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ALICE: Analysis & Learning Iterative Consecutive Executions Helga Ingimundardóttir Faculty of Industrial Eng., Mechanical Eng. and Computer Science University of Iceland 2016 Dissertationforthedegreeofdoctorofphilosophy ALICE: Analysis & Learning Iterative Consecutive Executions HelgaIngimundardóttir SchoolofEngineeringandNaturalSciences FacultyofIndustrialEng.,MechanicalEng.andComputerScience Reykjavík,June2016 AdissertationpresentedtotheUniversityofIcelandSchoolofEngineeringandNaturalSciences incandidacyforthedegreeofdoctorofphilosophy. Doctoralcommittee Prof.TómasPhilipRúnarsson FacultyofEngineering,UniversityofIceland Prof.GunnarStefánsson FacultyofPhysicalSciences,UniversityofIceland Prof.MichèleSebag ResearchdirectorCNRS,LRI,UniversitéParis-Sud Opponents Prof.EdmundKieranBurke ScienceandEngineering,QueenMaryUniversityofLondon Prof.KateSmith-Miles SchoolofMathematicalSciences,MonashUniversity ALICE:Analysis&LearningIterativeConsecutiveExecutions ©2016HelgaIngimundardóttir PrintedinIcelandbySvansprent ISBN978-9935-9307-9-8 Alltfyrirmóðurmína iv Eitherthewellwasverydeep,orshefellveryslowly,forshehad plentyoftimeasshewentdowntolookaboutherandtowonder whatwasgoingtohappennext. Narrator Abstract Overtheyearstherehavebeenmanyapproachestocreatedispatchingrulesforscheduling. Re- centpasteffortshavefocusedondirectsearchmethods(e.g. geneticprogramming)ortraining ondata(e.g.supervisedlearning).Thedissertationwillexaminethelatterandgiveaframework calledAnalysis&LearningIterativeConsecutiveExecutions(ALICE)onhowtodoiteffectively. Definingtrainingdataasfφ(x(k));y(k)gK 2 Dthedissertationwillshow:i)samplesφ(x) i i k=1 i D shouldrepresenttheinduceddatadistribution . Thisdonebyupdatingthelearnedmodelin anactiveimitationlearningfashion;ii)y islabelledusinganexpertpolicyviaasolver;iii)data i needstobebalanced, asthesetisunbalancedw.r.t. thedispatchingstepk, andiv)toimprove uponlocalisedstepwisefeaturesφ,it’spossibletoincorporate(K(cid:0)k)roll-outswherethelearned modelcanbeconstruedasadeterministicpilotheuristic. Whenqueryinganexpertpolicy,thereisanabundanceofvaluableinformationthatcanbe utilisedforlearningnewmodels.Forinstance,it’spossibletoseekoutwhentheschedulingpro- cessismostsusceptibletofailure. Furthermore,generallystepwiseoptimality(orclassification accuracy)impliesgoodendperformance,hereminimisingthefinalmakespan. However,asthe impactofsuboptimalmovesisnotfullyunderstood,thenthemeasureneedstobeadjustedfor itsintendedtrajectory. Usingtheseguidelines,itbecomeseasiertocreatecustomdispatchingrulesforone’sparticular application. For this several different distributions of job-shop will be considered. Moreover, themachinelearningapproachisbasedonpreferencelearning,i.e.,whichpost-decisionstateis preferabletoanother. However,thatcouldeasilybesubstitutedforotherlearningmethodsor appliedtoothershop-constraintsorfamilyofschedulingproblemsthatarebasedoniteratively applyingdispatchingrules. v Niður,niður,niður!