EVOLVINGBUILDINGBLOCKSFORDESIGNUSINGGENETIC ENGINEERING A FORMAL APPROACH.

Abstract. This paper presents a formal approach to the evolution of a representation for use in a design process. The approach adopted is based on concepts associated with genetic engineering. An initial set of genes representing elementary building blocks

EVOLVINGBUILDINGBLOCKSFORDESIGNUSINGGENETICENGINEERING:AFORMALAPPROACH.

JOHNS.GEROANDVLADIMIRA.KAZAKOV

KeyCentreofDesignComputing,

DepartmentofArchitecturalandDesignScience,

TheUniversityofSydney,NSW2006Australia.

e-mail:john,kaz@arch.su.edu.au

Abstract.Thispaperpresentsaformalapproachtotheevolutionofarepresentationforuseinadesignprocess.Theapproachadoptedisbasedonconceptsassociatedwithgeneticengineering.Aninitialsetofgenesrepresentingelementarybuildingblocksisevolvedintoasetofcomplexgenesrepresentingtargetedbuildingblocks.Thesetargetedbuild-ingblockshavebeenevolvedbecausetheyaremorelikelytoproducedesignswhichex-hibitdesiredcharacteristicsthanthecommencingelementarybuildingblocks.Thetar-getedbuildingblockscanthenbeusedinadesignprocess.Thepaperpresentsaformalevolutionarymodelofdesignrepresentationsbasedongeneticalgorithmsandusespatternrecognitiontechniquestoexecuteaspectsofthegeneticengineering.Thepaperdescribeshowthestatespaceofpossibledesignschangesovertimeandillustratesthemodelwithanexamplefromthedomainoftwo-dimensionallayouts.Itconcludeswithadiscussionofstyleindesign.

1.Introduction

Thereisanincreasingunderstandingoftherolethatadesignlanguageanditsrep-resentationplayintheef ciencyandef cacyofanydesignprocesswhichusesthatlanguage(Coyneetal.,1990;Geroetal.,1994).Arecurringissueiswhatistheappropriategranularityofalanguage.Ifbuildingblockswhichconstitutetheelementsofadesignmapontoadesignlanguagethenthequestionbecomeswhatisanappropriatescaleforthosebuildingblocksintermsofthe naldesign.Atoneextremewehaveparameterisedrepresentationswherethestructureofadesignis xed,allthevariableswhichgotode neadesignareprede nedandwhatisleftistodeterminethevaluesofthosevariables.Thisde nesaverysmalldesignspace,smallintermsofallthepossibledesignswhichmightbeabletobeproducedforthatdesignsituation.Attheotherextremewehaveelementarybuild-ingblockswhichcanbecombinedinaverylargevarietyofwaysandwhich,asa

Abstract. This paper presents a formal approach to the evolution of a representation for use in a design process. The approach adopted is based on concepts associated with genetic engineering. An initial set of genes representing elementary building blocks

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Se

Figure1.

ingblocks,

variables,isthedesignspaceproducedbyallthepossiblecombinationsoftheelementarybuild-isthedesignspaceproducedbyallthecombinationsofthevaluesoftheparameterisedisthedesignspaceofinterestingdesignsforthedesignsituation.

consequencede neaverylargedesignspace,thevastpartofwhichcoversdesignswhicharelikelytobeuninterestingintermsofthecurrentdesignsituation.Thedesignsproducedbytheparameteriseddesignrepresentationsareasubsetofthosecapableofbeingproducedbytheelementarybuildingblockrepresentation,Fig-ure1.Examplesofbuildingblockrepresentationsincludeconstructivesystemssuchasdesigngrammarsasexempli edbyshapegrammars(Stiny,1980b).Ex-amplesofparameterisedvariablerepresentationsincludeawidevarietyofdesignoptimizationformulations(Gero,1985).

Theadvantageoftheuseoftheelementarybuildingblocksrepresentationisthecoverageoftheentiredesignspacetheyprovide,whereastheadvantageoftheparameterisedvariablerepresentationistheef ciencywithwhichasolutioncanbereached.

Wepresenthereaformalapproachwhichgeneratesatargetedrepresentationofadesignproblem.Atargetedrepresentationistheonewhichcloselymapsontotheproblemathand.Asanexampleconsideralayoutplanningprobleminarchi-tecturaldesign.Onerepresentationmaybeatthematerialmolecularlevel,wheremoleculescanbecombinedtomakeavarietyofmaterialsandparticularcombina-tionsinspaceproducephysicalobjects;herethepotentialsolutionspaceincludesdesignswhichbearnorelationstoarchitecture.Atargetedrepresentationsmaybetorepresentroomssuchthatthepotentialsolutionspaceprimarilyincludesdesignswhichareallrecognizablyarchitecturallayouts.

