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

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

Speaker: Chen-Nien TsaiSpeaker: Chen-Nien Tsai

2006/10/30 2

ReferenceReference

►Qingsong Lu, Betsy George, and Shashi ShQingsong Lu, Betsy George, and Shashi Shekhar, “ekhar, “Capacity Constrained Routing Algorithms Capacity Constrained Routing Algorithms for Evacuation Planning: A Summary of Refor Evacuation Planning: A Summary of Resultssults,” Advances in Spatial and Temporal Dat,” Advances in Spatial and Temporal Databases, Proceeding of 9th International Syabases, Proceeding of 9th International Symposium on Spatial and Temporal Databmposium on Spatial and Temporal Databases (SSTD'05), Angra dos Reis, Brazil, Augases (SSTD'05), Angra dos Reis, Brazil, August 22-24, 2005. ust 22-24, 2005.

2006/10/30 3

OutlineOutline

► IntroductionIntroduction►Problem FormulationProblem Formulation►Proposed ApproachProposed Approach

Capacity Constrained Route Planner Capacity Constrained Route Planner (CCRP)(CCRP)

►Performance EvaluationPerformance Evaluation►SummarySummary

2006/10/30 4

Introduction (1/4)Introduction (1/4)

►Evacuation Planning is critical for Evacuation Planning is critical for numerous applications.numerous applications. Disaster emergency managementDisaster emergency management Homeland defense preparationHomeland defense preparation

►The goal is to produce evacuation plans The goal is to produce evacuation plans that identify routes and schedules to that identify routes and schedules to evacuate affected populations to safety.evacuate affected populations to safety.

2006/10/30 5


►Traffic assignment-simulation approachTraffic assignment-simulation approach Uses traffic simulation tools.Uses traffic simulation tools. May take a long time to complete a simulation.May take a long time to complete a simulation.

►Route-schedule planning approachRoute-schedule planning approach Uses network flow and routing algorithms to Uses network flow and routing algorithms to

produce origin-destination routes and produce origin-destination routes and schedules.schedules.

Many researcher use linear programming Many researcher use linear programming method to find the optimal solution.method to find the optimal solution.

2006/10/30 6


►Linear Programming MethodLinear Programming Method Can produce optimal solutions for Can produce optimal solutions for

evacuation planning.evacuation planning. It is useful for evacuation scenarios with It is useful for evacuation scenarios with

moderate size networks.moderate size networks. It is not suitable for large network size.It is not suitable for large network size.

►The complexity is The complexity is 6( )O n

2006/10/30 7

Introduction (4/4)Introduction (4/4)►Heuristic routing and scheduling Heuristic routing and scheduling

algorithmsalgorithms Produce sub-optimal evacuation plan.Produce sub-optimal evacuation plan. Reduce computational cost.Reduce computational cost. It is useful for evacuation scenarios with It is useful for evacuation scenarios with

large size networks.large size networks. The authors proposed The authors proposed Capacity Capacity

Constrained Route PlannerConstrained Route Planner► The complexity isThe complexity is

( log )O pn n

2006/10/30 8

OutlineOutline




2006/10/30 9

Problem Formulation (1/2)Problem Formulation (1/2)

► Input:Input: A A transportation networktransportation network with capacity with capacity

constraints on constraints on nodesnodes and and edgesedges, , travel travel timetime on edges, the total number of on edges, the total number of evacueesevacuees and their initial locations, and and their initial locations, and locations of locations of evacuation destinationsevacuation destinations..

►OutputOutput An evacuation plan.An evacuation plan.

2006/10/30 10

Problem Formulation (2/2)Problem Formulation (2/2)

►Objective:Objective: Minimize the evacuation egress time.Minimize the evacuation egress time. Minimize the computation cost.Minimize the computation cost.

►Constraint:Constraint: Edge travel time preserves FIFO property.Edge travel time preserves FIFO property. Edge travel time reflects delays at Edge travel time reflects delays at

intersections.intersections. Limited amount of computer memory.Limited amount of computer memory.