Ætlaðiþettaaldreiaðtakaenda?Hvaðskyldi éghafahrapaðmargakílómetra? Lísa Ágrip Tilerumargaraðferðirviðaðbúatilákvarðanareglurfyriráætlanagerð. Undanfariðhefuráher- slan í fræðunum verið á beina leit (t.d. gentíska bestun) eða gagnaþjálfun, en ein aðferð við þaðsíðarnefndaerstýrðurlærdómur. Íritgerðinniverðursúaðferðskoðuðnánarogsettfram líkan kallað Lærdómur ítrekunarreiknirita og samtakagreining algríma (LÍSA) um hvernig megi framkvæmaþessagreininguáskilvirkanmáta. Látumþjálfunargögninverafφ(x(k));y(k)gK 2 Dogritgerðinmunsýna: i)úrtökφ(x) i i k=1 i D þurfaaðveraísamræmiviðgagnadreifinguna semverðurunninúrhenni. Þettaergertmeð þvíaðuppfæralærðalíkaniðmeðvirkunámsferlibyggðuáeftirlíkingum;ii)y ermerktmeðþví i aðnotaendurgjöfsérfræðings(gertmeðbestun); iii)gögninþurfaaðveraíjafnvægi, þarsem gagnasettiðeríójafnvægimeðtillititilskrefsk;einnigiv)tilaðbetrumbætalýsinguánúverandi stöðuφ,erhægtaðnotaútspilunfyrirnæstu(K(cid:0)k)skref,þaðeraðendalokumákvarðanaferilsins. Þámátúlkalærðalíkaniðsemfyrirframákveðnaútspilunarreglu. Þegar sérfræðingur er spurður, verður til mikið af gagnlegum upplýsingum sem hægt er að nýtatilaðlæranýlíkön. Tilaðmyndaerhægtaðkomastaðþvíhvenæríákvarðanaferlinuer líklegastaðmistökeigisérstað.Yfirleittgefaháarlíkuráþvíaðbestaákvörðunsétekin(eðaþjál- funarnákvæmni)tilkynnagóðalokaframmistöðu,þ.e.íþessusamhengiaðlágmarkaheildartíma fyriralltákvarðanaferlið. Þarsemafleiðingarrangraákvarðanaeruekkialltafþekktar,þáerbetra aðuppfæramatiðmeðtillititilákvarðanatökunnarsjálfrar. Með þessari greiningu er einfaldara að búa til sérhæfðar ákvarðanareglur fyrir hverja nýja notkun. Í ritgerðinni verða skoðaðar nokkrar mismunandi tegundir af verkniðurröðun á vélar. Þaraðaukiverðurvélnámiðbyggtáákjósanlegribestun,þarsemgerðurergreinarmunuráþví hvaðastöðurerubetrikosturenaðrar. Ákjósanlegribestunværiþóhægtaðskiptaútfyriraðrar námsaðferðir,hægtværiaðbætaviðfleiriskorðumáverkefniðeðabeitasömunámsaðferðáaðra tegundafverkefnumafsvipuðumtoga. vi IthinkIshouldunderstandthatbetter,ifIhaditwrittendown:but Ican’tquitefollowitasyousayit. Alice Contents Listingoffigures xi Listingoftables xiii Listingofalgorithms xv Listingofpublications xvi Nomenclature xviii I Prologue 1 1 Introduction 3 1.1 Rice’sframeworkforalgorithmselection . . . . . . . . . . . . . . . . . . . . 4 1.2 Previouswork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.4 Supplementarymaterial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.5 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2 Job-shopSchedulingProblem 13 2.1 Mathematicalformulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.2 Constructionheuristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.3 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.4 Singleprioritybaseddispatchingrules . . . . . . . . . . . . . . . . . . . . . . 21 2.5 Featuresforjob-shop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.6 Compositedispatchingrules . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.7 Rice’sframeworkforjob-shop . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3 Problemgenerators 29 3.1 Job-shop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 vii 3.2 Flow-shop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.3 Benchmarkproblemsuite . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 4 Problemdifficulty 35 4.1 Distributiondifficulty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 4.2 Definingeasyversushardschedules . . . . . . . . . . . . . . . . . . . . . . . 39 4.3 Consistencyofprobleminstances . . . . . . . . . . . . . . . . . . . . . . . . 42 4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 5 EvolutionarySearch 47 5.1 Experimentalsetting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 5.2 Performancemeasures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 5.3 Experimentalstudy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 5.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 6 GeneratingTrainingData 57 6.1 Job-shoptreerepresentation . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 6.2 Labellingschedulesw.r.t.optimaldecisions . . . . . . . . . . . . . . . . . . . 59 6.3 Computationalgrowth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 6.4 Trajectorysamplingstrategies . . . . . . . . . . . . . . . . . . . . . . . . . . 60 7 AnalysingSolutions 65 7.1 Makingoptimaldecisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 7.2 Makingsuboptimaldecisions . . . . . . . . . . . . . . . . . . . . . . . . . . 66 7.3 Optimalityofextremalfeatures . . . . . . . . . . . . . . . . . . . . . . . . . 69 7.4 Simpleblendeddispatchingrule . . . . . . . . . . . . . . . . . . . . . . . . . 77 7.5 Featureevolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 7.6 Emergenceofproblemdifficulty . . . . . . . . . . . . . . . . . . . . . . . . . 79 7.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 8 PreferenceLearning 87 8.1 Ordinalregressionforjob-shop . . . . . . . . . . . . . . . . . . . . . . . . . 87 8.2 Selectingpreferencepairs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 8.3 Scalabilityofdispatchingrules . . . . . . . . . . . . . . . . . . . . . . . . . . 90 8.4 Rankingstrategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 8.5 Trajectorystrategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 8.6 Stepwisesamplingbias . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 8.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 viii

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I can't quite follow it as you say it. Alice. Contents. Listing of figures xi .. 2.3 Gantt chart of a partial JSP schedule 8.4 Main statistics for deviation from optimality, ρ, based on various stepwise sam- 11.2 Main statistics for {φi}24 .. “The only real mistake is the one from which we le
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ALICE: Analysis & Learning Iterative Consecutive Executions Helga Ingimundardóttir Faculty of Industrial Eng., Mechanical Eng. and Computer Science University of Iceland 2016 Dissertationforthedegreeofdoctorofphilosophy ALICE: Analysis & Learning Iterative Consecutive Executions HelgaIngimundardóttir SchoolofEngineeringandNaturalSciences FacultyofIndustrialEng.,MechanicalEng.andComputerScience Reykjavík,June2016 AdissertationpresentedtotheUniversityofIcelandSchoolofEngineeringandNaturalSciences incandidacyforthedegreeofdoctorofphilosophy. Doctoralcommittee Prof.TómasPhilipRúnarsson FacultyofEngineering,UniversityofIceland Prof.GunnarStefánsson FacultyofPhysicalSciences,UniversityofIceland Prof.MichèleSebag ResearchdirectorCNRS,LRI,UniversitéParis-Sud Opponents Prof.EdmundKieranBurke ScienceandEngineering,QueenMaryUniversityofLondon Prof.KateSmith-Miles SchoolofMathematicalSciences,MonashUniversity ALICE:Analysis&LearningIterativeConsecutiveExecutions ©2016HelgaIngimundardóttir PrintedinIcelandbySvansprent ISBN978-9935-9307-9-8 Alltfyrirmóðurmína iv Eitherthewellwasverydeep,orshefellveryslowly,forshehad plentyoftimeasshewentdowntolookaboutherandtowonder whatwasgoingtohappennext. Narrator Abstract Overtheyearstherehavebeenmanyapproachestocreatedispatchingrulesforscheduling. Re- centpasteffortshavefocusedondirectsearchmethods(e.g. geneticprogramming)ortraining ondata(e.g.supervisedlearning).Thedissertationwillexaminethelatterandgiveaframework calledAnalysis&LearningIterativeConsecutiveExecutions(ALICE)onhowtodoiteffectively. Definingtrainingdataasfφ(x(k));y(k)gK 2 Dthedissertationwillshow:i)samplesφ(x) i i k=1 i D shouldrepresenttheinduceddatadistribution . Thisdonebyupdatingthelearnedmodelin