The Multiple Pheromone Ant Clustering Algorithm

180 Pages·2014·1.46 MB·English

by  Jan Chircop

Some pages of this thesis may have been removed for copyright restrictions.

If you have discovered material in AURA which is unlawful e.g. breaches copyright, (either
yours or that of a third party) or any other law, including but not limited to those relating to
patent, trademark, confidentiality, data protection, obscenity, defamation, libel, then please
read our Takedown Policy and contact the service immediately
T M P
HE ULTIPLE HEROMONE
A C A
NT LUSTERING LGORITHM
VOL 1 OF 1
JAN CHIRCOP
DoctorofPhilosophyinComputerScience
ASTON UNIVERSITY
MAY 2014
(cid:13)c JanChircop,2014
JanChircopassertshismoralrighttobeidentifiedastheauthorofthisthesis
Thiscopyofthethesishasbeensuppliedonconditionthatanyonewhoconsultsitis
understoodtorecognisethatitscopyrightrestswithitsauthorandthatnoquotationfromthe
thesisandnoinformationderivedfromitmaybepublishedwithoutappropriatepermissionor
acknowledgement.
1
ASTONUNIVERSITY
ThesisSummary
TheMultiplePheromoneAntClusteringAlgorithm
byJan CHIRCOP
Degree: DoctorofPhilosophy
May2014
AntColonyOptimisationalgorithmsmimicthewayantsusepheromonesformarkingpathsto
importantlocations. Pheromonetracesarefollowedandreinforcedbyotherants,butalsoevap-
orateovertime. Asaconsequence,optimalpathsattractmorepheromone,whilstthelessuseful
paths fade away. In the Multiple Pheromone Ant Clustering Algorithm (MPACA), ants detect
features of objects represented as nodes within graph space. Each node has one or more ants
assignedtoeachfeature. Antsattempttolocatenodeswithmatchingfeaturevalues,depositing
pheromonetracesontheway. Thisuseofmultiplepheromonevaluesisakeyinnovation.
Ants record other ant encounters, keeping a record of the features and colony membership
of ants. The recorded values determine when ants should combine their features to look for
conjunctions and whether they should merge into colonies. This ability to detect and deposit
pheromone representative of feature combinations, and the resulting colony formation, renders
thealgorithmapowerfulclusteringtool.
The MPACA operates as follows: (i) initially each node has ants assigned to each feature; (ii)
ants roam the graph space searching for nodes with matching features; (iii) when departing
matchingnodes,antsdepositpheromonestoinformotherantsthatthepathgoestoanodewith
theassociatedfeaturevalues;(iv)antfeatureencountersarecountedeachtimeanantarrivesat
a node; (v) if the feature encounters exceed a threshold value, feature combination occurs; (vi)
asimilarmechanismisusedforcolonymerging.
The model varies from traditional ACO in that: (i) a modified pheromone-driven movement
mechanismisused;(ii)antslearnfeaturecombinationsanddepositmultiplepheromonescents
accordingly;(iii)antsmergeintocolonies,thebasisofclusterformation.
The MPACA is evaluated over synthetic and real-world datasets and its performance compares
favourablywithalternativeapproaches.
2
Acknowledgements
Withoutthepatienceandassistanceofseveralpeoplethisthesiswouldhavenevermaterialised.
A thesis which required a considerable amount of commuting, in conjunction with a full time
jobinanareaunrelatedtothefieldofresearchwasharderthanIcouldhaveeverimagined.
Iimmeasurablythankmysupervisor, Dr. ChristopherBuckinghamwhowashappytodedicate
extrahourswhenrequiredandmetwithmeinnumerabletimesafterofficehours. Furthermore,I
wouldalsoliketothankDr. M.ChliandProf. F.Guinand,respectivelytheinternalandexternal
examinersfortheirhelpfulfeedbackonthethesis.
Otherimportantpeopletothankincludemyfamilyfortheirunfailingsupportandlastly,butnot
theleast,Stephwhogotontotheridewithmeattheverystart,andbytheend,eventhoughthe
ridegotbumpy,wasstilltheretoencouragemethroughit.
