1sangho kim, university of minnesota contraflow transportation network reconfiguration for...

1 Sangho Kim, University of Minnesota

Contraflow Transportation Network Reconfigurationfor Evacuation Route Planning

Sangho Kim

Advisor: Shashi ShekharDepartment of Computer Science

University of [email protected]


Overview

• Motivation & Problem Definition• Related Work & Contribution• Proposed Approaches• Evaluation• Conclusion & Future Work


MotivationMotivation & Problem DefinitionRelated Work & ContributionProposed HeuristicsEvaluationConclusion & Future Work

Contraflow increases capacity by reversing the direction of roads• Hurricane evacuation• Terrorist attack evacuation• Major sporting events• Highway reconstruction • Reversible laneWashington DC, I-95 reversible roadway

for peak-period HOV-3 vehicles(source: roadtothefuture.com)


Motivation (cont.)Motivation & Problem DefinitionRelated Work & ContributionProposed ApproachesEvaluationConclusion & Future Work

vs

Observations during Rita Evacuation [2]

• "High-occupancy-vehicle lanes went unused, as did many inbound lanes of highways, because authorities inexplicably waited until late Thursday to open some up.“• "As congestion worsened state officials announced that contraflow lanes would be established on I-45, 290 and I-10. But by mid-afternoon, with traffic immobile on 290, the plan was dropped, stranding many and prompting other to reverse course. 'We need that route so resources can still get into the city,' explained an agency spokeswoman."

[1] B. Wolshon et al., National Review of Hurricane Evacuation Plans and Policies, 2002[2] T. Litman, Lessons from Katrina and Rita, 2006

Idea is Simple• Potential remedy to solve congestions during evacuations• 11/18 coastal states threatened by hurricanes consider it [1].

Challenging for Large Network• Currently, handcrafted from empirical or engineering guess• Computerized contraflow design needed for - Optimized contraflow network configuration - Accurate estimation of evacuation time

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Motivation (cont.)Motivation & Problem DefinitionRelated Work & ContributionProposed HeuristicsEvaluationConclusion & Future Work

• Why contraflow problem is challenging? (with results from brute-force enumeration experiment)

– Small network with 17 edges.– Two types of flips allowed (↓↓ or ↑↑)– Total # of possible configurations: 217 = 131,072– Feasible configurations: 89,032– # of configurations with min evacuation time: 346 (0.26%)– If three types are allowed (↓↓, ↓↑ or ↑↑), 317 > 100 million.


Problem Definition

• Given:a. Transportation network, directed graph G(V, E)b. Each vertex has initial occupancy and capacityc. Each directed edge has capacity, travel time and an initial directiond. Source and destination vertices

• Find:Contraflow network configuration (i.e., desired direction for each edge)

• Objective:Minimize evacuation time

• Constraints:a. Travel time and capacity are constantb. Edge direction can be flipped to allow contraflow

c. Edge is the smallest unit of contraflow

Motivation & Problem DefinitionRelated Work & ContributionProposed ApproachesEvaluationConclusion & Future Work


Simple Contraflow ExampleMotivation & Problem DefinitionRelated Work & ContributionProposed ApproachesEvaluationConclusion & Future Work

A B

D

E(1,2)(1,2)

(1,4)

(1,2)

(1,3)(1,2)

(4,1)(4,1)

{40,40} {0,10}

{0,∞}

C(1,3)

(1,3)

{0,10}

(travel time, edge capacity)

{initial occupancy, node capacity}

{20,20}

Evacuation Time: 22

A B

D

E(1,4)

(1,5)

(1,5)

(4,2)

{40,40} {0,10}

{0,∞}

C

(1,7)

{0,10}{20,20}

Evacuation Time: 11

A B

D

E(1,4)

(1,5)

(1,5)

(4,2)

{40,40} {0,10}

{0,∞}

C

(1,7)

{0,10}{20,20}Evacuation Time: 14


Overview



Related Works

• G. Hamza-Lup & K. A. Hua, “Enhancing intelligent transportation systems to improve and support homeland security”, IEEE ITS, 2004Summary: Breadth-First graph traversal, Multicast routing problemLimitations: Single source model, Does not consider capacity of edges

• H. Tuydes & A. Ziliaskopoulos. “Network re-design to optimize evacuation contraflow” presented at 83rd TRB, 2004. / “Tabu-based heuristic for optimization of network evacuation contraflow”, presented at 85rd TRB, 2006Summary: Relies on mathematical programming or Tabu-based searchLimitations: Mesoscopic network model Not scalable,

Search-based heuristic Not scalable

• G. Theodoulou and B. Wolshon. “Alternative methods to increase the effectiveness of freeway contrafloow evacuation”, JTRB, 2004Summary: CORSIM microscopic contraflow simulation over New Orleans Limitations: Labor intensive network coding Not flexible to generate

various scenarios, hard to compare alternative parameters



Our ContributionMotivation & Problem DefinitionRelated Work & ContributionProposed ApproachesEvaluationConclusion & Future Work

• Present the computational structure of the contraflow problem.– Small or large problems are easily handled.– Medium size problem is computationally challenging, needs heuristics.