anactiveimitationlearningfashion;ii)y islabelledusinganexpertpolicyviaasolver;iii)data i needstobebalanced, asthesetisunbalancedw.r.t. thedispatchingstepk, andiv)toimprove uponlocalisedstepwisefeaturesφ,it’spossibletoincorporate(K(cid:0)k)roll-outswherethelearned modelcanbeconstruedasadeterministicpilotheuristic. Whenqueryinganexpertpolicy,thereisanabundanceofvaluableinformationthatcanbe utilisedforlearningnewmodels.Forinstance,it’spossibletoseekoutwhentheschedulingpro- cessismostsusceptibletofailure. Furthermore,generallystepwiseoptimality(orclassification accuracy)impliesgoodendperformance,hereminimisingthefinalmakespan. However,asthe impactofsuboptimalmovesisnotfullyunderstood,thenthemeasureneedstobeadjustedfor itsintendedtrajectory. Usingtheseguidelines,itbecomeseasiertocreatecustomdispatchingrulesforone’sparticular application. For this several different distributions of job-shop will be considered. Moreover, themachinelearningapproachisbasedonpreferencelearning,i.e.,whichpost-decisionstateis preferabletoanother. However,thatcouldeasilybesubstitutedforotherlearningmethodsor appliedtoothershop-constraintsorfamilyofschedulingproblemsthatarebasedoniteratively applyingdispatchingrules. v Niður,niður,niður!Ætlaðiþettaaldreiaðtakaenda?Hvaðskyldi éghafahrapaðmargakílómetra? Lísa Ágrip Tilerumargaraðferðirviðaðbúatilákvarðanareglurfyriráætlanagerð. Undanfariðhefuráher- slan í fræðunum verið á beina leit (t.d. gentíska bestun) eða gagnaþjálfun, en ein aðferð við þaðsíðarnefndaerstýrðurlærdómur. Íritgerðinniverðursúaðferðskoðuðnánarogsettfram líkan kallað Lærdómur ítrekunarreiknirita og samtakagreining algríma (LÍSA) um hvernig megi framkvæmaþessagreininguáskilvirkanmáta. Látumþjálfunargögninverafφ(x(k));y(k)gK 2 Dogritgerðinmunsýna: i)úrtökφ(x) i i k=1 i D þurfaaðveraísamræmiviðgagnadreifinguna semverðurunninúrhenni. Þettaergertmeð þvíaðuppfæralærðalíkaniðmeðvirkunámsferlibyggðuáeftirlíkingum;ii)y ermerktmeðþví i aðnotaendurgjöfsérfræðings(gertmeðbestun); iii)gögninþurfaaðveraíjafnvægi, þarsem gagnasettiðeríójafnvægimeðtillititilskrefsk;einnigiv)tilaðbetrumbætalýsinguánúverandi stöðuφ,erhægtaðnotaútspilunfyrirnæstu(K(cid:0)k)skref,þaðeraðendalokumákvarðanaferilsins. Þámátúlkalærðalíkaniðsemfyrirframákveðnaútspilunarreglu. Þegar sérfræðingur er spurður, verður til mikið af gagnlegum upplýsingum sem hægt er að nýtatilaðlæranýlíkön. Tilaðmyndaerhægtaðkomastaðþvíhvenæríákvarðanaferlinuer líklegastaðmistökeigisérstað.Yfirleittgefaháarlíkuráþvíaðbestaákvörðunsétekin(eðaþjál- funarnákvæmni)tilkynnagóðalokaframmistöðu,þ.e.íþessusamhengiaðlágmarkaheildartíma fyriralltákvarðanaferlið. Þarsemafleiðingarrangraákvarðanaeruekkialltafþekktar,þáerbetra aðuppfæramatiðmeðtillititilákvarðanatökunnarsjálfrar. Með þessari greiningu er einfaldara að búa til sérhæfðar ákvarðanareglur fyrir hverja nýja notkun. Í ritgerðinni verða skoðaðar nokkrar mismunandi tegundir af verkniðurröðun á vélar. Þaraðaukiverðurvélnámiðbyggtáákjósanlegribestun,þarsemgerðurergreinarmunuráþví hvaðastöðurerubetrikosturenaðrar. Ákjósanlegribestunværiþóhægtaðskiptaútfyriraðrar námsaðferðir,hægtværiaðbætaviðfleiriskorðumáverkefniðeðabeitasömunámsaðferðáaðra tegundafverkefnumafsvipuðumtoga. vi IthinkIshouldunderstandthatbetter,ifIhaditwrittendown:but Ican’tquitefollowitasyousayit. Alice Contents Listingoffigures xi Listingoftables xiii Listingofalgorithms xv Listingofpublications xvi Nomenclature xviii I Prologue 1 1 Introduction 3 1.1 Rice’sframeworkforalgorithmselection . . . . . . . . . . . . . . . . . . . . 