OPTIMIZATION OF STATION LOCATIONS AND TRACK ALIGNMENTS FOR RAIL TRANSIT LINES ...

232 Pages·2012·3.8 MB·English

ABSTRACT

Title: OPTIMIZATION OF STATION LOCATIONS AND
TRACK ALIGNMENTS FOR RAIL TRANSIT LINES

Xiaorong Lai, Doctor of Philosophy, 2012

Directed by: Dr. Paul Schonfeld, Professor
Department of Civil & Environmental Engineering

Designing urban rail transit systems is a complex problem, which involves the
determination of station locations, track geometry, right-of-way type, and various
other system characteristics. The existing studies overlook the complex interactions
between railway alignments and station locations in a practical design process. This
study proposes a comprehensive methodology that helps transit planners to
concurrently optimize station locations and track alignments for an urban rail transit
line. The modeling framework resolves the essential trade-off between an
economically efficient system with low initial and operation cost and an effective
system that provides convenient service for the public. The proposed method
accounts for various geometric requirements and real-world design constraints for
track alignment and stations plans. This method integrates a genetic algorithm (GA)
for optimization with comprehensive evaluation of various important measures of
effectiveness based on processing Geographical Information System (GIS) data.
The base model designs the track alignment through a sequence of preset
stations. Detailed assumptions and formulations are presented for geometric
requirements, design constraints, and evaluation criteria. Three extensions of the base
model are proposed. The first extension explicitly incorporates vehicle dynamics in
the design of track alignments, with the objective of better balancing the initial
construction cost with the operation and user costs recurring throughout the system’s
life cycle. In the second extension, an integrated optimization model of rail transit
station locations and track alignment is formulated for situations in which the
locations of major stations are not preset. The concurrent optimization model searches
through additional decision variables for station locations and station types, estimate
rail transit demand, and incorporates demand and station cost in the evaluation
framework. The third extension considers the existing road network when selecting
sections of the alignment. Special algorithms are developed to allow the optimized
alignment to take advantage of links in an existing network for construction cost
reduction, and to account for disturbances of roadway traffic at highway/rail
crossings. Numerical results show that these extensions have significantly enhanced
the applicability of the proposed optimization methodology in concurrently selecting
rail transit station locations and generating track alignment.
OPTIMIZATION OF STATION LOCATIONS AND TRACK ALIGNMENTS FOR
RAIL TRANSIT LINES

By

Xiaorong Lai

Dissertation submitted to the Faculty of the Graduate School of the
University of Maryland, College Park, in partial fulfillment
of the requirements for the degree of
Doctor of philosophy
2012

Advisory Committee:
Professor Paul Schonfeld, Chair/Advisor
Professor Ali Haghani
Professor Subramanian Raghavan
Professor Manoj K. Jha
Assistant Professor Cinzia Cirillo
© Copyright by
Xiaorong Lai
2012
Dedication

To my wife, Ying Liu

And to our wonderful daughter, Alyson Yuxuan
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Acknowledgements

First and foremost, I would like to express my sincerest gratitude to my
advisor, Professor Paul Schonfeld, for his academic guidance, encouragement and
support over the past five years. I am very grateful for his willingness to meet even
after the normal working hours, and I have greatly benefited and inspired from
discussion with him. I feel very fortunate to have been his student.
I also wish to thank my committee members, Professor Ali Haghani, Professor
Subramanian Raghavan, Professor Manoj Jha and Professor Cinzia Cirillo, for their
precious comments and suggestions on my dissertation. Special thanks go to
Professor Manoj Jha in providing valuable thoughts and references throughout my
research.
I would also like to thank my parents and three elder sisters for all the support
they have provided me over the years.
Finally, and most importantly, I would like to thank my wife, Ying Liu, for
always standing by my side through the good times and the bad times. It was her love,
encouragement, and support that helped me the most,
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Table of Contents
Dedication ..................................................................................................................... ii 
Acknowledgements ...................................................................................................... iii 
Table of Contents ......................................................................................................... iv 
List of Tables ............................................................................................................. viii 
List of Figures .............................................................................................................. ix

Chapter 1: Introduction ................................................................................................. 1 
1.1 Research Background ......................................................................................... 1 
1.2 Research Objectives ............................................................................................ 3 
1.3 Thesis Organization ............................................................................................ 5

