Capacity Constrained Routing Algorithms for Evacuation Planning A

Capacity Constrained Routing Algorithms for Evacuation Planning: A Summary of Results Speaker: Chen-Nien Tsai 2006/10/30

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 9 th International Symposium on Spatial and Temporal Databases (SSTD'05), Angra dos Reis, Brazil, August 22 -24, 2005. 2006/10/30 2

Outline ► Introduction ► Problem Formulation ► Proposed Approach § Capacity Constrained Route Planner (CCRP) ► Performance Evaluation ► Summary 2006/10/30 3

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. 2006/10/30 4

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. 2006/10/30 5

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 2006/10/30 complexity is 6

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 ► 2006/10/30 The complexity is 7

Outline ► Introduction ► Problem Formulation ► Proposed Approach § Capacity Constrained Route Planner (CCRP) ► Performance Evaluation ► Summary 2006/10/30 8

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. 2006/10/30 9

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. 2006/10/30 10

An Example 2006/10/30 11

An Evacuation Plan 2006/10/30 12

Outline ► Introduction ► Problem Formulation ► Proposed Approach § Capacity Constrained Route Planner (CCRP) ► Performance Evaluation ► Summary 2006/10/30 13

CCRP Searches for route R with the earliest destination arrival time. 2. Computes the actual amount of evacuees that will travel through route R. (affected by the available capacity of route R) 3. The algorithm continues to iterate until all evacuees reach destination. 1. 2006/10/30 14

CCRP 2006/10/30 15

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S 0 2006/10/30 17

The Complexity of CCRP ► We assume § n: the number of nodes § m: the number of edges § p: the number of evacuees ► The 2006/10/30 complexity of CCRP is 18

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The comparison ► MRCCP 2006/10/30 is another heuristic algorithm. 20

Outline ► Introduction ► Problem Formulation ► Proposed Approach § Capacity Constrained Route Planner (CCRP) ► Performance Evaluation ► Summary 2006/10/30 21

Experiment Design 2006/10/30 22

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? 2006/10/30 23

The Effect on the Number of Evacuees (1/3) # of nodes: 5000 # of source nodes: 2000 2006/10/30 24

The Effect on the Number of Evacuees (2/3) # of nodes: 5000 # of source nodes: 2000 2006/10/30 25

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. 2006/10/30 26

The Effect on the Number of Source Nodes (1/3) # of nodes: 5000 # of evacuees: 5000 2006/10/30 27

The Effect on the Number of Source Nodes (2/3) # of nodes: 5000 # of evacuees: 5000 2006/10/30 28

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. 2006/10/30 29

Are the algorithms scalable (3/3) # of source nodes: 10 # of evacuees: 5000 2006/10/30 30

Are the algorithms scalable (1/3) # of source nodes: 10 # of evacuees: 5000 2006/10/30 31

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. 2006/10/30 32

Outline ► Introduction ► Problem Formulation ► Proposed Approach § Capacity Constrained Route Planner (CCRP) ► Performance Evaluation ► Summary 2006/10/30 33

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. 2006/10/30 34

Summary (2/2) ► Capacity Constrained Route Planner (CCRP) § Produces high quality solution § Reduces the computational cost 2006/10/30 35