Inordertosimplifyouranalysisweconsiderdesignswhichareassembledfrom

Abstract. This paper presents a formal approach to the evolution of a representation for use in a design process. The approach adopted is based on concepts associated with genetic engineering. An initial set of genes representing elementary building blocks

EvolvingBuildingBlocksforDesignUsingGeneticEngineering

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Figure2.ThesetofbuildingblocksforFroebel’skindergartengifts(Stiny,1980b).

some nitecollectionofspatialelements(wecallthembuildingblocksorcompon-ents)alongwithassemblyrules.Itisassumedthattheassemblyrulesdonotaffectthecomponents-thedesignobjectisaunionofnon-overlappingbuildingblocks.Westartwithsomesetofbuildingblockswhichwecallelementarycomponents.Itisassumedthattheycannotbedecomposedintoanysmallerones.Wecallasetofbuildingcomponentsandassemblyrulesarepresentationofthedesignproblemandthesetofelementarycomponentsandcorrespondingrulesthebasicrepresent-ation.Wecallitarepresentationbecauseitimplicitlyde nesthesetofalldesigns(designstatespace)whichcanbeproducedusingthissetofbuildingblocksandassemblyrules.

ThekindergartengiftsofFroebel(Stiny,1980b)isatypicalexampleofsuchtypesofdesignproblem.Oneofmanypossibleelementaryrepresentationsandas-semblyrulesforitisshowninFigures2and3.Onecaneasilyextenditbyaddingfurtherelementarybuildingblocksand/orfurtherassemblyrules.

Targetedrepresentations

uallythedesignerisinterestedinsomeparticularclassofdesigns.Assumewehavesomeadditionalsetofcompositebuildingblocksandanadditionalsetofassemblyrulestohandlethem.Wecancalculatethenumberofthesecompositebuildingblockswhichcanbefoundinallpossibledesignsinthatparticularclassandthenumberofelementarybuildingblocksusedtobuildtherestofthesedesigns(eachelementarybuildingblockshouldbecountedonlyonceasamemberofcompositebuildingorelementarybuildingblock,thelargestcompositeblocksarecounted rstandtheelementaryblocksarecountedlast).Thenwecancalculatethefrequencyofusageofthesecompositebuildingblocksandelementarybuildingblocksintheentiredesignspace.Thesamevaluescanbecalculatedforalldesignswhichhavethepropertyorpropertiesweareinterestedin.Ifthefrequencyoftheusageofthecompositebuildingblocksismuchhigherforthedesignsofinterestthanforalldesignsbuiltfromtheelementarybuildingblockandthefrequencyofelementarycomponentsusageismuchlowerthanthatofthecompositebuildingblocksforthedesignspaceofinterestthenwecanusethecompositebuildingblocksinstead

Abstract. This paper presents a formal approach to the evolution of a representation for use in a design process. The approach adopted is based on concepts associated with genetic engineering. An initial set of genes representing elementary building blocks

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Figure3.ThesetofsixassemblyrulesforFroebel’skindergartengifts.

ofelementaryonetoproducedesignsofinterestwithmuchhigherprobability.Inotherwordsarepresentationexistswhichmapsintotheareaofinterestoftheentiredesignspace.Letuscallitthetargetedrepresentationfortheparticularclassofdesigns.Obviouslydifferenttargetedrepresentationscanbeproducedwhichcor-respondtodifferentsetsofcompositebuildingblocks.Wecharacterizetheserep-resentationsbytheir“complexity”whichisde nedrecursivelyas:0-complexityforthebasicrepresentation,1-complexityfortherepresentationwhosebuildingblocksareassembledfromelementarybuildingblocks,2-complexityfortherep-resentationwhosebuildingblocksareassembledfromthebuildingblocksof0-complexityand1-complexity,etc.Assumeanevolutionoccursinanabstractspaceofcomplexrepresentations:initiallyonlyelementarybuildingblocksexistthenacycleproceedswhenanewsetofcompositebuildingblocksisproducedfromtheoneswhicharecurrentlyavailable.Thenarepresentationofi-complexity(andbuildingblocksofi-complexity)simplymeansthatcompositebuildingblocksofthisrepresentationhavebeenproducedduring-thstepofthisevolution.

Differentcompositebuildingblocksofthesame-complexitymaycontaindif-ferentnumbersofelementarybuildingblocks:forexample,assumesomebuild-ingblockof3-complexitycontains3elementarybuildingblocksandoneofthecompositebuildingblocksof4-complexityisassembledfrom2buildingblocksof3-complexityandthuscontains6elementarycomponentsandanotheroneisas-sembledfromoneblockof3-complexityandoneblockof0-complexityandthuscontains4elementarycomponents.Itisalsoclearthatbecausetherearedifferentwaystoassemblethesamecompositebuildingblockitmaybeproducedmultiple

Abstract. This paper presents a formal approach to the evolution of a representation for use in a design process. The approach adopted is based on concepts associated with genetic engineering. An initial set of genes representing elementary building blocks

EvolvingBuildingBlocksforDesignUsingGeneticEngineering5

(a)

(b)(c)

Figure4.Thesetofcompositebuildingblocksofdifferentcomplexityforbuildingastaircase;(a)1-complexity,(b)and(c)2-complexity.

timesinrepresentationsofdifferentcomplexitylevelduringtheevolution.

Thesearchforareasonablygooddesignusingthebasicrepresentationisverydif cultbecausesigni cantpartofthesearcheffortiswastedinthesearchofun-usefulpartsofthedesignspace.Ifthetargetedrepresentationisusedinsteadofele-mentaryonetheprobabilityofproducingdesignsofinterestbecomesmuchhigher,thedesignspacebecomessmallerandthedesignproblemlesscomplicatedandeasiertodealwith.Theapproachpresentedinthisarticleautomaticallygeneratesthehierarchyofmoreandmorecomplexbuildingblocks(ingeneral);oneswhicharemoreandmoreclosetothetargetedrepresentationswhicharecapableofpro-ducingbetterandbetterdesigns.