• Explore 3 alternative methods according to the structure– Small Problem: Integer Programming (IP): Optimal contraflow network– Medium Problem: Greedy

• Scalable for large network• High quality solution• Faster than IP

– Large Problem: Min-cut Max-flow, suitable for infinite # of evacuees• Evaluations by analytical and experimental methods

– Using bigger scenarios than previous works. (i.e., 10 times larger)


Overview

• Motivation & Problem Definition• Related Work & Contribution• Proposed Approaches

– Proposed Approaches– Design Decision

• Evaluation• Conclusion & Future Work


Proposed Approach 1

Integer Programming


• Integer Programming (IP)Integer programming uses a model similar to linear programming in that the objective function and constraint functions are linear. In integer programming, however, some or all the variables are required to be integer.

• IP Formulation of Contraflow Problem

Variables: • = set of nodes• = set of source and sink nodes• = set of edges• = initial occupancy in node i• = vertex capacity of node i• = edge capacity of edge (i,j)• = travel time of edge (i,j)• = number of occupancy in node i at time t• = 1 iff there is flow on any edge at interval (t-1,t]• = predetermined upper-bound of evacuation time• = 1 iff edge (i,j) is used for the contraflow

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Proposed Approach 3

Greedy• Congestion Index

– CongestionIndex(e) = FlowHistory(e) / (Capacity(e) x EvacuationTime)• Degree of Contraflow (DoC)

– DoC(Greconfigured) = Number of Flipped Edges / Total Number of Edges

• Idea Behind Greedy Algorithm– Edges having more congestion history on original configuration are more

influential in the decision of edge flips.

Algorithm Greedy(Goriginal, Doc)1. run route planner to produce FlowHistory and Evac.Time on Gorignal; 2. for all edge e in Gorignal, CongestionIndex(e) = FlowHistory(e) / (Capacity(e) x Eva.Time); 3. sort edges by CongestionIndex(e) in descending order;4. Greonfigured = Gorignal; 5. for each (i;j) in the first DoC% edges in the sorted edge set, Greconfigured.flip((j;i));6. return Greonfigured;


A B

D

E34%39%

29%

59%

95%0%

0%82%

C14%

89%


Sorted(DoC == 60%)

A B

D

E

CFinal Configuration

A B

D

E(1,2)(1,2)

(1,3)

(1,2)

(1,2)(1,2)

(4,1)(4,1)

{40,40} {0,10}

{0,∞}

C(1,2)

(1,3)

{0,10}{20,20}Flow History &

Evac. Time (22) fromRoute Planner

Proposed Approach 3

Greedy Example

(travel time, edge capacity)

Edge CI (%)

B-EA-BD-EC-DD-BB-DB-AD-C E-BE-D

958982593934291400

Congestion Index %

A B

D

E1517

19

26

420

018

C6

59



Proposed Approach 4

Min-cut Max-flow• Min-Cut Max-Flow Theorem (Ford-Fulkerson, 1956)

– The value of the max-flow is equal to the value of the min-cut.– Max-flow goes through the Min-cut ( = bottleneck or choke-capacity)

• Suitable for infinite overload degree• Travel time and demand are not included• Idea Behind Min-cut Max-flow Algorithm

– Consider min-cut as a bottleneck in a given network.– Increase the bottleneck capacity by contraflow

Algorithm Min-cut_Max-flow(G)1. while (max_flownew > max_flowold)2. find min-cut of G;3. flip edges across min-cut toward destination;4. max_flowold = max_flownew;5 max_flownew = max_flow(G);6. return G;



Proposed Approach 4

Min-cut Max-flow Example

Final Configuration

A B

D

E(2)(2)

(4)

(2)

(3)(2)

(1)(1)

C(3)

(3) (edge capacity)

A B

D

E(2)(2)

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C(3)

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A B

D

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Max Flow = 4

Max Flow = 5

Max Flow = 7


Design Decision 1

Overload Degree & Dominance Zone

Overload Degree = # of Evacuees / Bottleneck Capacity w/o Contraflow


0 1 Small Large Infinite

No contraflow

needed

Integer Programming

Greedy Min-cut Max-flow

Overload Degree No Overload

Small Large Infinite

Use of Route Planner

Iterative One-time None

ResultQuality

Optimal No ContraflowNeeded

Integer Programming

Heuristic Greedy Greedy Min-cut Max-flow

S0 V2

V1

V3

V5

V4

V6

V8

V7

V9

V11

V10

V12

T13

1010

99

99 9 9

8 8

99

44

882

255

66

11

88

1010

99

22

77

11

11

101066

6

8

10

6

12 12

4 10

88

121211

Bottleneck Capacity w/o Contraflow = 22


Design Decision 2

Choice of Route Planner


• The role of route planner in contraflow system– Evaluates reconfigured network by providing evacuation egress time– Generates flow history to measure edge utility

• Optimal route planner– How it works?

