Integrated Optimization in Public Transport Planning

195 Pages·2020·4.446 MB·English

by  Philine Schiewe

Springer Optimization and Its Applications 160
Philine Schiewe
Integrated
Optimization in
Public Transport
Planning
Springer Optimization and Its Applications
Volume 160
SeriesEditors
PanosM.Pardalos ,UniversityofFlorida
MyT.Thai ,UniversityofFlorida
HonoraryEditor
Ding-ZhuDu,UniversityofTexasatDallas
AdvisoryEditors
RomanV.Belavkin,MiddlesexUniversity
JohnR.Birge,UniversityofChicago
SergiyButenko,TexasA&MUniversity
FrancoGiannessi,UniversityofPisa
VipinKumar,UniversityofMinnesota
AnnaNagurney,UniversityofMassachusettsAmherst
JunPei,HefeiUniversityofTechnology
OlegProkopyev,UniversityofPittsburgh
SteffenRebennack,KarlsruheInstituteofTechnology
MauricioResende,Amazon
TamásTerlaky,LehighUniversity
VanVu,YaleUniversity
GuoliangXue,ArizonaStateUniversity
YinyuYe,StanfordUniversity
AimsandScope
Optimizationhascontinuedtoexpandinalldirectionsatanastonishingrate.New
algorithmicandtheoreticaltechniquesarecontinuallydevelopingandthediffusion
into other disciplines is proceeding at a rapid pace, with a spot light on machine
learning, artificial intelligence, and quantum computing. Our knowledge of all
aspects of the field has grown even more profound. At the same time, one of the
most striking trends in optimization is the constantly increasing emphasis on the
interdisciplinary nature of the field. Optimization has been a basic tool in areas
not limited to applied mathematics, engineering, medicine, economics, computer
science,operationsresearch,andothersciences.
The series Springer Optimization and Its Applications (SOIA) aims to publish
state-of-the-art expository works (monographs, contributed volumes, textbooks,
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coveredinclude,butarenotlimitedto,nonlinearoptimization,combinatorialopti-
mization,continuousoptimization,stochasticoptimization,Bayesianoptimization,
optimalcontrol,discreteoptimization,multi-objectiveoptimization,andmore.New
totheseriesportfolioincludeWorksattheintersectionofoptimizationandmachine
learning,artificialintelligence,andquantumcomputing.
Volumes from this series are indexed by Web of Science, zbMATH, Mathematical
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Moreinformationaboutthisseriesathttp://www.springer.com/series/7393
Philine Schiewe
Integrated Optimization in
Public Transport Planning
PhilineSchiewe
FachbereichMathematik
TechnischeUniversita¨tKaiserslautern
Kaiserslautern,Germany
ISSN1931-6828 ISSN1931-6836 (electronic)
SpringerOptimizationandItsApplications
ISBN978-3-030-46269-7 ISBN978-3-030-46270-3 (eBook)
https://doi.org/10.1007/978-3-030-46270-3
MathematicsSubjectClassification:49-XX,49Q22
©SpringerNatureSwitzerlandAG2020
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Contents
1 Introduction .................................................................. 1
1.1 Outline................................................................... 2
1.2 LiteratureOverview..................................................... 3
1.2.1 LinePlanning ................................................... 4
1.2.2 Timetabling ..................................................... 5
1.2.3 VehicleScheduling ............................................. 7
1.2.4 Integration....................................................... 8
1.3 ProblemDefinitions..................................................... 10
1.3.1 Preliminaries.................................................... 11
1.3.2 PreliminariesPublicTransportPlanning ...................... 12
1.3.3 LinePlanning ................................................... 12
1.3.4 Timetabling ..................................................... 15
1.3.5 VehicleScheduling ............................................. 21
1.3.6 PublicTransportPlan........................................... 26
1.3.7 Multi-CriteriaOptimization.................................... 27
1.4 DataSets................................................................. 28
1.4.1 DataSetsmall ................................................ 29
1.4.2 DataSettoy.................................................... 29
1.4.3 DataSetgrid.................................................. 29
1.4.4 DataSetregional ........................................... 30
1.4.5 DataSetlong-distance................................... 30
2 IntegratingTimetablingandPassengerRouting......................... 33
2.1 ModelingtheIntegratedProblem ...................................... 33
2.2 TwoApproachesforReducingtheProblemSize...................... 38
2.2.1 CombiningShortestPathRoutingwithRoutingAlong
FixedPaths...................................................... 38
2.2.2 APreprocessingAlgorithm .................................... 43
2.3 ComputationalExperiments............................................ 45
2.3.1 WhichODPairsShouldBeRouted? .......................... 47
2.3.2 InfluenceofPreprocessingandChosenIPFormulation...... 48
v
vi Contents
2.3.3 ComparingHeuristicLBandHeuristicUB ................... 48
2.3.4 BestConfigurationwithBounds............................... 50
2.3.5 BoundsforDataSettoy....................................... 51
2.3.6 DataSetlong-distance................................... 51
2.4 AddingTimeSlices..................................................... 52
2.5 ASATFormulationwithTimeSlices.................................. 56
2.5.1 ModelingFeasibility............................................ 58
2.5.2 ObjectiveFunction.............................................. 60
2.6 Summary ................................................................ 64
3 IntegratingLinePlanning,Timetabling,andPassengerRouting ...... 65