AssumeweworkwiththerepresentationofthekindergartenblocksshowninFigures2and3andaretryingtodesignatwo-levelbuildingwithwalkingac-cessfromone oortothenext.Thesearchforadesignwiththispropertyisquitedif cultbecauseonlyaverysmallfractionofallfeasibleobjectsexhibitsitandtheprobabilityofdiscoveringthecombinationofbuildingblockswhichmakesastaircaseduringthesearchislow.However,ifweaddacompositeobjectof1-complexity(Figure4)andcorrespondingassemblyrulesFigure5totherepres-entationweincreasethisprobability,andifweaddacompositebuildingblockwith2-complexity(Figure4)thenthisprobabilityincreasesfurther.

Geneticengineering

Geneticengineering,asusedinthispaper,isderivedfromgeneticengineeringno-tionsrelatedtohumaninterventioninthegeneticsofnaturalorganisms.Inthege-neticsofnaturalorganismswedistinguishthreeclasses:thegeneswhichgotomakethegenotype,thephenotypewhichistheorganicexpressionofgenotype,andthe tnessofthephenotypeinitsenvironment.Whenthereisauniqueidenti- able tnesswhichisperformingparticularlywellorparticularlybadlyamongstallthe tnessofinterestwecanhypothesizethatthereisauniquecauseforitand

Abstract. This paper presents a formal approach to the evolution of a representation for use in a design process. The approach adopted is based on concepts associated with genetic engineering. An initial set of genes representing elementary building blocks

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Figure5.Thesetofadditionalassemblyrulesforhandlingcompositebuildingblocks.thatthisuniquecausecanbedirectlyrelatedtotheorganism’sgeneswhichap-pearinastructuredforminitsgenotype.Geneticengineeringinconcernedwithlocatingthosegeneswhichproducethe tnessunderconsiderationandinmodify-ingthosegenesinsomeappropriatemanner.Thisisnormallydoneinastochasticprocesswhereweconcentrateonpopulationsratherthanonindividuals.

Organismswhichperformwell(orbadly)inthe tnessofinterestaresegreg-atedfromtheseorganismswhichdonotexhibitthat tnessordosoonlyinamin-imalsense.Thisbifurcatesthepopulationintotwogroups.Thegenotypesoftheformerorganismsareanalysedtodeterminewhethertheyexhibitcommonchar-acteristicswhicharenotexhibitedbytheorganismsinthelattergroup(Figure6).Iftheyaredisjunctive,thesegenesareisolatedonthebasisthattheyarerespons-iblefortheperformanceofthe tnessofinterest.Innaturalgeneticengineeringtheseisolatedgenesareeithertheputativecauseofpositiveornegative tness.Ifnegativethentheyaresubstitutedforby“good”geneswhichdonotgeneratethenegative tness.Iftheyareassociatedwithpositive tnesstheyarereusedinotherorganisms.Itisthislaterpurposewhichmapsontoourareaofinterest.

Onecaninterprettheproblemof ndingthetargetedsetofbuildingblocksasananalogofthegeneticengineeringproblem: ndingtheparticularcombin-ationsofgenes(representingelementarybuildingblocks)ingenotypeswhichareresponsibleforthepropertiesofinterestofthedesignsandregularusageofthesegeneclusterstoproducedesignswithdesiredfeatures.

Abstract. This paper presents a formal approach to the evolution of a representation for use in a design process. The approach adopted is based on concepts associated with genetic engineering. An initial set of genes representing elementary building blocks

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‘‘good’’ genotypes‘‘bad’’ genotypes

Figure6.Thegenotypesofthe“good”membersofpopulationallexhibitgenecombinations,X,whicharenotexhibitedbythegenotypesofthe“bad”members.Thesegenecombinationsaretheonesofinterestingeneticengineering.

2.Buildingblocks

Thus,weestablishthatdifferentbuildingblocksde nedifferentdesignstatespaces(whichare,intheirturn,thesubsetsoftheentirebasicdesignspace).Moreform-allyweassumethatforthedesignspaceofinterestasetofcompositebuildingblocksexistswhichissuf cienttobuildanydesignofinterestfromit(orwhicharesuf cienttobuildasigni cantpartofanyofthesedesignsofinterest).

Wesearchforthesebuildingblocksusingtheconsequenceoftheassumptionmadeintheintroductionaboutfrequenciesofcompositecomponentsusage:onav-eragethesamplingsetofdesignswiththedesiredcharacteristics(the“good”ones)containsmoreofsuchcompositebuildingblocksthanthesamplingsetofdesignsthatdonothavethesecharacteristics(the“bad”ones).Insomecasesitiseventrueinadeterministicsense-thatonlythedesignswhichcanbebuiltcompletelyfromsomesetofcompositebuildingblockspossesstheobjectivecharacteristics,alltherestoftheentirebasicstatespacedoesnothavethem.Onecaneasilycomeupwithcorrespondingexamples.