3
Contents
Abstract 2
Acknowledgements 3
Contents 4
ListofFigures 8
ListofTables 9
Abbreviations 10
1 Introduction 13
1.1 ProblemofDataExplosionandMotivation . . . . . . . . . . . . . . . . . . . 13
1.2 UnderstandingandInterpretingData: Top-DownandBottom-Upapproaches . 14
1.3 SwarmIntelligence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.3.1 Self-organisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.3.2 Stigmergy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.3.3 PositiveFeedback . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.3.4 ACOinaNutshell . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.4 ObjectivesofthisThesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.4.1 TheNewACOModel . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.4.2 EvaluationTechniques . . . . . . . . . . . . . . . . . . . . . . . . . . 20
1.4.2.1 Datasets . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
1.4.3 MPACAOverview . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
1.5 Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
1.6 OrganisationofWork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
1.7 ChapterConclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2 LiteratureReview 23
2.1 ChapterOverview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.2 ClusteringandClassification . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.2.1 DefinitionofClustering . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.2.1.1 TheClusteringproblemasanNP-hardProblem . . . . . . . 25
2.2.2 OperandswithinClusteringAlgorithms . . . . . . . . . . . . . . . . . 25
2.2.2.1 Architectures. . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.2.2.2 DistanceMetrics . . . . . . . . . . . . . . . . . . . . . . . . 25
2.2.2.3 SimilarityMetrics-DistanceastheSimilarityProxy . . . . . 27
2.2.2.4 CurseofDimensionality . . . . . . . . . . . . . . . . . . . . 29
2.2.3 ComparingModels . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.2.3.1 ExternalEvaluationTechniques . . . . . . . . . . . . . . . . 29
2.2.4 GeneralClusteringTechniques . . . . . . . . . . . . . . . . . . . . . . 31
4
2.2.4.1 HierarchicalClustering . . . . . . . . . . . . . . . . . . . . 31
2.2.4.2 FlatorPartitionalClustering . . . . . . . . . . . . . . . . . 33
2.2.4.3 Density-basedClustering . . . . . . . . . . . . . . . . . . . 35
2.2.4.4 Graph-theoreticClusteringapproaches . . . . . . . . . . . . 36
2.2.5 TheRelevanceofTraditionalClusteringAlgorithms . . . . . . . . . . 37
2.3 SwarmIntelligence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.3.1 GeneralSwarmIntelligenceApproaches. . . . . . . . . . . . . . . . . 39
2.3.2 ParticleSwarmOptimisation . . . . . . . . . . . . . . . . . . . . . . . 40
2.3.3 Bio-InspiredSIAlgorithms . . . . . . . . . . . . . . . . . . . . . . . 41
2.3.3.1 BeeColonyAlgorithms . . . . . . . . . . . . . . . . . . . . 41
2.3.3.2 AntAlgorithms . . . . . . . . . . . . . . . . . . . . . . . . 42
2.3.4 TowardstheAntColonyOptimisationMeta-Heuristic . . . . . . . . . 43
2.3.4.1 RelevanceandnoveltytotheMPACA . . . . . . . . . . . . 47
2.4 ConclusionsfromSIliterature . . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.5 AntAlgorithmsandtheirApplicationtoClustering . . . . . . . . . . . . . . . 48
2.5.1 FundamentalOperatorsBehindtheChosenModels . . . . . . . . . . . 48
2.5.1.1 TypeI-KnowledgeStructureFormingAnts . . . . . . . . . 49
2.5.1.2 TypeII-AntAggregationsandAnts’Self-Aggregation . . . 49
2.5.1.3 Type III - Clustering Inspired by the Chemical Recognition
SystemofAnts . . . . . . . . . . . . . . . . . . . . . . . . 51
2.5.1.4 TypeIV-ClusteringusingAntColonyOptimisationAlgorithms 52
2.5.2 ComparisonCriteria . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
2.6 SelectedModelsinDetail . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
2.6.1 TypeI-ClusteringusingAnts’Self-Aggregation . . . . . . . . . . . . 57
2.6.1.1 TheAntTreeAlgorithm . . . . . . . . . . . . . . . . . . . . 57