4 1.2 Previouswork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.4 Supplementarymaterial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.5 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2 Job-shopSchedulingProblem 13 2.1 Mathematicalformulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.2 Constructionheuristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.3 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.4 Singleprioritybaseddispatchingrules . . . . . . . . . . . . . . . . . . . . . . 21 2.5 Featuresforjob-shop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.6 Compositedispatchingrules . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.7 Rice’sframeworkforjob-shop . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3 Problemgenerators 29 3.1 Job-shop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 vii 3.2 Flow-shop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.3 Benchmarkproblemsuite . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 4 Problemdifficulty 35 4.1 Distributiondifficulty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 4.2 Definingeasyversushardschedules . . . . . . . . . . . . . . . . . . . . . . . 39 4.3 Consistencyofprobleminstances . . . . . . . . . . . . . . . . . . . . . . . . 42 4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 5 EvolutionarySearch 47 5.1 Experimentalsetting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 5.2 Performancemeasures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 5.3 Experimentalstudy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 5.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 6 GeneratingTrainingData 57 6.1 Job-shoptreerepresentation . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 6.2 Labellingschedulesw.r.t.optimaldecisions . . . . . . . . . . . . . . . . . . . 59 6.3 Computationalgrowth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 6.4 Trajectorysamplingstrategies . . . . . . . . . . . . . . . . . . . . . . . . . . 60 7 AnalysingSolutions 65 7.1 Makingoptimaldecisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 7.2 Makingsuboptimaldecisions . . . . . . . . . . . . . . . . . . . . . . . . . . 66 7.3 Optimalityofextremalfeatures . . . . . . . . . . . . . . . . . . . . . . . . . 69 7.4 Simpleblendeddispatchingrule . . . . . . . . . . . . . . . . . . . . . . . . . 77 7.5 Featureevolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 7.6 Emergenceofproblemdifficulty . . . . . . . . . . . . . . . . . . . . . . . . . 79 7.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 8 PreferenceLearning 87 8.1 Ordinalregressionforjob-shop . . . . . . . . . . . . . . . . . . . . . . . . . 87 8.2 Selectingpreferencepairs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 8.3 Scalabilityofdispatchingrules . . . . . . . . . . . . . . . . . . . . . . . . . . 90 8.4 Rankingstrategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 8.5 Trajectorystrategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 8.6 Stepwisesamplingbias . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 8.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 viii

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I can't quite follow it as you say it. Alice. Contents. Listing of figures xi .. 2.3 Gantt chart of a partial JSP schedule 8.4 Main statistics for deviation from optimality, ρ, based on various stepwise sam- 11.2 Main statistics for {φi}24 .. “The only real mistake is the one from which we le
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