Capacity Constrained Routing Algorithms for Evacuation Planning: A Summary of Results

1. Capacity Constrained Routing Algorithms for Evacuation Planning: A Summary of Results Speaker: Chen-Nien Tsai

2. Reference • Qingsong Lu, Betsy George, and Shashi Shekhar, “Capacity Constrained Routing Algorithms for Evacuation Planning: A Summary of Results,” Advances in Spatial and Temporal Databases, Proceeding of 9th International Symposium on Spatial and Temporal Databases (SSTD'05), Angra dos Reis, Brazil, August 22-24, 2005.

3. Outline • Introduction • Problem Formulation • Proposed Approach • Capacity Constrained Route Planner (CCRP) • Performance Evaluation • Summary

4. Introduction (1/4) • Evacuation Planning is critical for numerous applications. • Disaster emergency management • Homeland defense preparation • The goal is to produce evacuation plans that identify routes and schedules to evacuate affected populations to safety.

5. Introduction (2/4) • Traffic assignment-simulation approach • Uses traffic simulation tools. • May take a long time to complete a simulation. • Route-schedule planning approach • Uses network flow and routing algorithms to produce origin-destination routes and schedules. • Many researcher use linear programming method to find the optimal solution.

6. Introduction (3/4) • Linear Programming Method • Can produce optimal solutions for evacuation planning. • It is useful for evacuation scenarios with moderate size networks. • It is not suitable for large network size. • The complexity is

7. Introduction (4/4) • Heuristic routing and scheduling algorithms • Produce sub-optimal evacuation plan. • Reduce computational cost. • It is useful for evacuation scenarios with large size networks. • The authors proposed Capacity Constrained Route Planner • The complexity is

8. Outline • Introduction • Problem Formulation • Proposed Approach • Capacity Constrained Route Planner (CCRP) • Performance Evaluation • Summary

9. Problem Formulation (1/2) • Input: • A transportation network with capacity constraints on nodes and edges, travel time on edges, the total number of evacuees and their initial locations, and locations of evacuation destinations. • Output • An evacuation plan.

10. Problem Formulation (2/2) • Objective: • Minimize the evacuation egress time. • Minimize the computation cost. • Constraint: • Edge travel time preserves FIFO property. • Edge travel time reflects delays at intersections. • Limited amount of computer memory.

11. An Example

12. An Evacuation Plan

13. Outline • Introduction • Problem Formulation • Proposed Approach • Capacity Constrained Route Planner (CCRP) • Performance Evaluation • Summary

14. CCRP • Searches for route R with the earliest destination arrival time. • Computes the actual amount of evacuees that will travel through route R. (affected by the available capacity of route R) • The algorithm continues to iterate until all evacuees reach destination.

15. CCRP

17. S0

18. The Complexity of CCRP • We assume • n: the number of nodes • m: the number of edges • p: the number of evacuees • The complexity of CCRP is

20. The comparison • MRCCP is another heuristic algorithm.

21. Outline • Introduction • Problem Formulation • Proposed Approach • Capacity Constrained Route Planner (CCRP) • Performance Evaluation • Summary

22. Experiment Design

23. We Want to Know... • How does the number of evacuees affect the performance of the algorithms? • How does the source nodes affect the performance of the algorithms? • Are the algorithms scalable to the size of the network?

24. The Effect on the Number of Evacuees (1/3) # of nodes: 5000 # of source nodes: 2000

25. The Effect on the Number of Evacuees (2/3) # of nodes: 5000 # of source nodes: 2000

26. The Effect on the Number of Evacuees (3/3) • CCRP produces high quality solutions with much less run-time than that of NETFLO. • The run-time of CCRP is scalable to the number of evacuees.

27. The Effect on the Number of Source Nodes (1/3) # of nodes: 5000 # of evacuees: 5000

28. The Effect on the Number of Source Nodes (2/3) # of nodes: 5000 # of evacuees: 5000

29. The Effect on the Number of Source Nodes (3/3) • The solution quality of CCRP is not affected by the number of source nodes. • The run-time of CCRP is scalable to the number of source nodes.

30. Are the algorithms scalable (3/3) # of source nodes: 10 # of evacuees: 5000

31. Are the algorithms scalable (1/3) # of source nodes: 10 # of evacuees: 5000

32. Are the algorithms scalable (3/3) • Given a fixed number of evacuees and source nodes, the solution quality of CCRP increase as the network size increases. • The run-time of CCRP is scalable to the size of the network.

33. Outline • Introduction • Problem Formulation • Proposed Approach • Capacity Constrained Route Planner (CCRP) • Performance Evaluation • Summary

34. Summary (1/2) • Linear programming method • Can produce optimal solutions for evacuation planning. • The complexity is too high. • Heuristic algorithms • Produce sub-optimal evacuation plan. • Reduce computational cost.

35. Summary (2/2) • Capacity Constrained Route Planner (CCRP) • Produces high quality solution • Reduces the computational cost