3rd ARRIVAL Review Meeting [Patras, 12 May 2009] – WP3 Presentation

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

3rd ARRIVAL Review Meeting [Patras, 12 May 2009] – WP3 PresentationMatteo Fischetti 2

WP3 – Participants

• CTI

• UniKarl

• EUR

• ULA

• TUB

• UniBo

• DEI

• UPVLC

• SNCF

3rd ARRIVAL Review Meeting [Patras, 12 May 2009] – WP3 PresentationMatteo Fischetti 3

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

3rd ARRIVAL Review Meeting [Patras, 12 May 2009] – WP3 PresentationMatteo Fischetti 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

3rd ARRIVAL Review Meeting [Patras, 12 May 2009] – WP3 PresentationMatteo Fischetti 5

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

3rd ARRIVAL Review Meeting [Patras, 12 May 2009] – WP3 PresentationMatteo Fischetti 6

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

3rd ARRIVAL Review Meeting [Patras, 12 May 2009] – WP3 PresentationMatteo Fischetti 7

Problems & Corrective Actions

• No significant deviation from the WP3 workplan occurred

in the third year

3rd ARRIVAL Review Meeting [Patras, 12 May 2009] – WP3 Presentation 8

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:

Matteo Fischetti

3rd ARRIVAL Review Meeting [Patras, 12 May 2009] – WP3 Presentation 9

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) => 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)

Matteo Fischetti

3rd ARRIVAL Review Meeting [Patras, 12 May 2009] – WP3 Presentation 10

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

Matteo Fischetti

3rd ARRIVAL Review Meeting [Patras, 12 May 2009] – WP3 Presentation

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

Matteo Fischetti 11

3rd ARRIVAL Review Meeting [Patras, 12 May 2009] – WP3 Presentation

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

Matteo Fischetti 12

Over-conservative!

Over-conservative!

3rd ARRIVAL Review Meeting [Patras, 12 May 2009] – WP3 Presentation

Comparison

Matteo Fischetti 13

- 49.2%

- 25 % delay over the day by using Recoverable Robustness

Time

Maximal Propagated Delay in min

3rd ARRIVAL Review Meeting [Patras, 12 May 2009] – WP3 Presentation

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 14

3rd ARRIVAL Review Meeting [Patras, 12 May 2009] – WP3 Presentation

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 B&C code)

Matteo Fischetti 15

3rd ARRIVAL Review Meeting [Patras, 12 May 2009] – WP3 PresentationMatteo Fischetti 16

D3.6: Improved Algorithms for Robust and Online Timetabling

and for Timetable Information Updating

D3.5: New Methods for Robust Timetabling Involving

Stochasticity

Journals and Chapters in Books:

Technical Reports:

11

22

Deliverables & Publications

Conferences:

34

3rd ARRIVAL Review Meeting [Patras, 12 May 2009] – WP3 PresentationMatteo Fischetti 17

WP3 - Effort

Total3

years

1st

plan1st

actual1st

own2nd 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 yearplan

3rd yearactual

3rd yearown

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