Neema Nassir, Mark Hickman, and Hong Zheng Department of Civil Engineering and Engineering Mechanic...

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Neema Nassir, Mark Hickman, and Hong ZhengDepartment of Civil Engineering and Engineering Mechanic

The University of Arizona, Tucson, AZ

INFORMS 2011 Annual Meeting November 12-16, Charlotte, NC

A Heuristic for Solving the Evacuation Contraflow Problem

atlas

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Contents

Introduction

Evacuation Control Strategies

Contraflow Design, Literature- Mathematical Formulation- Existing Heuristics

Proposing a Heuristic for Contraflow Design- Network Flow Transformation of SD-SODTA- Heuristic- Small Network Application

Conclusions

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Traffic lines Interstate 45 leaving Houston as Hurricane Ike approaches the Texas Gulf Coast. September 11, 2008 in The Woodlands, Texas.

Introduction- Motivation

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Woodlands, TX. Sept. 11, 2008 Contraflow Reconfiguration

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Introduction

ADOT Project SPR-679:

“Platform for Evaluating Emergency Evacuation Strategies – Phase II”

Develop a scalable integrated optimization platform of evacuation strategies in case of a disaster happening.

Propose optimal evacuation strategies for Tucson and Phoenix, AZ.

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Evacuation Strategies

Optimal bus routing to assist carless evacuees

Contraflow design- lane closure

Staged evacuation (scheduling)

Signal control in emergency evacuation

Crossing elimination strategies

Destination choice

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Contents

Introduction

Evacuation Control Strategies

Contraflow Design, Literature- Mathematical Formulation- Existing Heuristics

Proposing a Heuristic for Contraflow Design- Network Flow Transformation of SD-SODTA- Heuristic- Small Network Application

Conclusions

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Mathematical ProgrammingCTM Based System Optimal DTA with Capacity Reversibility

Tuydes and Ziliaskopoulos(2006)

r

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Mathematical ProgrammingSingle Destination System Optimal DTA with Capacity Reversibility

Tuydes and Ziliaskopoulos(2006)

r

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Existing Heuristics for Contraflow Design

Tuydes and Ziliaskopoulos (2006)

Tabu Search Simulation-Based Heuristic. (VISTA for Evanston, IL)

Basic idea: Heuristic is based on an insight into optimality conditions, by studying the dual problem and complementary slackness conditions.

(If two coupled cells (or links) bear approximately the same level of congestion through the whole duration of the analysis, not necessarily at the same time, the capacity is distributed optimally. Otherwise, the system can be managed better by reversing some capacity from a less congested cell (link) to the more congested one.)

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Contents

Introduction

Evacuation Control Strategies

Contraflow Design, Literature- Mathematical Formulation- Existing Heuristics

Proposing a Heuristic for Contraflow Design- Network Flow Transformation of SD-SODTA- Heuristic- Small Network Application

Conclusions

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Number of vehicles exited the network in time interval t

t=1 t=2 t=3

Number of vehicles exited the network from the beginning to t (cumulative)

Zheng and Chiu (2011)

SD-SODTA and Earliest Arrival Flow

t=0 t=1 t=2 t=3

9 vehicles

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t=1 t=2 t=3

Number of vehicles existing in the network at time t

t=0 t=1 t=2 t=3

9 vehicles

Zheng and Chiu (2011)

Number of vehicles exited the network in time interval t

SD-SODTA and Earliest Arrival Flow

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t=1 t=2 t=3

Number of vehicles existing in the network at time t

SODTA = Minimize Red Boxes = Maximize Green Boxes = Earliest Arrival Flow

Zheng and Chiu 2011

Number of vehicles exited the network in time interval t

max Z =

SD-SODTA and Earliest Arrival Flow

t=0 t=1 t=2 t=3

9 vehicles

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Zheng and Chiu, 2011

Network Transformation of Cell-based SD SODTA

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Proposing a Heuristic for SD-SODTA Contraflow Design

The basic idea is to: Relax the capacities of each direction of the links to the total capacity of link,

Find the SO solution in the relaxed network,

Start from the infeasible solution and gradually move towards the feasible region, with least objective degradation.

