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atlas. INFORMS 2011 Annual Meeting  November 12-16, Charlotte, NC A Heuristic for Solving the Evacuation Contraflow Problem. Neema Nassir, Mark Hickman, and Hong Zheng Department of Civil Engineering and Engineering Mechanic The University of Arizona, Tucson, AZ. Contents.

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Neema nassir mark hickman and hong zheng

atlas

INFORMS 2011 Annual Meeting 

November 12-16, Charlotte, NC

A Heuristic for Solving the Evacuation Contraflow Problem

Neema Nassir, Mark Hickman, and Hong Zheng

Department of Civil Engineering and Engineering Mechanic

The University of Arizona, Tucson, AZ


Neema nassir mark hickman and hong zheng

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


Neema nassir mark hickman and hong zheng

Introduction- Motivation

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


Neema nassir mark hickman and hong zheng

 Woodlands, TX.  Sept. 11, 2008

Contraflow Reconfiguration


Neema nassir mark hickman and hong zheng

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.


  • Neema nassir mark hickman and hong zheng

    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


    Neema nassir mark hickman and hong zheng

    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


    Neema nassir mark hickman and hong zheng

    Mathematical Programming

    CTM Based System Optimal DTA with Capacity Reversibility

    r

    Tuydes and Ziliaskopoulos

    (2006)


    Neema nassir mark hickman and hong zheng

    Mathematical Programming

    Single Destination System Optimal DTA with Capacity Reversibility

    r

    Tuydes and Ziliaskopoulos

    (2006)


    Neema nassir mark hickman and hong zheng

    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.)


    Neema nassir mark hickman and hong zheng

    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


    Neema nassir mark hickman and hong zheng

    SD-SODTA and Earliest Arrival Flow

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

    Number of vehicles exited the network in time interval t

    9 vehicles

    t=1 t=2 t=3

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

    Zheng and Chiu (2011)


    Neema nassir mark hickman and hong zheng

    SD-SODTA and Earliest Arrival Flow

    Number of vehicles existing in the network at time t

    Number of vehicles exited the network in time interval t

    9 vehicles

    t=1 t=2 t=3

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

    Zheng and Chiu (2011)


    Neema nassir mark hickman and hong zheng

    SD-SODTA and Earliest Arrival Flow

    max Z =

    Number of vehicles existing in the network at time t

    Number of vehicles exited the network in time interval t

    9 vehicles

    t=1 t=2 t=3

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

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

    Zheng and Chiu 2011


    Neema nassir mark hickman and hong zheng

    Network Transformation of

    Cell-based SD SODTA

    Zheng and Chiu, 2011


    Neema nassir mark hickman and hong zheng

    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.


    Neema nassir mark hickman and hong zheng

    Infeasibility in SODTA Solution- Relaxed Network

    Feasible

    Relax

    Infeasible


    Neema nassir mark hickman and hong zheng

    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


    Neema nassir mark hickman and hong zheng

    Small Network Example- Single Lane Links


    Neema nassir mark hickman and hong zheng

    Cell-Based Network

    Cell-Based Network


    Neema nassir mark hickman and hong zheng

    Cell-Based Network

    Cell-Based Network

    Original Cell Based Network

    Number of Cells: 105

    Number of Connectors: 164


    Neema nassir mark hickman and hong zheng

    Cell-Based Network

    Cell-Based Network

    Relaxed Cell Based Network

    Number of Cells: 203

    Number of Connectors: 430


    Neema nassir mark hickman and hong zheng

    1st Scenario

    D2=15

    at time 0

    D4=15

    at time 0

    D1=100

    at time 0

    D5=15

    at time 0

    D3=15

    at time 0


    Neema nassir mark hickman and hong zheng

    Optimal Flow in Relaxed Network

    1st Scenario

    D2=15

    at time 0

    D4=15

    at time 0

    D1=100

    at time 0

    D5=15

    at time 0

    D3=15

    at time 0


    Neema nassir mark hickman and hong zheng

    Algorithm Solution

    1st Scenario

    D2=15

    at time 0

    Original Network Optimal Flow = 3083

    Relaxed Network Optimal Flow = 3083

    No Capacity Violations

    Feasible!

    No Link Reversals

    D4=15

    at time 0

    D1=100

    at time 0

    D5=15

    at time 0

    D3=15

    at time 0


    Neema nassir mark hickman and hong zheng

    2nd Scenario

    D2=15

    at time 0

    D4=15

    at time 0

    D1=15

    at time 0

    D5=200

    at time 0

    D3=15

    at time 0


    Neema nassir mark hickman and hong zheng

    Optimal Flow in Relaxed Network

    2nd Scenario

    D2=15

    at time 0

    D4=15

    at time 0

    D1=15

    at time 0

    D5=200

    at time 0

    D3=15

    at time 0


    Neema nassir mark hickman and hong zheng

    Algorithm solution

    2nd Scenario

    D2=15

    at time 0

    Original Network Optimal Flow = 5295

    Relaxed Network Optimal Flow = 4906

    No Capacity Violations

    Feasible!

    Two Link Reversals Needed

    Improvement= 7.3%

    D4=15

    at time 0

    D1=15

    at time 0

    D5=200

    at time 0

    D3=15

    at time 0


    Neema nassir mark hickman and hong zheng

    Optimal Flow in Relaxed Network

    3rd Scenario

    D2=15

    at time 0

    D4=15

    at time 0

    D1=15

    at time 0

    D5=200

    at time 5

    D3=15

    at time 0


    Neema nassir mark hickman and hong zheng

    Optimal Flow in Relaxed Network

    3rd Scenario

    D2=15

    at time 0

    D4=15

    at time 0

    D1=15

    at time 0

    ?

    D5=200

    at time 5

    ?

    D3=15

    at time 0


    Neema nassir mark hickman and hong zheng

    Algorithm Solution

    3rd Scenario

    D2=15

    at time 0

    D4=15

    at time 0

    D1=15

    at time 0

    ?

    Relaxed Network ……………..……….obj=5764

    First iteration:

    Cut 1920.……………………………….obj=5795

    Cut 20’19’..…………………………….obj=5800

    Second Iteration:

    Cut 2627………………..………………obj=5795

    Cut 27’26’.………………………………obj=6072

    Feasible!

    Cut 1920 and 2627………….….obj=5795 

    D5=200

    at time 5

    ?

    D3=15

    at time 0


    Neema nassir mark hickman and hong zheng

    Algorithm Solution

    3rd Scenario

    D2=15

    at time 0

    D4=15

    at time 0

    D1=15

    at time 0

    Original Network Optimal Flow = 6224

    Relaxed Network Optimal Flow = 5764

    Reconfigured Network Optimal Flow = 5795

    Two Links Capacity Violations

    Two Link Reversals Needed

    Improvement= 6.8%

    D5=200

    at time 5

    D3=15

    at time 0


    Neema nassir mark hickman and hong zheng

    Conclusions

    • The relaxed network SODTA :

    • Gives an insight to the pattern of evacuation flow

    • Largely confines the feasible set

    • 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

    Comment, suggestions and questions?


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