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 Presentation
WP3 – Participants
• CTI
• UniKarl
• EUR
• ULA
• TUB
• UniBo
• DEI
• UPVLC
• SNCF
Matteo Fischetti
3rd ARRIVAL Review Meeting [Patras, 12 May 2009] – WP3 Presentation
2
Problem Areas
• Robust and on-line timetable design
– Find a period or aperiodic train timetable (& 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
Matteo Fischetti
3rd ARRIVAL Review Meeting [Patras, 12 May 2009] – WP3 Presentation
3
Main Achievements during
the 3rd year
– 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
– Enhancing the performance of MIP solvers by improving the
quality of generated cuts and of heuristics used
Matteo Fischetti
3rd ARRIVAL Review Meeting [Patras, 12 May 2009] – WP3 Presentation
4
Recommendation from 2nd
review & Actions taken
• Effectiveness of new MIP techniques evaluated on railways
instances (as recommended by the referees) and reported
in TR-0237 and D6.3
• No significant deviation from the WP3 workplan occurred
in the third year
Matteo Fischetti
3rd ARRIVAL Review Meeting [Patras, 12 May 2009] – WP3 Presentation
5
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
6
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.:
•
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
uniform allocation of buffer times (e.g. 7% nominal travel time)
3rd ARRIVAL Review Meeting [Patras, 12 May 2009] – WP3 Presentation
7
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
8
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
Matteo Fischetti
3rd ARRIVAL Review Meeting [Patras, 12 May 2009] – WP3 Presentation
9
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
3rd ARRIVAL Review Meeting [Patras, 12 May 2009] – WP3 Presentation
10
Comparison
Maximal Propagated Delay in min
- 49.2%
Time
- 25 % delay over the day by using
Recoverable Robustness
Matteo Fischetti
3rd ARRIVAL Review Meeting [Patras, 12 May 2009] – WP3 Presentation
11
Improved MIP techniques
•
Railways problems are often modelled as difficult MIPs  even finding a
feasible solution may be very challenging
•
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)
•
Successfully evaluated on specific MIP instances from different railways
applications (timetable, crew scheduling, etc.)
Matteo Fischetti
3rd ARRIVAL Review Meeting [Patras, 12 May 2009] – WP3 Presentation
12
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:
11
Conferences:
22
Technical Reports:
34
Matteo Fischetti
3rd ARRIVAL Review Meeting [Patras, 12 May 2009] – WP3 Presentation
13
WP3 - Effort
3rd year
actual
3rd year
own
7.5
8.6
2
2
3
3
5
3
1
1
3
0
6
8
0
4
5.3
0
4
3
3
0
3
3
0
3
0
3
3
0
3
3
0
3.33
4.8
2.3
3.33
4.8
2.4
3.33
5.4
1.9
23
3
3
0
8
8
0
10
10
0
SNCF
9
1.5
1.5
0
3.5
2.38
0
4
3
0
Total
113
34.33
35.81
11.3
37.83
40.77
7.40
38.83
44.3
8.9
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
EUR
8
4
4
1
3
ULA
19
9
11
0
TUB
8
2
1
UniBo
9
3
DEI
10
UPVLC
Matteo Fischetti
3rd year
plan
3rd ARRIVAL Review Meeting [Patras, 12 May 2009] – WP3 Presentation
14