2006/10/30 11

An ExampleAn Example

2006/10/30 12

An Evacuation PlanAn Evacuation Plan

2006/10/30 13

OutlineOutline




2006/10/30 14

CCRPCCRP

1.1. Searches for route R with the earliest Searches for route R with the earliest destination arrival time.destination arrival time.

2.2. Computes the actual amount of Computes the actual amount of evacuees that will travel through evacuees that will travel through route R. (affected by the available route R. (affected by the available capacity of route R)capacity of route R)

3.3. The algorithm continues to iterate The algorithm continues to iterate until all evacuees reach destination.until all evacuees reach destination.

2006/10/30 15

CCRPCCRP

2006/10/30 16

2006/10/30 17

S0

2006/10/30 18

The Complexity of CCRPThe Complexity of CCRP

►We assumeWe assume nn: the number of nodes: the number of nodes mm: the number of edges: the number of edges pp: the number of evacuees: the number of evacuees

►The complexity of CCRP is The complexity of CCRP is ( log )O pn n

2006/10/30 19

( )O p

( )O n

( log )O n n

2006/10/30 20

The comparisonThe comparison

►MRCCP is another heuristic algorithm.MRCCP is another heuristic algorithm.

2006/10/30 21

OutlineOutline




2006/10/30 22

Experiment DesignExperiment Design

2006/10/30 23

We Want to Know...We Want to Know...

►How does the number of evacuees affect How does the number of evacuees affect the performance of the algorithms?the performance of the algorithms?

►How does the source nodes affect the How does the source nodes affect the performance of the algorithms?performance of the algorithms?

►Are the algorithms scalable to the size of Are the algorithms scalable to the size of the network?the network?

2006/10/30 24

The Effect on the The Effect on the Number of Evacuees (1/3) Number of Evacuees (1/3)

# of nodes: 5000

# of source nodes: 2000

2006/10/30 25


# of nodes: 5000


2006/10/30 26


►CCRP produces high quality solutions CCRP produces high quality solutions with much less run-time than that of with much less run-time than that of NETFLO.NETFLO.

►The run-time of CCRP is scalable to the The run-time of CCRP is scalable to the number of evacuees.number of evacuees.

2006/10/30 27

The Effect on the The Effect on the Number of Source Nodes (1/3)Number of Source Nodes (1/3)

# of nodes: 5000

# of evacuees: 5000

2006/10/30 28


# of nodes: 5000

# of evacuees: 5000

2006/10/30 29


►The solution quality of CCRP is not The solution quality of CCRP is not affected by the number of source affected by the number of source nodes.nodes.

►The run-time of CCRP is scalable to the The run-time of CCRP is scalable to the number of source nodes.number of source nodes.

2006/10/30 30

Are the algorithms scalable Are the algorithms scalable (3/3)(3/3)


# of evacuees: 5000

2006/10/30 31

Are the algorithms scalable Are the algorithms scalable (1/3)(1/3)# of source nodes: 10

# of evacuees: 5000

2006/10/30 32

Are the algorithms scalable Are the algorithms scalable (3/3)(3/3)

►Given a fixed number of evacuees and Given a fixed number of evacuees and source nodes, the solution quality of source nodes, the solution quality of CCRP increase as the network size CCRP increase as the network size increases.increases.

►The run-time of CCRP is scalable to the The run-time of CCRP is scalable to the size of the network.size of the network.

2006/10/30 33

OutlineOutline




2006/10/30 34

Summary (1/2)Summary (1/2)

►Linear programming methodLinear programming method Can produce optimal solutions for Can produce optimal solutions for

evacuation planning.evacuation planning. The complexity is too high.The complexity is too high.

►Heuristic algorithmsHeuristic algorithms Produce sub-optimal evacuation plan.Produce sub-optimal evacuation plan. Reduce computational cost.Reduce computational cost.

2006/10/30 35

Summary (2/2)Summary (2/2)

►Capacity Constrained Route Planner (CCRCapacity Constrained Route Planner (CCRP)P) Produces high quality solutionProduces high quality solution Reduces the computational costReduces the computational cost

Documents

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