Inthenextsectionwedescribeanevolutionaryalgorithmwhichgenerates“good”and“bad”samplingsetsusingthecurrentsetofbuildingblock(setofelementaryblockatthebeginning)andusegeneticengineeringconceptstodeterminenewcompositeblockswhichareclosertothe“targeted”onesthanthecurrentsetofbuildingblocks.Thesetwostepsproceedincyclewhilethe“good”samplingsetconvergestothesamplingsetfromthedesireddesignstatespaceandthesetof

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bFigure7.Theassembly(transformation)rulesusedintheexample.

complexbuildingblockscomescloserandclosertothetargetedset.

Ifthebasicassumptionaboutmorefrequentuseofsomecompositebuildingblockstogeneratetheparticularclassofdesignsisnottrueforsomeproblemthenthetargetedrepresentationforthisproblemdoesnotexistandthealgorithmwhichisproposedbelowwillnotgenerateanimprovedrepresentationbutwillbeequi-valenttothealgorithmforsolvingtheroutinedesignproblem(GeroandKazakov,1995)andwillsimplygeneratetheimproveddesigns.

Ifthesequenceofassemblyactionsiscodedasarealvectorthentheproblemof ndingthecomplexbuildingblocksbecomestheproblemof ndingthekeypatternsinthecodingvector-thecombinationsofcodeswithinitwhicharelikelytobeassociatedwiththepropertyofinterestinthedesigns.Thevastarsenalofpatternrecognitionmethodscanbeusedtosolvethisproblem.Essentiallytheyarejustsearchmethodsforsubsetsinacodingsequencewhichonaveragearemorefrequentlyobservedinobjectswithdesiredcharacteristicsthanintherestofthepopulation.

Letusillustratetheexecutionofthecyclejustoutlinedusingasimple2-dimensionalgraphicalexample.Wewilldescribeitinmoredetaillaterbutfornowonitissuf- cienttosaythatthereisonlyoneelementaryblockhere-thesquareandthatadesignisassembledfromcubesusingthe8rulesshowninFigure7.Anydesigncanbecodedasasequenceoftheserulesusedtoassembleit.Assumewearetryingtoproduceadesignwhichhasthemaximumnumberofholesinitandthateachdesigncontainsnotmorethan20squares.WestartthecyclebygeneratingasetofcodingsequencesandcorrespondingdesignsFigure8.Thenwenoticethatanum-ber(4)ofthedesignshavethemaximalnumberofholes(designs1,2,4,and7-the“good”samplingset)containthecompositebuildingblockandthatforthreeofthemtheircodingsequencescontainthepattern.Wealsonoticethatonlyafew(noneinthiscase)ofthedesignswithoutholes(designs3,5,8and10-the“bad”samplingset)containthisblockandnonecontainthispatternintheircodingsequence.Thenwecangeneratethenextpopulationofcodingsequencesusingthe

asanewrulewhichusesthecompositebuildingblockidenti edsequence

inthedesign.Assumingthatweemploysomeoptimizationmethodtogeneratethisnewpopulationwecanexpectthatthe“good”samplingsetfromthenewpop-

Abstract. This paper presents a formal approach to the evolution of a representation for use in a design process. The approach adopted is based on concepts associated with genetic engineering. An initial set of genes representing elementary building blocks

EvolvingBuildingBlocksforDesignUsingGeneticEngineering

design 2design 39

good{3,2,2,6,5,8,2,1,4,4,3,1}design 6

{2,3,2,3,4,3,5,6,5,1,6,2}design 9

neutral{6,4,1,2,3,4,5,2,1,7,4}

Figure8.Theidenti cationofthepattern

inthegenotypesof“good”designs.andcorrespondingcompositebuildingblock

ulationisbetterthanthepreviousone(thatis,thedesignswhichbelongtoithaveonaveragemoreholesthantheonesfromtheprevious“good”samplingset).Thenweagaintrytoidentifythepatternswhicharemorelikelytobefoundindesignsfromthis“good”samplingsetthanfromthe“bad”one.Thistimethesepatternsmaycontainthepreviouslyidenti edpattersasacomponent.Thenwegenerateanewpopulationofdesignsusingtheseadditionalpatternsequencesofrulesasanadditionalassemblyruleandsoon.

Thesizesofthesamplingsetsinrealisticsystemsislikelytobemuchlarger

Abstract. This paper presents a formal approach to the evolution of a representation for use in a design process. The approach adopted is based on concepts associated with genetic engineering. An initial set of genes representing elementary building blocks

10JohnS.GeroANDVladimirA.Kazakov

thantheonesinthisexampleandmuchmoresophisticatedtechniques(PearsonandMiller,1992)shouldbeemployedtosingleoutthesekeypatterns.