3.1 ModelingtheIntegratedProblem ...................................... 65
3.2 ExtensionsoftheModel................................................ 69
3.3 ReducingtheProblemSize............................................. 69
3.3.1 DeterminingwhichStationsSufficeforTransferring......... 71
3.3.2 APreprocessingAlgorithm .................................... 75
3.3.3 RoutingonFixedPaths......................................... 80
3.4 ComputationalExperiments............................................ 83
3.4.1 InfluenceofPreprocessing ..................................... 84
3.4.2 InfluenceofAddingFixedPassengerRoutes ................. 85
3.4.3 InfluenceoftheNumberofRoutedODPairs................. 86
3.4.4 FindingSolutionsforDifferentPreferences................... 88
3.5 Summary ................................................................ 89
4 IntegratingTimetablingandVehicleScheduling......................... 91
4.1 ModelingtheIntegratedProblem ...................................... 91
4.2 ComputationalExperiments............................................ 96
4.3 Summary ................................................................ 97
5 IntegratingLinePlanning,Timetabling,PassengerRouting
andVehicleScheduling...................................................... 99
5.1 ModelingtheIntegratedProblem ...................................... 99
5.1.1 Structure......................................................... 100
5.1.2 AnIPFormulation.............................................. 101
5.1.3 ComputationalExperiments.................................... 105
5.2 AnalysisoftheStructure................................................ 107
5.2.1 Decompositions................................................. 108
5.2.2 ComputationalExperiments.................................... 109
5.3 Summary ................................................................ 116
6 TwoHeuristicApproachesforIntegratingPublicTransport
Problems...................................................................... 117
6.1 ALook-AheadHeuristic................................................ 117
6.1.1 Look-AheadEnhancements.................................... 118
6.1.2 ComputationalExperiments.................................... 124
Contents vii
6.2 AnIterativeRe-OptimizationApproach............................... 128
6.2.1 ModellingtheRe-OptimizationProblems..................... 128
6.2.2 IterationScheme................................................ 142
6.2.3 ComputationalExperiments.................................... 147
6.3 Summary ................................................................ 153
7 GeneralMulti-StageProblems ............................................. 155
7.1 SequentialandMulti-StageProblems.................................. 155
7.2 PriceofSequentiality................................................... 160
7.3 RelationtoIntegratedPublicTransportProblems..................... 168
8 DiscussionandConclusion.................................................. 171
9 Outlook........................................................................ 175
A SupplementaryMaterial .................................................... 177
B FrequentlyUsedNotations.................................................. 181
Bibliography...................................................................... 185
Acknowledgements
As this book is an outgrowth of my thesis, I want to start by thanking my
supervisor Anita Schöbel for her support through all stages of writing. Thank you
foryourpatience,enthusiasm,andalwaysaskingtherightquestions!Nomatterhow
muchwasonyourplate,youalwaysmadetimeforgivingadvice—fromstubborn
implementation problems to developing new ideas for research topics. I also want
tothankmyco-supervisorAnjaFischerforherhelpfuladviceandmanyinteresting
lecturesaswellasRalfBorndörferforagreeingtoco-refereemythesis.
ManythanksalsogototheDFGresearchunitFOR2083forthefinancialsupport
butmuchmoreimportantlyfortheinspirationalenvironment.Theregularmeetings
andfruitfuldiscussionswereagreathelpforbetterunderstandinghowmyresearch
fits into the wider context of public transport planning, not only considered from
a mathematical point of view but also from a computer science and engineering
perspective.
Many of the results presented here would not have been developed without
my co-authors Peter Großmann, Jonas Harbering, Marco Lübbecke, Karl Nachti-
gall, Julius Pätzold, Christian Puchert, Stefan Ruzika, Alexander Schiewe, Marie
Schmidt,andAnitaSchöbel.Thankyouforthegreatcollaborations!Manythanks
also go to Michael Bastubbe and Florentin Hildebrand for helping with the
implementations. I also want to thank the LinTim-Team consisting of Sebastian
Albert,JonasHarbering,JuliusPätzold,AlexanderSchiewe,andAnitaSchöbelfor
theirconstantdevelopmentandmaintenanceofLinTim!
The AG Optimierung both in Göttingen and Kaiserslautern always provided a
greatworkingenvironment.Thankyouallforaddingjointlunchbreaks,choirprac-
tice, cake and ice-cream sessions, hiking tours, and triathlons to the mathematical
day-to-day life. Special thanks go to Alex, Corinna, Lisa, and Julius for proof-
reading parts of this book as well as to the anonymous referees. Your input was
extremelyhelpful!
I cannot imagine the last years without the support of my family and friends.
Especiallymyparentsandparents-in-lawmadesurethatwritingwasasenjoyable
aspossiblebyprovidingasheerendlesssupplyofadvice,support,love,andcake,
nomatterwhattimeofday.Thankyouverymuch!
ix
x Acknowledgements
Lastbutnotleast,mythanksgotoAlex,Emelie,andLeana!ThankyouEmelie
andLeana,forimprovingeverysingledayandmakingsureIwasnotworkingtoo
much.ThankyouAlex,foryoursupportinallmattersoflifeandforalwayshaving
myback!
Kaiserslautern,Germany PhilineSchiewe