2.6.2 TypeII-ClusteringusingAntAggregationsandAnts’Self-Aggregation 59
2.6.2.1 StandardAntClusteringAlgorithm(SACA) . . . . . . . . . 59
2.6.2.2 Self-Aggregationwithina2DGrid . . . . . . . . . . . . . . 62
2.6.2.3 AntAggregationthroughPheromoneina2DGrid . . . . . . 63
2.6.3 Type III - Clustering Inspired by the Chemical Recognition System of
Ants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
2.6.4 TypeIV-ClusteringusingAntColonyOptimisationAlgorithms . . . . 70
2.6.4.1 Multi-ObjectiveProblemSolving . . . . . . . . . . . . . . . 70
2.6.4.2 Multi-ColonyandMulti-PheromoneACOApproaches. . . . 71
2.6.4.3 AntColonyOptimisation(ACO)anditsApplicationtoClus-
tering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
2.6.4.4 ACOAppliedtoGraphPartitioning . . . . . . . . . . . . . . 75
2.6.4.5 RuleLearningAlgorithms . . . . . . . . . . . . . . . . . . . 82
2.7 ChapterConclusionandIntroductiontotheMPACA . . . . . . . . . . . . . . 86
3 TheMPACAModel 87
3.1 ChapterOverview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
3.2 IntroductiontotheMPACA . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
3.2.1 RelationshiptotheGenericAntColonyAlgorithm . . . . . . . . . . . 88
3.3 TheMainModelArchitectureandProcesses . . . . . . . . . . . . . . . . . . . 88
3.3.1 Partially-ConnectedGraphSpace . . . . . . . . . . . . . . . . . . . . 90
3.3.2 ConnectingNodesandMeasuringDistances . . . . . . . . . . . . . . 90
3.3.3 Multiple-stepswithinEdges . . . . . . . . . . . . . . . . . . . . . . . 92
3.4 PlacingAntsonNodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
3.4.1 AssigningFeaturestoAnts . . . . . . . . . . . . . . . . . . . . . . . . 92
3.4.2 FeatureMatchingaNode . . . . . . . . . . . . . . . . . . . . . . . . . 93
3.5 AntMovement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5
3.5.1 Pheromone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
3.5.1.1 AntDepositState . . . . . . . . . . . . . . . . . . . . . . . 94
3.5.1.2 PheromoneQuantityDeposited . . . . . . . . . . . . . . . . 94
3.5.1.3 PheromoneEvaporation . . . . . . . . . . . . . . . . . . . . 95
3.5.2 EdgeSelectionMechanism . . . . . . . . . . . . . . . . . . . . . . . . 96
3.5.3 AntEncounters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
3.5.3.1 IdentifyingAntFeatureEncounters . . . . . . . . . . . . . . 98
3.5.3.2 DataStructuresforRecordingEncounters . . . . . . . . . . 98
3.5.4 MergingFeaturesandColonies . . . . . . . . . . . . . . . . . . . . . 100
3.5.4.1 MergingFeatures: ALearningandForgettingMechanism . . 100
3.5.4.2 ColonyMerging . . . . . . . . . . . . . . . . . . . . . . . . 101
3.6 OverallOperationoftheMPACA . . . . . . . . . . . . . . . . . . . . . . . . 102
3.7 TheMPACAandClusterDerivation . . . . . . . . . . . . . . . . . . . . . . . 105
3.7.1 MappingColoniestoClusters . . . . . . . . . . . . . . . . . . . . . . 105
3.7.2 TerminationCriteria . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
3.7.3 ClusterMembershipandEvaluation . . . . . . . . . . . . . . . . . . . 105
3.7.3.1 CentroidClusterMembershipCalculation . . . . . . . . . . 106
3.8 TheMPACAParameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
3.8.1 ASyntheticDatasetforDemonstratingtheParameters’Impact . . . . . 106
3.8.2 BaselineAnalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
3.8.3 DomainInitialisationAnalysis . . . . . . . . . . . . . . . . . . . . . . 109
3.8.3.1 MaximumEdgeLengthParameter . . . . . . . . . . . . . . 110
3.8.3.2 StepSizeParameter . . . . . . . . . . . . . . . . . . . . . . 111
3.8.4 AntInitialisationAnalysis . . . . . . . . . . . . . . . . . . . . . . . . 113
3.8.4.1 AntComplementParameter . . . . . . . . . . . . . . . . . . 113
3.8.4.2 DetectionRangeforOrdinalDimensionsParameter . . . . . 114
3.8.5 PheromoneDepositionandMovementAnalysis . . . . . . . . . . . . . 115
3.8.5.1 Pheromone quantity, maximum coefficient and the evapora-
tionparameters . . . . . . . . . . . . . . . . . . . . . . . . 115