3.Evolvingbuildingblocks

Foramoreformalanalysisoftheevolutionofthebuildingblocksweusetheshapegrammarformalism(Stiny,1980a).Itconsistsofanorderedsetofinitialshapesandanorderedsetofshapetransformationruleswhichareappliedrecursively.Aparticulardesignwithinthegivengrammariscompletelyde nedbyacontrolvectorwhichde nestheinitialshapeandtransformationrulesappliedateachstageofrecursiveshapegeneration.AccordingtothediscussionintheIntroduc-tionweconsideraparticularclassofshapegrammarsimilartothekindergartengrammar(Stiny,1980b),whereanyshapeisanon-overlappingunionofbuildingblocksandfeasibleshapetransformationsareaddition,replacementordeletionofthebuildingblocks.

beasetofcurrentlyavailablebuildingblocks,andbeasetofassemblyrulesapplicabletotheseblocks.,,,,Thenthecontrolvector

de nesthepopulationofdesigns,.,isavariable.Thelengthofthecontrolvector

Ifweaddnewcomplexbuildingblock

andnewassemblyrulesforitshandlingthenwegetanewextendedsetofrules,,and.

whichcorrespondstothevectorwhoseNowwecanproducethedesign

componentsbelongtotheextendedand.Notethattheadditionalbuildingblocksandassemblyrulesaregeneratedrecursively:theyarecompletelyde nedintermsofthepreviousand.

Weassumethatthedesignproblemhasaquanti ableobjectivevector-function,andcanbeformulatedasoptimizationproblemLet

(1)

Theproblem(1)overtherepresentationwitha xedsetofbuildingcompon-entsandassemblerulescanbesolvedusinganyofoptimizationmethods(GeroandKazakov,1995)butthestochasticalgorithmslikegeneticalgorithms(Hol-land,1975)andsimulatedannealing(Kirkpatricketal.,1983)lookmostprom-isingatthemoment.Wehavechosenthegeneticalgorithm.

Theevolutionarymethodhasthefollowingstructure:

Algorithm

.Takethesetofelementarybuild-(0).Initialization.Setcounterofiteration

andcorrespondingassemblyrules.Generatesomeingblocks

Abstract. This paper presents a formal approach to the evolution of a representation for use in a design process. The approach adopted is based on concepts associated with genetic engineering. An initial set of genes representing elementary building blocks

EvolvingBuildingBlocksforDesignUsingGeneticEngineering11

randompopulationof,calculateand.Settherelativethresholds;theyareusedduringanevolutionforthedesign’sranking

stagetodividethedesigninto“good”,“bad”and“neutral”samplingsets,thatis,thepartsofpopulationwhichexhibit()best,()worseandintermediaterel-ative tnesslevel.

(1)Evolutionofcomplexbuildingblocks.Foreverycomponentoftheobjective

dividethepopulationinto3groups:function

,“good”(

“bad”(,and“neutral”(therestofpopulation).

Determinecombinations,ofthecurrentbuildingblockswhichdistinguishthe“good”samplingsetfromthe“bad”onestatisticallysigni cantlyusinganyoneofthepatternrecognitionalgorithms.

.Addcorres-Addittothecurrentsetofbuildingblocks

pondingnewassemblyrulesto.

(2)putenewpopulationusingavailablein-formationaboutcurrentpopulation.Thecom-ponentsofbelongtothenewextendedand.Thedependsontheop-timizationmethodemployed.Ifthegeneticalgorithmhasbeenchosenthen

istobecalculatedusingstandardcrossoverandmutationoperations.Becausetheupdatedgrammarincludesthegrammarfromthepreviousgenerationthesearchmethodguaranteesthatthenewpopulationisbetterthanthepreviousone(atleastnoworse)andthenew“good”samplingsetisclosertosamplingsetofthedesignstatespaceofinterest.

(3)Repeatsteps(1)and(2)untilthestopconditionsaremet.

Thestopconditionsusuallyaretheterminationorslowingdownoftheim-provementinand/ortheendofnewbuildingblocksgeneration.

4.Example

Evolvingthetargetedrepresentation

Asanexamplewetaketheproblemofthegenerationofa2-dimensionalblockdesignonauniformplanargrid(derivedfrom(GeroandKazakov,1995)).Thereisjustoneelementarycomponenthere-asquareandtheeightassemblyrules(trans-formationrulesintermsofashapegrammar)whichareshowninFigure7.Ifthepositionwherethecurrentassemblyruletriestoplacethenextsquareisalreadytakenthenallthesquaresalongthisdirectionareshiftedtoallowtheplacementofnewsquare.Itisassumedthatthetransformationruleatthe-thassemblingstageis

-thstage.Thecharacterist-appliedtotheelementaryblockaddedduringthe

icsofinterestaregeometricpropertiesofthegenerateddesign.Inordertodemon-stratetheidea,assumethatthegenerateddesigncannotconsistofmorethan32

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Figure9.Thefractionofcompositebuildingblocksinthetotalpoolofbuildingblocksusedtoassemblethepopulationvs.generationnumber.Theobjectivefunctionhastwocomponents:theareaofclosedholesandthenumberofconnectionsbetweenholesandtheoutsidespace.Theinitialsetofbuildingblockscontainsonlyelementarybuildingblocks.Evolutionproceedsuntilitnaturallydiesoff.

elementarycomponents.Wegenerateanewpopulationduringthestage(2)oftheAlgorithmusingthemodi cationofthesimplegeneticalgorithmtailoredtohandlemultidimensionalobjectivefunctions(GeroandKazakov,1995).Weimplementaverysimplepatternrecognitionalgorithmbasedonthestatisticalfrequencyana-lysesofdoubleandtripleelementbuildingblockswithahighcut-offthresholdfortheacceptanceofthepatterns.Formorecomplexsystemsmoresophisticatedtechniqueisneeded.

