EVOLVINGBUILDINGBLOCKSFORDESIGNUSINGGENETIC ENGINEERING A FO(5)

(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

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

12

0.9JohnS.GeroANDVladimirA.Kazakov0.8

TOTAL FRACTION OF COMPLEX GENES 0.70.60.50.40.3

0.2

0.1020406080100GENERATIONS120140160180

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

EvolvingBuildingBlocksforDesignUsingGeneticEngineering

0.8

1-COMPLEXITY2-COMPLEXITY3-COMPLEXITY4-COMPLEXITY5-COMPLEXITY6-COMPLEXITY7-COMPLEXITY8-COMPLEXITY130.7

FRACTION OF COMPLEX GENES 0.60.50.40.30.2

0.1

0020406080100GENERATIONS120140160180

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.

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