• Convert given network into time expanded graph (/w upper bound)• Apply minimum-cost flow solver (e.g., NETFLO, RELAX, RNET, CS)• Post-process flow history to get evacuation egress time

– Pros: optimal evacuation time– Cons: based on Linear Programming long runtime, prior upper bound guess

• Heuristic route planner (CCRP [2])– How it works?

• Divide demand into multiple groups according to the available capacity• Assign routes by earliest destination arrival time

– Pros: scalable to network size, less memory– Cons: not optimal

[2] Q. Lu, B. George, and S. Shekhar, Capacity Constrained Routing Algorithms for Evacuation Planning: A Summary of Results, SSTD 2005


Design Decision 3

Domain Knowledge


• Use of Domain Knowledge

• Edge Granularity– Large: e.g., interstate highway level

• Pros: appropriate for large scale evacuation, fast runtime• Cons: requires aggregated demand node, ignores alternative routes

– Small: e.g., local street level• Pros: appropriate for small network including pedestrian evacuation• Cons: slow runtime due to the large # of edges

• Choice of Edge Cost– Travel time: no pre-processing required, does no use edge utility– Flow: represents edge utility, but high capacitated edges have priority– Congestion: tackles the core problem of evacuation

Capacity Travel time # of Evacuees Congestion

Greedy √ √ √ √

IP √ √ √

Min-cut Max-flow √


Overview

• Motivation & Problem Definition• Related Work & Contribution• Proposed Approaches• Evaluation

– Analytical Evaluation– Experimental Evaluation

• Conclusion & Future Work



– n vertices and m edges in original network; C = max edge weight– T: time horizon in GT; p: occupancy; T ≈ p

• Optimal Route Planner: Relax– Bertsekas: there is no known polynomial complexity bound for relaxation method.

• Optimal Route Planner: CS (Cost Scaling)– Combine Goldberg’s timebound with GREEDY: O(n3p3log(npC))

• Heuristic Route Planner: CCRP– O(p (m + 2Cn))

GREEDY w/ CCRP is faster than GREEDY w/ CS

Analytical Evaluation

Choice of Route Planner



– n vertices and m edges in original network; C = max edge weight– T: time horizon in GT; p: occupancy; T ≈ p

• The MIN-CUT is faster than GREEDY w/ CCRPif p > 9nlog3n / (3 + 2C)n

Analytical Evaluation

GREEDY vs. MIN-CUT


Experimental Evaluation

Experiment Design



• Setup: C++ / PIII 650MHz WS / 2Gb Memory / Linux

• Nuclear power plant - Location: Monticello, MN- # of evacuees: 42,000- 47 vertices + 148 edges- Evac. Time: 4hr 32min(272min)

- Edge granularity: high with Interstate highway and arterials

2

1

4

3

6

9

14

5

10

13

7 11

12

18

23

24

19

25

16 21

20

22

26

27

46 28

29

30

31

38

39

45

32

34 4140

4233 35

36 43

4437

8

17

15

47



Exp. Setup and Dataset 1




Dataset 2

Network Generator Software

• Network generator software canspecify user defined evacuationscenarios with variable evacuation zone

• Road data: – TP+, Mn/DOT basemap

• Demographic data:– Census 2000, TP+ O/D data

• Edge granularity: – low with local roads

SelectedScenarios

ZoneSize(mile)

# ofOccupancy(Demand)

# of Nodes

# ofEdges

OverloadDegree

Minneapolis CBD .5 117,643 111 287 1131 148,007 277 674 119

2 269,635 562 1443 112

St. Paul CBD .5 53,938 153 369 671 84,678 247 608 79

2 139,994 402 1033 86

Mall of America .5 8,878 32 55 110

1 27,406 84 159 103

2 43,689 170 381 52




CPLEX for IP Approach• Commercial mathematical programming optimizer

– solves Integer programming and very large Linear programming problems and has recently added Quadratic programming [4].

– designed to solve large, difficult problems where other linear programming solvers fail or are unacceptably slow.

– exceptionally fast and robust, providing exceptional reliability even for poorly scaled or numerically difficult problems.