Duringthe rstiterationwebeginwiththesetofbuildingblockswhichcon-tainsonlytheelementaryonesandsearchforthedesignswithmaximalareaofen-closedholesandmaximalnumberofconnectionsbetweentheholesandoutsidespace.Theevolutionwasallowedtoproceeduntilastableconditionwasreached.TheresultareshowninFigures9and10.Byplottingthefractionofthecomplexbuildingblocksinthetotalpoolofbuildingblocksusedtoassemblethepopula-tionatdifferentgenerationsFigure9,onecanseehowcomplexbuildingblocksbecomedominantandhowitsfractionreachesastablelevelafter110-120itera-tions.ThefractionsofbuildingblocksofdifferentcomplexityinthetotalpoolatdifferentgenerationareshowninFigure10.Onecanseethatduringthe rst40generationsthetotalfractionofcompositebuildingblocksarisesmonotonically.Forthe rst10generationsthisriseiscompletelyprovidedbytheincreasingnum-berof1-complexitycompositebuildingblocksinthepopulation.Then(from15to30generations)thefractionof1-complexityblocksremainsstablebutthenum-berof2-complexitybuildingblocksincreasesandprovidesthecontinuingincrease

Abstract. This paper presents a formal approach to the evolution of a representation for use in a design process. The approach adopted is based on concepts associated with genetic engineering. An initial set of genes representing elementary building blocks

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Figure10.Thefractionofcompositebuildingblockswithdifferentcomplexitiesinthetotalpoolofthebuildingblocksusedtoassemblethepopulationvs.generationnumber.This gureshowsthebuildingblocksofdifferentcomplexitieswhicharesummedtoproducethetotalfractionshowninFigure9.

inthetotalfractionofcompositebuildingblocks.Fromgenerations40to70thistotalfractionisstablewithapproximatelyhalfofbuildingblocksof1-complexityandhalfof2,3and4-complexities.Thenthenumberof1-complexityblocksandtotalnumberofcomplexblocksdeclinessharplyandfrom70until110generationatransitionalprocessoccurswithacomplexredistributionofpopulationsbetweenrepresentationswithdifferentcomplexities.Attheendofthisperiodthebuildingblocksof8-complexitysaturatethepopulationwhenthefractionsoftheothercom-plexbuildingblocksareshiftedtowardsanoiselevelonly.OneoftheevolutionpathsinthespaceofcomplexbuildingblocksisshowninFigure11(a).SomeofthedesignsproducedareshowninFigure11(b).Herearrowsshowwhichpre-viouslyevolvedcompositebuildingblocksareusedtoassemblethenewbuildingblock.The0-complexityblockanditscontributionsareomitted.Aswealreadynotedcompositeblocksofthesamecomplexitylevelsometimeshavedifferentnumbersofelementarycomponents.Coincidently,the5-complexityblockisre-producedagainintherepresentationsof6-,7-and8-complexitiesandisoneofthedominantblocksattheendoftheevolutionaryprocess.

Usingtargetedrepresentation.

Thesetoftargetedbuildingblocksevolvedduringthisprocessisthenusedasaninitialsetofbuildingblocksduringthesecondexperimentwhenweproducethedesignswithmaximaltotalareaofholesinsideandmaximalnumberofconnec-tionsbetweentheseholesinsidethestructure.Herethe tnessesareclosetobut

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Figure11.(a)Anexampleoftheevolutionarypathsintheevolutionofacomplexbuildingblock,(b)someofthedesignsproducedusingthesetofevolvedcomplexblocks.

Abstract. This paper presents a formal approach to the evolution of a representation for use in a design process. The approach adopted is based on concepts associated with genetic engineering. An initial set of genes representing elementary building blocks

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Figure12.Thefractionofcompositebuildingblockinthetotalpoolofbuildingblockusedtoas-semblethepopulationvs.generationnumber.Inthisexperimenttheobjectivefunctionisthenum-berofclosedholesandthenumberofconnectionbetweentheclosedholesinsidethestructure.Theinitialsetofbuildingblocksisinheritedfromthe rstexperimentandisthetargetedrepresentation.notthesameasthoseusedtoevolvethetargetedrepresentation.Thisexperimentisusedtotestwhetherthetargetedrepresentationislikelytobeusedmorethantheoriginal,elementarybuildingblocks.Ifthetargetedrepresentationisusedratherthantheelementarybuildingblocksthenwehaveachievedourgoalofevolvingarepresentationcanbeusedtoproducedesignswhichexhibitdesiredcharacterist-icsmorereadily.TheresultsareshowninFigures12and13.Onecanseethatthefractionofthecompositebuildingblocksusedtoproducethesedesignsreachesthesaturationlevelduringthe rstfewiterations.Thevisibleredistributionsofthepopulationbetweenthecompositebuildingblocksof5,6and7-complexitiesarepurelysuper cial-thisredistributionoccursbetweenthesamecompositebuildingblockswhicharepresentinalltheserepresentations.Evolutionoftherepresenta-tiondoesnotoccurduringthisexperiment-nonewcomplexbuildingblockwereevolved.Thiscanbeinterpretedasanindicationofclosenessofthetargetedrep-resentationsforbothproblems.Soifthetargetedrepresentationisevolvedforonesetofobjectivesthenitcanbeusefullyappliedtoanyoftheobjectivesetswhichareonlyslightlydifferenttoit.

