ARRIVAL

1
ARRIVAL WP3

• Algorithms for Robust and online Railway
  optimization Improving the Validity and
  realiAbility of Large scale systems
• WP3 Robust and Online
• Timetabling and
• Timetable Information Updating
• Matteo Fischetti (WP3 leader)
• DEI, University of Padova

Matteo Fischetti
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WP3 Participants

• CTI
• UniKarl
• EUR
• ULA
• TUB
• UniBo
• DEI
• UPVLC
• SNCF

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Problem Areas

• Robust and on-line timetable design
• Find a period or aperiodic train timetable (and
  platforming)
• Maximize the timetable efficiency and reliability
• Improve timetable robustness against train delays
  
• Online (real-time) timetable updates after major
  disruptions
• General MIP solution techniques
• MIP models often used to design timetables
• Develop improved MIP solution techniques
• Timetable information updating
• Modeling the timetable information efficiently
• New speedup techniques and fundamental data
  structures to
• support fast query answering

4
Broad objectives

• Develop methods for robust timetabling (and
  platforming)
• Develop methods for online/real-time timetable
  updating
• Develop methods for fast query answering in
  timetable systems
• Efficient data structures for a reactive update
  of the timetable information system
• Investigate the structure of hard MIP models
  arising in railways applications

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Objectives in the reporting period

• - Evaluation of new algorithms to find robust
  timetable and platforming solutions
• - Evaluation of new online (real-time) algorithms
  for timetable and platforming solution updating
• - Analysis of data structures and algorithms for
  online queries in timetable information updating
• - Analysis and evaluation of new approaches to
  hard MIPs

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Main Achievements

• Evaluation of new general models for dealing with
  uncertain data (light robustness recoverable
  robustness)
• Integration between robust timetabling planning
  and delay management policies
• Evaluation of heuristic methods for solving
  (online) train timetabling problems, and
  real-time tools to assists railway operators
• Efficient data structures and algorithms for
  efficient answering of shortest path queries and
  updating in very large networks
• Incorporation of robustness into train
  timetabling/routing models and evaluation of the
  robustness induced in the solution
• Enhancing the performance of MIP solvers by
  improving the quality of generated cuts and of
  heuristics used

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Problems Corrective Actions

• No significant deviation from the WP3 workplan
  occurred in the third year

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Fast timetable robustness improvement ?

• Problem
• optimized timetables might be too sensitive to
  disturbances
• need to adjust a given optimal timetable to be
  robust (allowing for some efficiency loss)?
• Goal
• To find a fast (yet accurate) algorithm to
  improve the robustness of a timetable
• Testing framework

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Matteo Fischetti
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Fast timetable robustness improvement

• Common assumptions for robustness training
  methods
• Allow for some percentage efficiency loss
• Limit the set of planning actions (good for small
  disturbances, leads to more tractable models)
  gt add buffer times ( stretch travel
  times)
• Robustness training methods tested
• Unif. uniform allocation of buffer times (e.g.
  7 nominal travel time)?
• Fat scenario-based stochastic programming
  formulation, aiming at minimizing expected delay
• Slim heuristic version of Fat leading to a more
  tractable MIP formulation
• LR Light Robustness (ARRIVALTM)

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Matteo Fischetti
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Fast timetable robustness improvement
Results (10 efficiency loss w.r.t. the input
timetable)()?

• Unif. is very fast but is the worst in terms of
  robustness
• Fat achieves the best robustness but is very slow
• LR is a good compromise between robusteness and
  performances (1000x faster than Fat)?

() average on 4 real congested
corridors from Italian railway company
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Matteo Fischetti
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Robust Platforming

• Platforming
• For a set of trains over time in a station
  assign conflict-free
• Platforms
• Arrival and departure paths
• Disturbances
• Trains arriving late at the station area
• Prolongated stop boarding may delay departure
• Station utilization close to capacity
• Tight schedules ? high delay
  propagation

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Matteo Fischetti
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Robust Platforming

• Goal
• Keep throughput maximal
• Minimize propagated delay
• Possible approaches
• Classical robust optimization
• Application-specific state-of-the-art heuristics
• General-purpose method of recoverable robustness
  (ARRIVALTM)
• ? Robust Network Buffering

Over-conservative!
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Comparison
Maximal Propagated Delay in min
- 49.2
Time
- 25 delay over the day by using Recoverable
Robustness
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Improved MIP techniques

• Railways problems are often modelled as MIPs
• Typically huge and difficult instances ? very
  challenging even to find any feasible solution
• In practice, a sound heuristic may be the only
  option
• Feasibility Pump (FP) is a recently proposed
  heuristic embedded in most commercial/free MIP
  solvers (Cplex, CBC, Xpress, GLPK, etc.)
• New FP version (FP 2.0) developed within the
  ARRIVAL project by using Constraint Programming
  propagation techniques inside the standard FP
  shell
• Improved performance for both the success rate
  (ability of finding any feasible solution) and
  the solution quality (average optimality gap
  w.r.t. best-known sol. reduced from 77 to 35 on
  a large MIPLIB testbed)

Matteo Fischetti
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Improved MIP techniques
Large MIPlib testbed, avg. results (10 different
seeds for each instance) std (standard 1.0) vs.
prop (new 2.0) FP versions alone large
computing time allowed (standalone
heuristic) embed short comp. time allowed (FP
embedded in a BC code)
Matteo Fischetti
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Deliverables Publications
D3.5 New Methods for Robust Timetabling
Involving Stochasticity
D3.6 Improved Algorithms for Robust and Online
Timetabling and for Timetable Information
Updating
Journals and Chapters in Books
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Conferences
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34
Technical Reports
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WP3 - Effort
Total 3 years 1st plan 1st actual 1st own 2nd plan 2nd actual 2nd own
CTI 15 2.5 1.51 1 5 5.59 2
UniKarl 12 6 6 3 3 3 2
EUR 8 4 4 1 3 3 1
ULA 19 9 11 0 6 8 0
TUB 8 2 1 4 3 3 0
UniBo 9 3 3 0 3 3 0
DEI 10 3.33 4.8 2.3 3.33 4.8 2.4
UPVLC 23 3 3 0 8 8 0
SNCF 9 1.5 1.5 0 3.5 2.38 0
Total 113 34.33 35.81 11.3 37.83 40.77 7.40
3rd year plan 3rd year actual 3rd year own
7.5 8.6 2
3 3 5
1 3 0
4 5.3 0
3 3 0
3 3 0
3.33 5.4 1.9
10 10 0
4 3 0
38.83 44.3 8.9