– A sophisticated preprocessor is included to reduce the size of LP models.– provided with parallel version to achieve high performance

[4] en.wikipedia.org




Monticello, Overload Degree• Linear between evac. time and overload

degree• Greedy /w optimal route planner, Relax,

shows inferior scalability to greedy /w CCRP or min-cut max-flow.

• Runtime of min-cut max-flow is not affected by overload degree




Monticello Results

• Due to the manageable size of network and overload degree, we could perform experiments with GREEDY and IP.

• 14 min gap between GREEDY and IP• About 40% decrease in evacuation time

GREEDY/w RELAX

IP-CPLEX

10 sec 450 sec

Runtime




Monticello Result /w GREEDY

• Significant evac. time drop within 10% of DoC 10% out of entire edges can determine reconfigured n/w

• Heuristic route planner, CCRP, shows comparable results with optimal route planner, RelaxIV

http://images.google.com/imgres?imgurl=http://www.rubnitz.com/images/magnifier.jpg&imgrefurl=http://www.rubnitz.com/display.cfm%3Fpid%3Dproducts&h=225&w=269&sz=22&tbnid=mPpOB-67053o2M:&tbnh=90&tbnw=108&hl=en&start=10&prev=/images%3Fq%3Dmagnifier%26svnum%3D10%26hl%3Den%26lr%3D




Monticello Reconfigured N/W

Reconfigured Contraflow N/W with 10% Flips




GREEDY Result /w Metro DataMinneapolis CBD

St. Paul CBD




Statistics of GREEDY Results

IP GREEDY /w RELAX

GREEDY/w CCRP

Monticello 43% 38% 36%

Minneapolis CBD 51% 51%

St. Paul CBD 42% 42%

Mall of America 49% 50%

Average 45% 45%

Evacuation Time Reduction by Contraflow

Mall of America




Scalability Test /w Metro Data

• Results between # of nodes and runtime• Relax, CS and CCRP shows polynomial

increase in runtime with GREEDY• CCRP shows superior performance


Overview



Conclusion

• Contraflow is a challenging problem having combinatorial search space.

• We proposed three different approaches, i.e., integer programming, greedy and min-cut max-flow, according to the overload degree.

• Integer Programming is able to produce optimal contraflow network.• Greedy

– Suitable for large overload degree / large network.– Does not use route planner iteratively.– Becomes scalable with fast heuristic route planner (CCRP).

• Min-cut Max-flow is the fastest heuristic using limited domain knowledge. Suitable for infinite overload degree.



Future Work

• Dealing with dynamic situation changes during evacuation– Some locations are too congested– The path of hurricane changes

• Inbound traffic management for emergency vehicles• Partial lane reversal• Capacity varying edge model• More analytical evaluations• More extensive experiments

– More min-cut max-flow experiments– Effects of edge granularity



Q & A

?



Proposed Approach 2

Simulated Annealing

evac

tim

e

Global minPlateau Local min

network configurations

Procedure SimulatedAnnealingrepeat repeat NewS := perturb(S); if (h(NewS) < h(S)) or (random < e(h(S)-h(NewS))/T) then accept else do not accept until inner loop has been repeated iterations times; T := α * T; iterations := β * iterationsuntil out of time

5

10

15

20

25 evacuation time• Initial State: Original configuration w/o flips.

• Perturbation: ↓↓, ↓↑ or ↑↑• Objective f’n: Evacuation time• Cooling schedule & termination

condition are parameters.• Order of flippings is random.

Simulated Annealing



Proposed Approach 4

Min-cut Max-flow Example

S0 V2

V1

V3

V5

V4

V6

V8

V7

V9

V11

V10

V12

T13

1010

99

99 9 9

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44

882

255

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10106

6

334

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2 25

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121211

S0 V2

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V3

V5

V4

V6

V8

V7

V9

V11

V10

V12

T13

1010

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1010

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77

11

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10106

6

6

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10

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12 12

4 10

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121211

f = 22 f = 28

S0 V2

V1

V3

V5

V4

V6

V8

V7

V9

20

18

18 9 9

8 8

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44

882

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6

S0 V2

V1

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20

18

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99

44

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1111

6

V11

V10

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T13

10106

6

6

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f = 30

V11

V10

V12

T13

10106

6

6

8

10

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12 12

4 10

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24

f = 44



Framework


Route PlannerGreedy

Original Evacuation Network(with Source, Destination Vertices)

Flow History

ReconfiguredNetwork

TerminationConditionSatisfied?

EvacuationTime as

ObjectiveFunction

Final Evacuation Time

No

Yes

IP /w CPLEXPerturbedNetwork

Min-cutMax-flow

1sangho kim, university of minnesota contraflow transportation network reconfiguration for...

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