Effectsofincompleteevolution

Inthisexperimentwerepeatthe rstiterationbutstoptheevolutionprematurelyafteronly60generations.Afterthiswerepeattheseconditerationusingtheevolvedincompletesetofcompositebuildingblocks.TheresultsareshowninFigures14

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Figure13.Thefractionofcompositebuildingblockswithdifferentcomplexitiesinthetotalpoolofthebuildingblockusedtoassemblethepopulationvs.generationnumberintheexperiment.

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Figure14.Thefractionofcompositebuildingblockinthetotalpoolofbuildingblockusedtoas-semblethepopulationvs.generationnumber.Inthisexperimenttheobjectivefunctionisthenumberofclosedholesandthenumberofconnectionsbetweentheclosedholesinsidethestructure.Theini-tialsetofbuildingblocksisinheritedfrom rstiterationwhichhasbeenprematurelyterminatedatgeneration60.

and15.Inthiscasetheevolutionoftherepresentationcontinuesforaboutafur-ther10generationsandweendupwiththesamesetofevolvedcompositebuildingblocks.Thesaturationofthepopulationwiththecompositebuildingblocksisalsocompletedafterthese10generations.Thus,onecanstarttoevolvearepresenta-

Abstract. This paper presents a formal approach to the evolution of a representation for use in a design process. The approach adopted is based on concepts associated with genetic engineering. An initial set of genes representing elementary building blocks

EvolvingBuildingBlocksforDesignUsingGeneticEngineering

0.9170.8

0.7

FRACTION OF COMPLEX GENES 0.60.51-COMPLEXITY2-COMPLEXITY3-COMPLEXITY4-COMPLEXITY5-COMPLEXITY6-COMPLEXITY7-COMPLEXITY8-COMPLEXITY0.40.3

0.2

0.1

00102030GENERATIONS405060

Figure15.Thefractionofcompositebuildingblockswithdifferentcomplexitiesinthetotalpoolofthebuildingblockusedtoassemblethepopulationvs.generationnumberinthethirdexperiment.tionforonesetofobjectivesandthencontinueitforanothercloselyrelatedsetofobjectives.

Ifwecommencebytreatingtheproblemasoneof ndingimproveddesignsthenfromacomputationalviewpointthisformofevolutionspeedsuptheconver-

(intermsofthenumberofgenerationsgencetoimproveddesignsbyupto

required)whencomparedwithstandardgeneticalgorithms.Itappearsthattheuseofatargetedrepresentationcanleadtotheproductionofdesignswhicharelocallyoptimal.

However,ifweusethecompletionevolutionapproachpresentedinthesecondexperimentwegetfurtherimprovementsinperformance.WewillleavetotheDis-cussionsectionfurtherdiscussionoftheotheradvantagesoftheapproachpresen-ted.

5.Discussion

Theanalysisjustpresentedcanbeeasilyextendedtoincludegeneralobjectgram-marsoftypesdifferenttothekindergartengrammar.Theproposedapproachcanbeconsideredasanimplementationofthesimplestversionofthegeneticengin-eeringapproachtothegenericdesignproblem.Fromthetechnicalpointofviewthealgorithmpresentedisamixtureofastochasticsearchmethod(whichmaybeageneticalgorithm)andapatternrecognitiontechnique.

Thegeneticengineeringapproachcanbeappliedinasimilarfashiontotheproblemofthegenerationofa“suitable”shapegrammar(GeroandKazakov,1995)wherethecomplexbuildingblockscorrespondtotheevolvedgrammarrules.

Abstract. This paper presents a formal approach to the evolution of a representation for use in a design process. The approach adopted is based on concepts associated with genetic engineering. An initial set of genes representing elementary building blocks

18JohnS.GeroANDVladimirA.Kazakov

Asalreadymentionedintheanalysisofthenumericalexperiment,theevolvedrepresentationsarehighlyredundant-thesamecompositebuildingblocksareevolvedmanytimesalongthedifferentbranchesoftheevolutionarytrees.Theredundancylevelofthecurrentsetofcompositebuildingblockscanbereducedinanumberofdifferentways.Thesimplestisjusttodeletealltheredundantcopiesfromthecurrentset.Inthegeneralcase,wehaveto ndtheminimalrepresentationofthesubspacewhichcanbegeneratedusingthecurrentsetofcomplexbuildingblocks.Theintroductionofideasandmethodsfromgeneticengineeringintodesignsystemsbasedongeneticalgorithmsopensupanumberofavenuesforresearchintobothevolutionary-baseddesignsynthesisandintomodi edgeneticalgorithms.Indesignsystemsbasedonsuchmodi edgeneticalgorithmsitispossibletocon-sidertwodirections.

The rstistotreatthesequenceofthegeneswhichresultsincertainbehavioursor tnessperformancesasaformof‘emergence’,emergenceoftheschemarepres-entedbythatgenesequence.Theuseofthegeneticallyengineeredcomplexgeneschangesthepropertiesovertimeofthestatespaceswhicharebeingsearched.Thisallowsustoconsidertheprocessasbeingrelatedtodesignexplorationmodelledinaclosedworld.Theprecisemannerinwhichtheprobabilitiesassociatedwithstatesinthestatespacechangeisnotyetknown.Clearly,thisisalsoafunctionofwhethera xedlengthgenotypeencodingisusedornot.Ifavariablelengthgenotypeencodingisusedwiththegeneticallyengineeredcomplexgenesthentheshapeofthestatespaceremains xedbuttheprobabilitiesassociatedwiththestateswithinitchange.Ifa xedlengthgenotypeencodingisusedwiththege-neticallyengineeredcomplexgenesthentheshapeofthestatespacechangesinadditiontotheprobabilitiesassociatedwithstatesinthestatespace.