3.8.5.2 ResidualParameter . . . . . . . . . . . . . . . . . . . . . . 117
3.8.6 MergingThresholds . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
3.8.6.1 FeatureMergingThresholdParameter . . . . . . . . . . . . 118
3.8.6.2 ColonyMergingThresholdParameter . . . . . . . . . . . . 120
3.8.6.3 VisibilityonEdgeParameter . . . . . . . . . . . . . . . . . 121
3.8.6.4 Time-windowParameter. . . . . . . . . . . . . . . . . . . . 122
3.9 TheMPACAasaClassifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
3.9.1 TrainingTerminationCriteria . . . . . . . . . . . . . . . . . . . . . . 124
3.9.2 EvaluationoftheMPACAasaClassifier . . . . . . . . . . . . . . . . 124
3.10 NoveltyandContributionoftheMPACA . . . . . . . . . . . . . . . . . . . . 125
3.10.1 DistinctiveElementsoftheMPACA . . . . . . . . . . . . . . . . . . . 125
3.10.2 VariationsoftheMPACAfromtheTraditionalClusteringAlgorithms . 126
3.10.3 VariationsfromAntBasedClusteringLiterature . . . . . . . . . . . . 127
3.10.4 AdvantagesoftheMPACAArchitecture . . . . . . . . . . . . . . . . . 128
3.10.5 NoveltyinAntMovement . . . . . . . . . . . . . . . . . . . . . . . . 129
3.10.6 AbilitytoLearnandAcquireFeatures . . . . . . . . . . . . . . . . . . 130
3.10.7 MultiplePheromonesandMultipleColonies . . . . . . . . . . . . . . 131
3.11 ChapterConclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
4 TheMPACAApplied 133
4.1 ChapterOverview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
4.2 EvaluationCriteriaandExperimentSet-up . . . . . . . . . . . . . . . . . . . . 133
4.2.1 SyntheticDatasets: the2D-4Cand10D-10CDatasets . . . . . . . . . 134
6
4.2.2 Real-worldUCIdatasets . . . . . . . . . . . . . . . . . . . . . . . . . 134
4.2.2.1 Irisdataset . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
4.2.2.2 Winedataset . . . . . . . . . . . . . . . . . . . . . . . . . . 134
4.2.2.3 Soya-beandataset . . . . . . . . . . . . . . . . . . . . . . . 135
4.2.2.4 WisconsinBreastCancerdataset . . . . . . . . . . . . . . . 135
4.2.2.5 PimaIndiansDiabetesdataset . . . . . . . . . . . . . . . . . 135
4.2.2.6 Yeastdataset . . . . . . . . . . . . . . . . . . . . . . . . . . 135
4.3 ExperimentationFramework . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
4.3.1 BasicSet-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
4.3.2 AnalysisbasedonaSimulatedAnnealingTechnique . . . . . . . . . . 136
4.4 BaselineExperiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
4.4.1 ObservationsfromBaselineExperiments . . . . . . . . . . . . . . . . 141
4.4.2 EvaluatingtheMPACAClusteringPerformance. . . . . . . . . . . . . 142
4.5 SensitivityAnalysisofchosenParameters . . . . . . . . . . . . . . . . . . . . 146
4.5.1 SensitivityMetric . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
4.5.2 PheromoneDrivenversusaRandomModel . . . . . . . . . . . . . . . 147
4.6 Real-worldGRiSTandADVANCEdatasets . . . . . . . . . . . . . . . . . . . 148
4.6.1 GRiST-Mentalhealthriskassessment . . . . . . . . . . . . . . . . . 148
4.6.2 ADVANCE-Hub-and-SpokeLogisticsNetworks . . . . . . . . . . . . 150
4.6.2.1 PredictingShipments . . . . . . . . . . . . . . . . . . . . . 151
4.7 DiscussionofResultsAttained . . . . . . . . . . . . . . . . . . . . . . . . . . 154
5 ConclusionandFutureWork 155
5.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
5.1.1 UniquepropertiesoftheMPACA . . . . . . . . . . . . . . . . . . . . 156
5.1.1.1 ModifiedAntTransitionMechanism . . . . . . . . . . . . . 156
5.1.1.2 FeatureLearningandtheMulti-PheromoneMechanism . . . 156
5.1.1.3 Multi-ColonyClusteringviaColonyFormation . . . . . . . 157
5.1.2 GoalsandObjectivesmetbytheMPACA . . . . . . . . . . . . . . . . 157
5.2 AlternativePaths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
5.2.1 VariationintheAntTypes . . . . . . . . . . . . . . . . . . . . . . . . 158
5.2.2 AcquisitionofMultipleFeaturesonEachDimension . . . . . . . . . . 158
5.2.3 FeatureMergingwithNo-ForgettingMechanism . . . . . . . . . . . . 158
