Table Of ContentSPRINGER BRIEFS IN COMPUTER SCIENCE
Robert G. Reynolds
Culture on the
Edge of Chaos
Cultural
Algorithms and
the Foundations of
Social Intelligence
123
SpringerBriefs in Computer Science
Moreinformationaboutthisseriesathttp://www.springer.com/series/10028
Robert G. Reynolds
Culture on the Edge of Chaos
Cultural Algorithms and the Foundations
of Social Intelligence
RobertG.Reynolds
ComputerScienceDepartment
WayneStateUniversity
Detroit,MI,USA
ISSN2191-5768 ISSN2191-5776 (electronic)
SpringerBriefsinComputerScience
ISBN978-3-319-74169-7 ISBN978-3-319-74171-0 (eBook)
https://doi.org/10.1007/978-3-319-74171-0
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Contents
1 TheCulturalAlgorithm:CultureontheEdgeofChaos. . . . . . . . . 1
1.1 CulturalAlgorithms:Data-DrivenProblemSolvinginComplex
Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 CultureasaProblem-SolvingProcess. . . . . . . . . . . . . . . . . . . . 2
1.3 TheCulturalEngine. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4 CultureontheEdgeofChaos. . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.5 TheSocialOrganizationModels. . . . . . . . . . . . . . . . . . . . . . . . 8
1.6 OrganizationoftheBook. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2 CulturalAlgorithmFramework. . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2 TheCulturalAlgorithm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3 TheCulturalAlgorithmKnowledgeSources. . . . . . . . . . . . . . . . 15
2.4 TheCommunicationProtocol. . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.5 ThePopulationSpace. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.6 Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3 ModelingtheSocialFabric. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.2 HomogeneousTopologies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.3 HeterogeneousTopologies.. . . .. . . .. . . .. . . .. . . .. . .. . . .. 31
3.4 SubculturedHeterogeneousTopologies. . . . . . . . . . . . . . . . . . . 35
3.5 Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4 GeneratingChaos. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.2 TheConesWorldGenerator. . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.3 Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
5 SocialMetrics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
5.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
5.2 TheDispersionMetric:SocialTension. . . . . . . . . . . . . . . . . . . . 46
vii
viii Contents
5.3 TheMajorityWinScoresandtheInnovationCosts. . . . . . . . . . . 47
5.4 TrackingProblem-SolvingBehaviorinTermsoftheSocial
FabricMetrics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
5.5 Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
6 TheCulturalEngine:PuttingIndividualstoWork. . . . . . . . . . . . . 53
6.1 KnowledgeSwarmsandMaxwell’sDemon. . . . . . . . . . . . . . . . 53
6.2 TheBasicLawsofThermodynamics. . . . . . . . . . . . . . . . . . . . . 53
6.3 Maxwell’sDemon. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
6.4 TheCulturalEngine. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
6.5 Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
7 ComparingNuclearFamilyandExtendedFamilySocial
Organizations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
7.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
7.2 OverallPerformanceComparison. . . . . . . . . . . . . . . . . . .. . . . . 60
7.3 LearningCurves. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
7.4 t-TestsforPerformanceDifferences. . . . . . . . . . . . . . . . . . . . . . 68
7.5 UsingSocialMetricstoAssessEnginePerformance. . . . . . . . . . 69
7.6 Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
8 ThePowerofSubcultures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
8.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
8.2 OverallPerformanceComparison. . . . . . . . . . . . . . . . . . .. . . . . 78
8.3 SubculturalSupportofProblemSolvingPredictability. . . . . . . . 83
8.4 StatisticalComparisonofSubculturesandHomogeneous
Usingt-Tests. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
8.5 TheStatisticalComparisonofSubculturesandHeterogeneous
Usingt-Tests. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
8.6 TheAbilityofSubculturestoSupportIncreased
PopulationSize. . . .. . . . . .. . . . . . .. . . . . .. . . . . .. . . . . .. . 88
8.7 HowSubculturesImpactCulturalEnginePerformanceinTerms
oftheSocialMetrics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
8.8 Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
9 ConclusionsandFutureWork. . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
Chapter 1
The Cultural Algorithm: Culture
on the Edge of Chaos
1.1 Cultural Algorithms: Data-Driven Problem Solving
in Complex Systems
Traditionallyevolutionarycomputationhasfocusedonpopulation-basedmodels.In
thesemodels,apopulationofproblemsolversexchangeslimitedamountsofknowl-
edgeaboutaproblemtobesolvedandcanusethisknowledgetocollectivelysearch
for a solution. Each problem solver makes decisions based upon the knowledge
availabletoit.Thisapproachissuitableforproblemswheretheknowledgeneeded
tosolveaproblemislimited.
