Contraflow Transportation Network Reconfiguration for Evacuation Route Planning

1
Contraflow Transportation Network
Reconfigurationfor Evacuation Route Planning

• Sangho Kim
• Advisor Shashi Shekhar
• Department of Computer Science
• University of Minnesota
• sangho_at_cs.umn.edu

2
Overview

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

3
Motivation
Motivation Problem Definition Related Work
Contribution Proposed Heuristics Evaluation Conclu
sion Future Work

• Contraflow increases capacity
• by reversing the direction of roads
• Hurricane evacuation
• Terrorist attack evacuation
• Major sporting events
• Highway reconstruction
• Reversible lane

Washington DC, I-95 reversible roadway for
peak-period HOV-3 vehicles (source
roadtothefuture.com)
4
Motivation (cont.)
Motivation Problem Definition Related Work
Contribution Proposed Approaches Evaluation Conclu
sion Future Work

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

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
5
Motivation (cont.)
Motivation Problem Definition Related Work
Contribution Proposed Heuristics Evaluation Conclu
sion 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 gt
  100 million.

6
Problem Definition
Motivation Problem Definition Related Work
Contribution Proposed Approaches Evaluation Conclu
sion Future Work

• Given
• a. Transportation network, directed graph G(V,
  E)
• b. Each vertex has initial occupancy and
  capacity
• c. Each directed edge has capacity, travel time
  and an initial direction
• d. 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 constant
• b. Edge direction can be flipped to allow
  contraflow
• c. Edge is the smallest unit of contraflow

7
Simple Contraflow Example
Motivation Problem Definition Related Work
Contribution Proposed Approaches Evaluation Conclu
sion Future Work
40,40
0,10
(1,7)
A
B
initial occupancy, node capacity
(1,5)
(travel time, edge capacity)
(1,4)
E
0,8
(4,2)
40,40
0,10
(1,3)
A
B
(1,5)
D
C
Evacuation Time 11
(1,4)
(1,2)
0,10
20,20
(1,3)
40,40
0,10
E
0,8
(1,2)
(1,2)
(1,7)
A
B
(4,1)
(4,1)
(1,5)
(1,2)
D
C
(1,4)
E
(1,3)
0,8
0,10
20,20
(4,2)
Evacuation Time 22
(1,5)
D
C
Evacuation Time 14
0,10
20,20
8
Overview

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

9
Related Works
Motivation Problem Definition Related Work
Contribution Proposed Approaches Evaluation Conclu
sion Future Work

• G. Hamza-Lup K. A. Hua, Enhancing intelligent
  transportation systems to improve and support
  homeland security, IEEE ITS, 2004
• Summary Breadth-First graph traversal,
  Multicast routing problem
• Limitations 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, 2006
• Summary Relies on mathematical programming or
  Tabu-based search
• Limitations 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, 2004
• Summary CORSIM microscopic contraflow
  simulation over New Orleans
• Limitations Labor intensive network coding ?
  Not flexible to generate
• various scenarios, hard to compare alternative
  parameters

10
Our Contribution
Motivation Problem Definition Related Work
Contribution Proposed Approaches Evaluation Conclu
sion 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)

11
Overview

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

12
Proposed Approach 1Integer Programming
Motivation Problem Definition Related Work
Contribution Proposed Approaches Evaluation Conclu
sion Future Work

• 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
13
Proposed Approach 3Greedy
Motivation Problem Definition Related Work
Contribution Proposed Approaches Evaluation Conclu
sion Future Work

• 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 (ij) in the first DoC edges in the sorted edge set, Greconfigured.flip((ji)) 6. return Greonfigured
14
Proposed Approach 3Greedy Example
Motivation Problem Definition Related Work
Contribution Proposed Approaches Evaluation Conclu
sion Future Work
40,40
0,10
(1,3)
89
A
B
A
B
(1,3)
29
(1,2)
0
Edge CI ()
B-E A-B D-E C-D D-B B-D B-A D-C E-B E-D 95 89 82 59 39 34 29 14 0 0
(1,2)
95
E
E
(travel time, edge capacity)
(1,2)
(1,2)
0,8
34
39
(4,1)
82
(4,1)
0
(1,2)
59
D
C
D
C
(1,2)
14
0,10
20,20
Flow History Evac. Time (22) from Route Planner
Congestion Index
A
B
59
A
B
19
0
42
E
E
15
17
18
0
Sorted (DoC 60)
D
C
26
D
C
6
Final Configuration
15
Proposed Approach 4Min-cut Max-flow
Motivation Problem Definition Related Work
Contribution Proposed Approaches Evaluation Conclu
sion Future Work