Thesecondistotreatthegeneticallyengineeredcomplexgenesasameansofdevelopingarepresentationforpotentialdesigns.Afundamentalpartofdesign-ingisthedeterminationofanappropriaterepresentationofthecomponentswhichareusedinthestructure(Gero,1990)ofthedesign.Thisispartofthataspectofdesigningcalled‘formulation’,iethedeterminationofthevariables,theirre-lationshipsandthecriteriabywhichresultingdesignswillbeevaluated.Inmostcomputer-aideddesignsystemsthecomponentsmapdirectlyontovariables.Fur-ther,insuchsystemsthevariablesarespeci edattheoutset,asaconsequencethereisanunspeci edmappingbetweenthesolutionscapableofbeingproducedandthevariableschosentorepresenttheideaswhicharetobecontainedintheresultingdesigns.Thegeneticengineeringapproachdescribedprovidesameansofautomat-ingtherepresentationpartoftheformulationprocess.Thelevelofgranularityisdeterminedbythestabilityconditionoftheevolutionaryprocessorcanbedeterm-inedbytheuser.Thetargetedbuildingblocksprovideahigh-levelstartingpointforalllaterdesignswhicharetoexhibittherequiredcharacteristicsasevidencedintheearlierdesigns.Itisthislatterrequirementwhichismetbythisformalmethod.Thefollowingsimplepicturecanbeusedtosummarizethemodeldescribedin

Abstract. This paper presents a formal approach to the evolution of a representation for use in a design process. The approach adopted is based on concepts associated with genetic engineering. An initial set of genes representing elementary building blocks

EvolvingBuildingBlocksforDesignUsingGeneticEngineering19thispaper.Agroupofchildrenareplayingwiththe“Lego”gameusingnotmorethan50squares.Theyjointhemtogetherandwanttobuildtheobjectwiththelargestnumberofclosedspacesinside.Aftereachchildhasbuilthisorherob-jectthesupervisortriesto ndacombinationofsquareswhichispresentinmanyofthebestdesignsbutispresentinnoneoronlyinafewofunsatisfactorydesigns.Thenhemakesthiscombinationpermanentbygluingitscomponentstogetherandaddsabunchofsuchpermanentcombinationstothepoolofbuildingelementsavailabletothechildren.Thenthechildrenmakeanothersetofobjectsusingthesenewbuildingblocksaswellasanoldones.Thesupervisortriesto ndanother“good”compositeblockandtheprocessisrepeated.Thus,twostepsoccurineachcycle: rstchildrenmakeasetofnewdesignsfromcurrentlyavailableblocksandcombinationofblocksandsecondthesupervisortriestosingleouttheadditionalcombinationofblocksthatshouldbeemployed.Iftherearenosuchcombinationswhichdistinguish“good”designfromthe“bad”onesthenwewillnotgetnewcombinationsbutonlytheimproveddesigns.

Style

Thechoiceofparticularvariablesandcon gurationsofvariablesisadetermin-antofthestyleofthedesign(Simon,1975).Thelabel‘style’canbeusedinatleasttwoways:eithertodescribeaparticularprocessofdesigningorasameansofdescribingarecognizablesetofcharacteristicsofadesign.Thus,itispossibletotalkaboutthe‘Gothic’styleinbuildingsorthe‘hightech”styleofconsumergoods.Preciselywhatgoestomakeupeachofthesestylesisextremelydif culttoarticulateeventhoughweabletorecognizeeachofthesestyleswithverylittledif culty.Anappropriatequestiontoposeis:howcanweunderstandwhatpro-ducesastyleduringtheformulationstageofadesigningprocess?Thisbringsusbacktotheconceptsdescribedinthispaper.

‘Thehistoryoftasteandfashionisthehistoryofpreferences,ofvariousactsofchoicebetweendifferentalternatives......[But]anactofchoiceisonlyofsymptomaticsigni cance,isexpressiveofsomethingonlyifwecanreallywanttotreatstylesassymptomaticofsomethingelse,wecannotdowithoutsometheoryofthealternatives’(Gombrich,quotedfrom(Simon,1975)).Ifweuseaparticularstyleasthe tnessofinterestthenitshouldbepossibletoutilisethegeneticengineeringapproachdescribedinthispapertodetermineifthereisauniquesetofgenesorgenecombinationswhichiscapableofbeingtheprogenitorsofthatstyle.Forthistooccursatisfactorilyaricherformofpatternrecognitionwillbeneededthanthatalludedtohere.Wewillneedtobeabletodetermineawidervarietyofgeneschemasinthegenotypesofthosedesignswhichexhibitthedesiredstyle.

Theuseofgeneticengineeringinevolvingschemasofinterestopensupapo-tentialsubsymbolicmodelofemergenceincludingtheemergenceofdomainse-

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