Chapter 2: Literature Review ........................................................................................ 8 
2.1 Design of Track Alignment ................................................................................ 8 
2.1.1 Alignment Optimization Models ............................................................... 10 
2.1.2 Design Considerations in Determining Track Alignment ......................... 16 
2.2 Selection of Rail Transit Stations ..................................................................... 21 
2.2.1. Transit Station Location Models ............................................................... 21 
2.2.2. Transit Ridership Forecasting Models ...................................................... 32 
2.3 Cost and Benefit Associated with Urban Rail Transit ...................................... 40 
2.3.1 Cost of Urban Rail Transit ......................................................................... 40 
2.3.1.1. Cost Items for Providing Rail Transit Service ................................... 40 
2.3.1.2. Costs for Utilizing Rail Transit Service ............................................. 46 
2.3.2 Benefit of Urban Rail Transit Operations .................................................. 48 
2.4 Summary ........................................................................................................... 56

Chapter 3: Optimizing Rail Transit Alignments That Connect Several Major Stations
..................................................................................................................................... 61 
3.1 Model Formulation ........................................................................................... 62 
3.1.1 Components of Rail Transit Alignment ..................................................... 62 
3.1.2 Geometric Constraints for Rail Transit Alignment .................................... 65 
3.1.2.1 Special Alignment Constraints at Rail Transit Stations ...................... 65 
3.1.2.2 General Geometric Requirements for Horizontal Track Alignment ... 66 
3.1.2.3 General Geometric Requirements for Vertical Track Alignment ....... 71 
3.1.3 Cost Formulation for Rail Transit Alignment ............................................ 73 
3.2 Algorithm .......................................................................................................... 73 
3.2.1 Representation of Candidate Track Alignments ........................................ 75 
3.2.1.1 Setting up Cutting Planes .................................................................... 75 
3.2.1.2 Locate Intersection Points ................................................................... 77 
3.2.1.3 Generate Horizontal Alignment .......................................................... 78 
3.2.1.4 Generate Vertical Alignment .............................................................. 80 
3.2.2 Calculation of the Cost Function ............................................................... 81 
3.2.2.1 Identify Cut/Fill Sections and Bridges/Tunnel Sections ..................... 81 
3.2.2.2 Calculate Earthwork Cost for Cut/Fill Sections .................................. 82 
3.2.2.3 Calculate Structure Costs for Bridge and Tunnel Sections ................. 84 
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3.2.2.4 Calculate Right-of-Way Costs ............................................................ 84 
3.3 Summary ........................................................................................................... 85

Chapter 4: Case Study and Sensitivity Analysis ......................................................... 87 
4.1 System Development ........................................................................................ 88 
4.1.1 System Framework .................................................................................... 88 
4.1.2 Principal System Modules ......................................................................... 90 
4.1.2.1 Input Module ....................................................................................... 90 
4.1.2.2 Optimization Module .......................................................................... 93 
4.1.2.3 Alignment Generation Module ........................................................... 94 
4.1.2.4 Cost Evaluation Module ..................................................................... 95 
4.1.2.5 Output Module .................................................................................... 96 
4.2 Case Study ........................................................................................................ 98 
4.2.1 Study Area ................................................................................................. 98 
4.2.2 Optimization Results ................................................................................ 100 
4.2.2.1 Comparison of the Optimized Horizontal Alignments with the
Empirical Alignment ..................................................................................... 100 
4.2.2.2 Comparison of the Optimized Profile with the Ground Elevation ... 101 
4.2.2.3 Comparison of the Cost Breakdown for the Optimized Alignments 102 
4.2.2.4 Comparison of the Efficiency of Algorithm Options ....................... 103 
4.3 Sensitivity Analysis ........................................................................................ 103 
4.3.1 Impact of Introducing Bridge and Tunnel Calculation in the Total Cost 103 
4.3.2 Impact of Cutting Plane Spacing ............................................................. 105 
4.3.3 Impact of Railway Alignment Design Parameters ................................... 107 
4.3.3.1 Design Speed .................................................................................... 107 
4.3.3.2 Maximum Grade ............................................................................... 109 
4.3.4 Impact of Genetic Algorithm Parameters ................................................ 110 
4.3.4.1 GA Population Size........................................................................... 111 
4.3.4.2 GA Mutation Rate Sensitivity Analysis ............................................ 112 
4.3.4.3 GA Crossover Rate Sensitivity Analysis .......................................... 112 
4.4 Variable Cutting Plane Spacing: Algorithm Improvement ............................. 114 
4.4.1 Methodology ............................................................................................ 114 
4.4.1.1 Minimal and Maximal Spacing Constraints ..................................... 114 
4.4.1.2 Encoding of Chromosomes ............................................................... 115 
4.4.1.3 Decoding of Chromosomes to Cutting Plane Spacings .................... 116 
4.4.2 Case Study ............................................................................................... 117 
4.4.2.1 Comparison of Optimized Costs ....................................................... 117 
4.4.2.2 Comparison of Convergence............................................................. 118 
4.4.2.3 Comparison of Optimized Horizontal Alignments ........................... 119 
4.5 Summary ......................................................................................................... 120