• 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 gt max_flowold) 2. find min-cut of G flip edges across min-cut toward destination max_flowold max_flownew 5 max_flownew max_flow(G) 6. return G
16
Proposed Approach 4Min-cut Max-flow Example
Motivation Problem Definition Related Work
Contribution Proposed Approaches Evaluation Conclu
sion Future Work
(edge capacity)
(3)
(7)
A
B
A
B
(4)
(5)
(2)
(3)
Max Flow 7
Max Flow 4
E
E
(2)
(2)
(2)
(2)
(1)
(2)
(1)
(2)
(5)
D
C
D
C
(3)
(3)
(7)
A
B
A
B
(4)
(5)
(5)
Max Flow 5
E
E
(2)
(2)
(2)
(2)
(2)
(2)
(2)
(5)
D
C
D
C
Final Configuration
(3)
17
Design Decision 1Overload Degree Dominance Zone
Motivation Problem Definition Related Work
Contribution Proposed Approaches Evaluation Conclu
sion Future Work
10
9
8
V1
V4
V7
V10
8
10
9
6
10
No contraflow needed
10
1
1
6
1
1
Integer Programming
Greedy
8
8
4
Min-cut Max-flow
4
10
10
10
4
6
9
8
9
8
S0
V2
V5
V8
V11
T13
9
8
8
9
8
2
12
2
2
9
10
12
9
9
1
1
12
12
1
5
2
1
9
5
Small
Large
Infinite
0
1
6
7
V3
V6
V9
V12
7
6
6

• Overload Degree
• of Evacuees / Bottleneck Capacity w/o Contraflow

Bottleneck Capacity w/o Contraflow 22
Overload Degree Overload Degree No Overload Small Large Infinite
Use of Route Planner Use of Route Planner Iterative One-time None
Result Quality Optimal No Contraflow Needed Integer Programming
Result Quality Heuristic No Contraflow Needed Greedy Greedy Min-cut Max-flow
18
Design Decision 2Choice of Route Planner
Motivation Problem Definition Related Work
Contribution Proposed Approaches Evaluation Conclu
sion Future Work

• 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

19
Design Decision 3Domain Knowledge
Motivation Problem Definition Related Work
Contribution Proposed Approaches Evaluation Conclu
sion Future Work

• 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 v v v v
IP v v v
Min-cut Max-flow v
20
Overview

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

21
Analytical EvaluationChoice of Route Planner
Motivation Problem Definition Related Work
Contribution Proposed Approaches Evaluation Conclu
sion 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 Goldbergs timebound with GREEDY
  O(n3p3log(npC))
• Heuristic Route Planner CCRP
• O(p (m 2Cn))
• ? GREEDY w/ CCRP is faster than GREEDY w/ CS

22
Analytical EvaluationGREEDY vs. MIN-CUT
Motivation Problem Definition Related Work
Contribution Proposed Approaches Evaluation Conclu
sion Future Work

• 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/ CCRP
• if p gt 9nlog3n / (3 2C)n

23
Experimental EvaluationExperiment Design
Motivation Problem Definition Related Work
Contribution Proposed Approaches Evaluation Conclu
sion Future Work
24
Experimental EvaluationExp. Setup and Dataset 1
Motivation Problem Definition Related Work
Contribution Proposed Approaches Evaluation Conclu
sion Future Work

• 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

7
11
23
47
18
5
24
12
2
8
10
4
13
19
14
25
15
20
26
1
9
27
16
31
21
3
46
28
45
22
38
29
17
6
39
30
32
34
41
33
35
40
42
36
43
37
44
25
Experimental EvaluationDataset 2
Motivation Problem Definition Related Work
Contribution Proposed Approaches Evaluation Conclu
sion Future Work

• Network generator software can
• specify user defined evacuation
• scenarios with variable evacuation zone
• Road data
• TP, Mn/DOT basemap
• Demographic data
• Census 2000, TP O/D data
• Edge granularity
• low with local roads

