.
Theywillprobablybeskeptical;theymustbeconvincedthattherecommendationsbeingmademakesense.
Usuallytheywillnotreallyunderstandthesophisticatedmathematicalandcomputertech-niquesusedtosolvetheproblem.
But,theyneedtobeconvincedthattherecommendationsaresound.
5.
ImplementationGiventheresultsoftheanalysis,thechoicemustbeimplemented.
Itmustbecommunicatedtothoseresponsibleforeffectingthechange,andtheprocessofchangemustbecontinuallymonitored.
Althoughthisframeworkcontainsfewerstepsthanmanyofthepro-posedmodelinglife-cycles,itarguablycapturestheessenceofhowmod-elsevolveovertime,startingwithidentifyingtheproblemandendingwithfinalresults.
Onecaneasilybelulledbythecleanpicturepresentedbyanysuchlife-cyclemodel.
Inactualmodelingprojects,progressdoesnotfollow221.
6.
TASKScleanlyandsurelyfromonestagetoanother.
Oftenproblemsthatareun-detectedinpreviousstagesareonlyuncoveredinlaterstages,forcingaretreatbacktoanearlierstagetofixtheundetectedproblem.
Inarecentstudy[9],[10]expertmodelerswerefoundtomovequiteoftenamongthedifferenttasksinthemodelinglife-cycle.
1.
6.
2VisualizationandtheModelingLifeCycleFromtheviewpointofvisualization,themodelinglife-cycletransformsvague,poorlydefinedrepresentationsofaproblemintoanunderstand-able,convincingsolutiontotheproblem.
Duringthemodelinglife-cycle,representationssuchasmathematicalformulations,inputstoalgorithms,programlistings,algorithmoutputs,amongotherscanbeofuse.
Thefieldofoptimizationhasconcentratedmostofitsenergyonmerelyonephaseofthemodelinglife-cycle:algorithmdevelopment.
Themodelinglife-cycle,ontheotherhand,involvesmanyotheractivities.
Represen-tationisacommonthreadunderlyingallthephasesofthemodelinglife-cycle.
Therefore,thestudyofthoserepresentationsshouldhelpimprovethechancesforsuccessinamodelingproject.
Differentrepresentationsarerequiredatdifferentphasesofthemod-elinglife-cycle(Table1.
2).
Inthenextchapter,foreachphaseofthemod-elinglife-cycle,wediscussappropriaterepresentations.
Inthefollowingchapter,wediscusshowthedifferentrepresentationscanbeusedtosup-portvariousaspectsofoptimization.
1.
6.
3SummaryThissectionhaspresentedseveralversionsofthemodelinglife-cycle.
Althoughtheydiffer,theyallbasicallyfollowthesameidea:modelingconsistsofavarietyofdifferenttasks.
Althoughactualmodelingprojectsareusuallyfarmessierthanthecleanpicturepresentedbytheselife-cyclemodels,thetaskslistedinthelife-cyclemodelsdoinfactoccur.
Thechaptersintherestofthispartofthebook(Chapters2-6)discusstheothertwocomponentsofourbasicframework,peopleandformat.
Chapter2discussesmodelsofhumanperceptionandcognition,aswellassomeofthedifferencesamongpeoplethathavebeenidentifiedbycog-nitivepsychologists.
Chapters3-6discussindetailtheories,frameworksandrecommendationsforthevarietyofdifferentrepresentationformatsthatcanbeusedtorepresentcomplexinformation.
PartIIofthebookconsidershowvisualizationcansupporteachphaseofthemodelinglife-cycle.
PartIIIofthebookdiscusseshowdifferentrepresentationformatscanbeusedtosupportoptimization.
23ModelAlgorithmSolutionResultsDevelop-Develop-AnalysisPresenta-mentmenttionTextAlgebraicProgram-StandardNarrativeLanguagesmingOutputLanguagesTablesSpread-MatrixMatrixSummarysheets;ImagesImagesTablesBlockStructuredStaticGraph-VisualPresentationPresentationGraphicsBasedLanguagesGraphicsGraphicsAnimatedorModelingbyAlgorithmAnimatedAlgorithmInteractiveExampleAnimationSensitivityAnimation;GraphicsAnalysisAnimatedSensitivityAnalysisSoundTouchTable1.
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