Data- or knowledge-driven systems on the other hand reflect problems gener-
ated by complex systems that can be described at many levels of detail where the
typeofknowledgeavailablemaychangefromleveltolevelinthesystemandwhere
manylevelsmayneedtobeexaminedinordertofindasolutiontoagivenproblem.
Jayyousi and Reynolds (2014) define a complex system as one made up of an
organized group of heterogeneous independent units who interact with their envi-
ronment and each other. They adapt based on feedback from the environment. In
other words, a complex system is a mixture of relatively simple components or
buildingblocksthatarecombinedtogetherthroughaseriesofbasicinteractions.The
interaction between these building blocks or basic units can produce emergent
behaviorsthatcannotbepredictedfromknowledgeoftheindividualunitsalone.
Acomplexsystemoftenhasthefollowingcharacteristics(JayyousiandReynolds
2014):
1. Relationshipsinacomplexsystemareoftennonlinear,i.e.,effectsarenotdirectly
proportionaltocauses.
2. Complexsystemscontainpositiveandnegativefeedbackloops.
3. Complex systems are open, i.e. usually far from equilibriums, but may form
patternsofstability.
©TheAuthor(s),underexclusivelicencetoSpringerInternationalPublishingAG, 1
partofSpringerNature2018
R.G.Reynolds,CultureontheEdgeofChaos,SpringerBriefsinComputerScience,
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2 1 TheCulturalAlgorithm:CultureontheEdgeofChaos
4. Complexsystemshavememory,i.e.,historymatters.
5. Complexsystemmayproduceemergentphenomena.
DataScienceisconcernedwiththedevelopmentofpredictivemodelsofcomplex
systemsthroughthe use oftools frommathematics,statistics,machinelearning, and
other disciplines. Complex systems can operate on numerous temporal and spatial
levels.Itisfrequentlythecasethatthedatacollectionprocessisconcentratedonone
level or another. Questions or hypotheses posed at the macro-level may not have
sufficientdatatotestthematthatlevel.Thus,itisimportantforadatascientisttobe
abletotraverselevelssuchthatquestionsaskedononelevelwithsparsedatacanbe
re-expressed at another level with sufficient data. As a result, the problem-solving
processcanmovefromonelevelofgranularitytoanotherbasedupondataavailability.
Theexample inFig.1.1correspondstoanancienturban centerintheValleyof
Oaxaca,Mexico,thatdatesto500BC(JayyousiandReynolds2014).Thediagram
shows three different levels of detail at which the system can be described: the
macro-level, the meso-level, and the micro-level. Hypotheses reflecting the overall
designofthecitycanbeexpressedatthemacro-level.Themeso-levelcorresponds
to the basic neighborhood or barrio structure within the city. The micro-level
describes the basic household terraces along with city structures. While the most
interesting general hypotheses can be posed at the macro-level, much of the data
collected by archaeologists was at the micro-level. So, the knowledge sources
needed at one level may be different from those needed at another level. For an
evolutionary algorithm to be successful as a tool for the data scientist, these
knowledge sources need to operate in parallel and communicate with each other
overthedifferentlevelsduringtheproblem-solvingprocess.Thus,thecomputation
isdirectedbytheneedsoftheknowledgesourcesratherthanthoseofthepopulation
ofproblemsolvers.Thepopulationofproblemsolversmediatesthetransmissionof
knowledgefromonelevelofabstractiontoanother.
Deep learning inits mostgeneral sense reflects this traversal ofdata abstraction
levels, from fine-grained detail to coarse grained detail and vice versa. While the
termdeeplearningisoftenrelatedtoworkinneuralnetworks,thegeneralprinciples
can,ofcourse,applytoalltypesoflearningapproachesusedwithcomplexsystems.
The Cultural Algorithm is a nature-inspired algorithm designed to navigate the
hierarchy of hypotheses often found associated with complex systems. As such,
wedesignateitasatoolformulti-levellearningincomplexsystems.
1.2 Culture as a Problem-Solving Process
CulturalAlgorithmsweredevelopedasamechanismbywhichtodealwithproblem
solving andlearning withincomplexsystemsbyReynolds (1979).Complexsocial
systems can be found at various scales, and the types of problems that they are
presentedwithareaffectedbythatscale.InFig.1.2,varioussocialsystemsthatare
used as the basis for models of social problem solving, such as Particle Swarm
Optimization(BrattonandKennedy2007)andAntColonysystems,arecomparedin
