1. Delft University of Technology – Erasmus University Rotterdam University of Twente – Radboud University Nijmegen University of Groningen Context-Aware Logistic Routing and Scheduling Adriaan ter Mors 12 – adriaan@almende.com Jonne Zutt 1 – j.zutt@tudelft.nl Cees Witteveen 1 – c.witteveen@tudelft.nl 1 Algorithmics, Faculty of EEMCS, TU Delft, Netherlands 2 Almende B.V., Rotterdam, Netherlands

2. ICAPS 2007 www.rstrail.nl Context-Aware Routing Given: –set of vehicles (agents) –infrastructure of resources –for each agent, a start and a destination location Find, for each agent, a shortest-time conflict-free path: –limited capacities –head-on conflicts –catching-up conflicts

3. Complexity of Context-Aware Routing Robot motion planning free movement in the x,y-plane avoid collisions with moving obstacles PSPACE-hard for single agent [Reif:1979] Multi-agent, context-aware only movement along lanes avoid collisions with other agents NP-complete Single-agent, context-aware only movement along lanes avoid collisions with other agents Solvable in polynomial time

4. ICAPS 2007 www.rstrail.nl Contents 1.Introduction: context-aware routing 2.Methods to solve context-aware routing 3.Advances in time window graph routing 4.Experimental results 5.Conclusions and future work

5. ICAPS 2007 www.rstrail.nl Methods for context-aware routing Fixed Path Scheduling –fixed path (or k fixed paths) of resources –determine times at which the resources are visited: velocity planning Time window graph routing –determine both which resources to go visit, and the times to visit them

6. ICAPS 2007 www.rstrail.nl SI:[5,6] [4,7] [5,7]D Example: multiple resource visits 0 1 2 3 4 7 810 1 234 5 6 8 6 9 7 J: K:

7. ICAPS 2007 www.rstrail.nl Context-aware routing: naïve approach 1.Associate reservation time windows with nodes in graph 2.Perform typical A* search: –open list of (node, time) pairs –pop element with smallest time value –expand to all neighboring nodes, unless a reservation forbids it [4,8) 5 10 6 11 s d

8. ICAPS 2007 www.rstrail.nl Naïve context-aware routing Problem: nodes may be expanded an exponential number of times 10 11 8 6 [12,14) [0,12) [14,∞) s d a b At most one visit for each free time window

9. ICAPS 2007 www.rstrail.nl Free time window graph Free time window: interval during which number of agents is smaller than capacity of a resource Free time window reachability: adjacency in space and time Time window graph routing: search through graph of free time windows

10. ICAPS 2007 www.rstrail.nl Previous work in TWGR Kim and Tanchoco 1991: Conflict-free shortest-time bidirectional AGV routeing Adapted Dijkstra search algorithm O(n 2 A 4 ) algorithm (n number of infrastructure resources, A number of agents) Inefficiency due to constraint checking in every iteration of the search algorithm: –catching-up conflicts –head-on conflicts

11. ICAPS 2007 www.rstrail.nl Improved time window graph routing A* algorithm that reduces complexity in two ways: 1.Complexity analysis shows limited number of arcs in free time window graph 2.No constraint checking during search: all constraints encoded in free time windows themselves Algorithm complexity: O(F · log(F) + n 2 A) (F number of free time windows, n number of infrastructure resources, A number of agents)

12. ICAPS 2007 www.rstrail.nl Arcs in free time window graph Proposition: # arcs ≤ |F i | + |F j | + 1 riri rjrj time 

13. ICAPS 2007 www.rstrail.nl Preventing head-on conflicts time

14. ICAPS 2007 www.rstrail.nl Preventing catching-up conflicts Determine leading and trailing vehicles Derive entry-time and exit-time intervals entry A 1 entry A 2 exit A 1 exit A 2 entryexit

15. ICAPS 2007 www.rstrail.nl Experimental results Airport taxi routing (Amsterdam Airport Schiphol) Comparison of fixed path scheduling and time window graph routing

16. ICAPS 2007 www.rstrail.nl CPU time comparison FPS TWGR Time [ms] Number of prior reservations

17. ICAPS 2007 www.rstrail.nl Plan cost comparison - setup for k = 0 to 3000 –make plan A with TWGR –make plan B with FPS –reserve plan A: add reservations to infrastructure derive new set of free time windows for k = 0 to 3000 –make plan A with TWGR –make plan B with FPS –reserve plan B: add reservations to infrastructure derive new set of free time windows Plan cost: arrival time at destination resource

18. ICAPS 2007 www.rstrail.nl reserve FPS plans reserve TWGR plans Plan cost comparison plan cost number of prior reservations TWGR provides spread of agents over space and time Using FPS repeatedly leads to overuse of key resources FPS TWGR

19. ICAPS 2007 www.rstrail.nl Conclusions and future work Time window graph routing can be fast Time window graph routing provides a good spread of reservations over space and time … but is it robust? Infrastructure topology and robustness Multi-objective routing

20. ICAPS 2007 www.rstrail.nl Questions?

21. ICAPS 2007 www.rstrail.nl Efficiency of agent-by-agent planning

22. ICAPS 2007 www.rstrail.nl Pickup and delivery transport Pickup and Delivery Transportation Problem: freight has to be transported from a source to a destination location respecting specified time intervals on a transport network with limited capacities and speeds. Limited capacities lead to conflicts. Malfunctioning resources (infrastructure and transport resources).

23. ICAPS 2007 www.rstrail.nl Applications AGV container terminals Taxiing of airplanes at an airport Inland shipping

24. ICAPS 2007 www.rstrail.nl 24 Port of Rotterdam (ECT)

25. ICAPS 2007 www.rstrail.nl Research questions What information is necessary to obtain efficient planning methods? What happens when varying workload, number of agents (scalability), incident level (normal to extreme circumstances, robustness)? What is the relation between performance and characteristics of the transport network?

26. ICAPS 2007 www.rstrail.nl Traplas OperationalPlanner PlanningSystem RoutePlanner Communication OPAuction OPScheduling OPGenerator OPLPAstar OPShortestPath

27. ICAPS 2007 www.rstrail.nl Empirical results Revising priorities

28. ICAPS 2007 www.rstrail.nl Empirical results Revising routes

29. ICAPS 2007 www.rstrail.nl Empirical results Revising routes

30. ICAPS 2007 www.rstrail.nl Hard instances for H&N

31. ICAPS 2007 www.rstrail.nl Transport network

32. ICAPS 2007 www.rstrail.nl Conflicts

33. ICAPS 2007 www.rstrail.nl Interface Traplas – TraplasViz # LOC timestamp id name cap dist spd type w h x y rot LOCATION 0 1 R48 101 15.17 1 0 1.0 1508 652 78261 33584 0 # ARC timestamp id name from to type direction ARC 0 3 EXIT_27_2-EXIT_09 1 6128 0 1 BEGIN 0 1190107322 SETTIMESCALE 0 1 TRNEW 0 0 TR(0) 3 1.0 1299 1 NEWCARG 0 79 O7 4 1.0 4423 DRV 0 55 5809 9296 2355 0 5.04453 CLAIM 5.04453 55 9296 PI 5.04453 DELAY 5.04453 0 UNLOAD 2552.48 132 7008 1036 2552.48 2562.48 RMCARG 2552.48 1036 TRDEL 2552.48 0 SYNC_TIMER 2552.48 3000

34. ICAPS 2007 www.rstrail.nl Example: catching-up conflict A1A1 A1A1 A2A2 A2A2 rjrj rkrk distance time AjAj AkAk AmAm