Selected Scenarios Zone Size (mile) of Occupancy (Demand) of Nodes of Edges Overload Degree
Minneapolis CBD .5 117,643 111 287 113
1 148,007 277 674 119
2 269,635 562 1443 112
St. Paul CBD .5 53,938 153 369 67
1 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
Network Generator Software
26
Experimental EvaluationCPLEX for IP Approach
Motivation Problem Definition Related Work
Contribution Proposed Approaches Evaluation Conclu
sion Future Work

• 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

27
Experimental EvaluationMonticello, Overload
Degree
Motivation Problem Definition Related Work
Contribution Proposed Approaches Evaluation Conclu
sion Future Work

• 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

28
Experimental EvaluationMonticello Results
Motivation Problem Definition Related Work
Contribution Proposed Approaches Evaluation Conclu
sion Future Work

• 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
29
Experimental EvaluationMonticello Result /w
GREEDY
Motivation Problem Definition Related Work
Contribution Proposed Approaches Evaluation Conclu
sion Future Work

• 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

30
Experimental EvaluationMonticello Reconfigured
N/W
Motivation Problem Definition Related Work
Contribution Proposed Approaches Evaluation Conclu
sion Future Work
Reconfigured Contraflow N/W with 10 Flips
31
Experimental EvaluationGREEDY Result /w Metro
Data
Motivation Problem Definition Related Work
Contribution Proposed Approaches Evaluation Conclu
sion Future Work
Minneapolis CBD
St. Paul CBD
32
Experimental EvaluationStatistics of GREEDY
Results
Motivation Problem Definition Related Work
Contribution Proposed Approaches Evaluation Conclu
sion Future Work
Mall of America
Evacuation Time Reduction by Contraflow
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
33
Experimental EvaluationScalability Test /w Metro
Data
Motivation Problem Definition Related Work
Contribution Proposed Approaches Evaluation Conclu
sion Future Work

• Results between of nodes and runtime
• Relax, CS and CCRP shows polynomial increase in
  runtime with GREEDY
• CCRP shows superior performance

34
Overview

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

35
Conclusion
Motivation Problem Definition Related Work
Contribution Proposed Approaches Evaluation Conclu
sion Future Work

• 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.

36
Future Work
Motivation Problem Definition Related Work
Contribution Proposed Approaches Evaluation Conclu
sion 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

37
Q A

• ?

38
Proposed Approach 2Simulated Annealing
Motivation Problem Definition Related Work
Contribution Proposed Approaches Evaluation Conclu
sion Future Work
Simulated Annealing
Global min
Local min
Plateau
Procedure SimulatedAnnealing repeat repeat
NewS perturb(S) if (h(NewS) lt
h(S)) or (random lt e(h(S)-h(NewS))/T)
then accept else do not accept
until inner loop has been repeated iterations
times T a T iterations ß
iterations until out of time
evac time
network configurations

• Initial State Original
• configuration w/o flips.
• Perturbation ??, ?? or ??
• Objective fn Evacuation time
• Cooling schedule termination condition are
  parameters.
• Order of flippings is random.

39
Proposed Approach 4Min-cut Max-flow Example
Motivation Problem Definition Related Work
Contribution Proposed Approaches Evaluation Conclu
sion Future Work
9
8
10
9
8
10
V1
V4
V7
V10
V1
V4
V7
V10
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6
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S0
V2
V5
V8
V11
T13
S0
V2
V5
V8
V11
T13
8
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4
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2
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2
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1
1
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1
1
12
12
5
2
9
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2
1
1
1
1
9
9
5
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3
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f 28
V3
V6
V9
V12
V3
V6
V9
V12
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3
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f 22
6
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V1
V4
V7
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V4
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V10
V10
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S0
V2
V5
V8
S0
V2
V5
V8
V11
T13
V11
T13
9
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18
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2
2
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5
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f 30
f 44
V3
V6
V9
V3
V6
V9
V12
V12
7
6
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6
6
40
Experimental EvaluationFramework
Motivation Problem Definition Related Work
Contribution Proposed Approaches Evaluation Conclu
sion Future Work
Original Evacuation Network (with Source,
Destination Vertices)
Route Planner
Perturbed Network
IP /w CPLEX
Flow History
Greedy
No
Evacuation Time as Objective Function
Termination Condition Satisfied?
Yes
Min-cut Max-flow
Reconfigured Network
Final Evacuation Time