Chapter 5: Optimizing Rail Transit Alignments to Account for Vehicle Dynamics 122 
5.1 Model Formulations ........................................................................................ 123 
5.1.1 Simulation of Vehicle Dynamics ............................................................. 124 
5.1.1.1 Acceleration Stage ............................................................................ 126 
5.1.1.2 Braking Stage: ................................................................................... 129 
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5.1.1.3 Cruising Stage: .................................................................................. 129 
5.1.1.4 Travel Time and Energy Consumption for a Round Trip ................. 130 
5.1.2 Estimation of System Cost ....................................................................... 131 
5.1.2.1 Initial Cost ......................................................................................... 131 
5.1.2.2 Operation Cost and User Cost........................................................... 132 
5.2 Case Study ...................................................................................................... 133 
5.2.1 Hypothetical Topography Scenario ......................................................... 134 
5.2.1.1 Scenario Design ................................................................................ 134 
5.2.1.2 Numerical Results ............................................................................. 135 
5.2.1.3 Sensitivity Analysis .......................................................................... 137 
5.2.2 Baltimore Red Line .................................................................................. 138 
5.2.2.1 Comparison of the Horizontal Alignments ....................................... 140 
5.2.2.2 Comparison of the Vertical Profile and Vehicle Dynamics .............. 141 
5.2.2.3 Comparison of Cost Breakdowns ..................................................... 143 
5.3 Summary ......................................................................................................... 144

Chapter 6: Concurrent Optimization of Rail Transit Alignment and Station Locations
................................................................................................................................... 146 
6.1 System Framework ......................................................................................... 147 
6.1.1 Additional Decision Variables for Station Locations and Station Type .. 148 
6.1.2 Forecast Rail Transit Demand ................................................................. 148 
6.2 Generation of the Candidate Pool of Potential Rail Transit Stations .............. 149 
6.3 Forecast of Rail Transit Demand .................................................................... 156 
6.3.1 Choice Modeling for Rail Travel Demand Forecast ................................ 156 
6.3.2 Impacts of Forecasted Rail Transit Ridership on Fitness Evaluation ...... 161 
6.3.2.1 Operation Cost Saving ...................................................................... 161 
6.3.2.2 User Cost Saving............................................................................... 163 
6.3.2.3 Station Costs ..................................................................................... 164 
6.4 Case Study ...................................................................................................... 164 
6.4.1 Data Preparation for the Proposed Concurrent Optimization Model ....... 165 
6.4.1.1 Data for Candidate Stations .............................................................. 165 
6.4.1.2 Data for Estimating Railway Travel Demand ................................... 168 
6.4.2 Model Results .......................................................................................... 172 
6.4.2.1 Comparison of the Two Optimization Methods ............................... 172 
6.4.2.2 Impact of Demand Variation on Optimization Results ..................... 174 
6.4.2.3 Statistical Test of Solution Goodness ............................................... 176 
6.5 Summary ......................................................................................................... 177

Chapter 7: Optimizing Rail Transit Alignment while Considering an Existing Road
Network..................................................................................................................... 179 
7.1 Problem Statement .......................................................................................... 180 
7.2 Modeling Procedures ...................................................................................... 182 
7.2.1 Select Candidate Links from the Existing Network ................................ 182 
7.2.2 GA Special Operator ................................................................................ 184 
7.2.3 Cost Estimation: ....................................................................................... 188 
7.2.3.1 Initial Costs ....................................................................................... 188 
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7.2.3.2 Vehicle Dynamics on Existing Networks ......................................... 189 
7.2.3.3 Operation Cost Saving and User Cost Saving .................................. 190 
7.3 Case Study ...................................................................................................... 190 
7.3.1 Existing Network Related Datasets ......................................................... 192 
7.3.2 Numerical Results .................................................................................... 194 
7.3.2.1 Horizontal Alignment Comparison ................................................... 195 
7.3.2.2 Cost Comparison ............................................................................... 197 
7.4 Summary ......................................................................................................... 198

Chapter 8: Research Summary and Future Work .................................................... 200 
8.1. Research Summary and Contributions........................................................... 200 
8.2. Future Work ................................................................................................... 204

Bibliography ............................................................................................................. 207 
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