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Infeasibility in SODTA Solution- Relaxed Network

Feasible

Infeasible

Relax

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Proposing a Heuristic for SD-SODTA Contraflow Design

Steps are:

1- For every link, relax the capacity of each direction to sum of the capacities in both directions,

2- Generate the network transformation, and find EAF in the relaxed network (traffic assignment),

3- Detect the streets which violate original capacities, choose the one with largest differential flow in two directions,

4- Cut back the capacity to the real capacity by closing the lanes with minimal degradation of objective function. Continue until feasibility is reached.

Warm start SODTA

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Small Network Example- Single Lane Links

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Cell-Based NetworkCell-Based Network

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Cell-Based NetworkCell-Based Network

Original Cell Based Network

Number of Cells: 105Number of Connectors: 164

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Cell-Based NetworkCell-Based Network

Relaxed Cell Based Network

Number of Cells: 203Number of Connectors: 430

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1st Scenario

D2=15 at time 0

D5=15 at time 0

D4=15 at time 0

D1=100at time 0

D3=15 at time 0

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Optimal Flow in Relaxed Network1st Scenario

D2=15 at time 0

D5=15 at time 0

D4=15 at time 0

D1=100at time 0

D3=15 at time 0

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Algorithm Solution1st Scenario

D2=15 at time 0

D5=15 at time 0

D4=15 at time 0

D1=100at time 0

D3=15 at time 0

Original Network Optimal Flow = 3083Relaxed Network Optimal Flow = 3083

No Capacity ViolationsFeasible!

No Link Reversals

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2nd Scenario

D2=15 at time 0

D5=200 at time 0

D4=15 at time 0D1=15

at time 0

D3=15 at time 0

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Optimal Flow in Relaxed Network2nd Scenario

D2=15 at time 0

D5=200 at time 0

D4=15 at time 0

D1=15at time 0

D3=15 at time 0

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Algorithm solution2nd Scenario

D2=15 at time 0

D5=200 at time 0

D4=15 at time 0

D1=15at time 0

D3=15 at time 0

Original Network Optimal Flow = 5295Relaxed Network Optimal Flow = 4906

No Capacity ViolationsFeasible!

Two Link Reversals NeededImprovement= 7.3%

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D2=15 at time 0

D5=200

at time 5

D4=15 at time 0

D1=15at time 0

D3=15 at time 0

Optimal Flow in Relaxed Network3rd Scenario

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D2=15 at time 0

D5=200

at time 5

D4=15 at time 0

D1=15at time 0

D3=15 at time 0

Optimal Flow in Relaxed Network3rd Scenario

?

?

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D2=15 at time 0

D5=200

at time 5

D4=15 at time 0

D1=15at time 0

D3=15 at time 0

Algorithm Solution3rd Scenario

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? Relaxed Network ……………..……….obj=5764First iteration:Cut 1920.……………………………….obj=5795Cut 20’19’..…………………………….obj=5800Second Iteration:Cut 2627………………..………………obj=5795Cut 27’26’.………………………………obj=6072Feasible!Cut 1920 and 2627………….….obj=5795

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D2=15 at time 0

D5=200

at time 5

D4=15 at time 0

D1=15at time 0

D3=15 at time 0

Algorithm Solution3rd Scenario

Original Network Optimal Flow = 6224Relaxed Network Optimal Flow = 5764Reconfigured Network Optimal Flow = 5795

Two Links Capacity ViolationsTwo Link Reversals Needed

Improvement= 6.8%

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Conclusions

The relaxed network SODTA :1. Gives an insight to the pattern of evacuation flow 2. Largely confines the feasible set3. Smartly chooses the candidates for reversing

The warm start assignment estimate is used to find the move direction towards feasible set.

The warm start assignment estimate can be possible by utilizing the network flow approach to SODTA.

Comment, suggestions and questions?