5.2.4 ClusterRepresentationinFirstOrderLogic . . . . . . . . . . . . . . . 158
5.3 AdvancesoftheAlgorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
5.4 CurrentLimitationsandRecommendedImprovements . . . . . . . . . . . . . 160
5.4.1 ParallelversusNon-Parallel . . . . . . . . . . . . . . . . . . . . . . . 160
5.4.2 ParametersandParameterAdjustment . . . . . . . . . . . . . . . . . . 161
5.4.3 TerminationCriteria . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
5.4.4 TacklingUnevenDatasets . . . . . . . . . . . . . . . . . . . . . . . . 161
5.5 Futurework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
5.5.1 BayesianClusterMembershipCalculation . . . . . . . . . . . . . . . . 162
5.5.2 K-NearestNeighbourhoodClusterMembershipCalculation . . . . . . 163
5.5.3 OngoingResearch . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
5.5.4 ApplicationoftheMPACAasaClassifier . . . . . . . . . . . . . . . . 165
5.6 ConcludingArguments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
7
List of Figures
1.1 Experimentalset-updemonstratingtheshortestpathfinding. . . . . . . . . . . 17
2.1 Dwellingsthatappertaintothetwoparishesandpossibleconfigurations. . . . . 24
2.2 EuclideanversusCityblockdistanceproblemdepiction . . . . . . . . . . . . . 26
2.3 Dendrogramrepresentationoftheanimalkingdomcategorisation . . . . . . . . 31
2.4 Density-reachabilityanddensity-connectivityintheDBSCAN . . . . . . . . . 35
2.5 Fireantscoalescetogethertoformabridgewiththeirbodies . . . . . . . . . . 49
2.6 Asequentialclusteringtaskofcorpsesperformedbyarealantcolony . . . . . 50
2.7 PrinciplesoftheANTCLUST . . . . . . . . . . . . . . . . . . . . . . . . . . 52
2.8 ClusteringasanOptimisationProblem . . . . . . . . . . . . . . . . . . . . . . 53
2.9 Thetournamentselectionmechanism . . . . . . . . . . . . . . . . . . . . . . 79
3.1 A finite state machine representing the changes in ant behaviour as it traverses
thegraph. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
3.2 Resultsofvaryingthemaximumedgelengthparameter . . . . . . . . . . . . . 110
3.3 Resultsofvaryingthestepsizeparameter . . . . . . . . . . . . . . . . . . . . 112
3.4 Resultsofvaryingtheantcomplementparameter . . . . . . . . . . . . . . . . 113
3.5 Resultsofvaryingthedetectionrangeforcontinuousdomainsparameter . . . . 115
3.6 Resultsofvaryingthepheromonerelatedparameters . . . . . . . . . . . . . . 116
3.7 Resultsofvaryingtheresidualparameter. . . . . . . . . . . . . . . . . . . . . 117
3.8 Resultsofvaryingthefeaturemergingparameter . . . . . . . . . . . . . . . . 119
3.9 Resultsofvaryingthecolonymergingparameter . . . . . . . . . . . . . . . . 120
3.10 Resultsofvaryingthevisibilityrangeparameter . . . . . . . . . . . . . . . . . 121
3.11 Resultsofvaryingthetime-windowparameter . . . . . . . . . . . . . . . . . . 123
4.1 Transportationinamultiplehub-and-spokelogisticssystem. . . . . . . . . . . 150
4.2 Fluctuationsinthenumberofpalletseachdayforaspecificdepot . . . . . . . 151
8
List of Tables
3.1 TheMPACAparametersettingsasappliedtotheSquare1dataset . . . . . . . . 108
4.1 Summaryoftheselecteddatasets . . . . . . . . . . . . . . . . . . . . . . . . . 136
4.2 TheMPACAasappliedtotheSquare1,2D-4C,10D-10C,IrisandWinedatasets. 138
4.3 TheMPACAasappliedtotheSoya-Bean,WBC,PimaandYeastdatasets. . . . 139
4.4 TheMPACAperformanceappliedoversyntheticdatasets . . . . . . . . . . . . 142
4.5 TheMPACAperformanceappliedoverreal-worlddatasets . . . . . . . . . . . 143
4.6 ParametersensitivityanalysisasappliedtotheIrisandWinedataset. . . . . . . 147
4.7 PheromoneDrivenversusaRandomModelappliedtotheIrisandWinedataset. 148
4.8 ParametersettingsfortheMPACAasappliedtotheGRiSTdataset . . . . . . . 149
4.9 ParametersettingsfortheMPACAasappliedtotheADVANCEdataset . . . . 153
4.10 ResultsoftheMPACAasappliedtotheADVANCEdataset. . . . . . . . . . . 154
5.1 ParallelversusNon-ParallelexecutionovertheIrisdataset . . . . . . . . . . . 160
9