ARRIVAL – WP3

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

2. WP3 – Participants • CTI • UniKarl • EUR • ULA • TUB • UniBo • DEI • UPVLC • SNCF

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

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

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

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

7. Problems & Corrective Actions • No significant deviation from the WP3 workplan occurred in the third year

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: 8 Matteo Fischetti

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) 9 Matteo Fischetti

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 10 Matteo Fischetti

11. Robust Platforming 11 • 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

12. 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!

13. Comparison Maximal Propagated Delay in min - 49.2% Time - 25 % delay over the day by using Recoverable Robustness

14. 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) 14 Matteo Fischetti

15. 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) 15 Matteo Fischetti

16. 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 34 Technical Reports:

17. WP3 - Effort