1. 1Sangho Kim, University of Minnesota Contraflow Transportation Network Reconfiguration for Evacuation Route Planning Sangho Kim Advisor: Shashi Shekhar Department of Computer Science University of Minnesota sangho@cs.umn.edu

2. 2Sangho Kim, University of Minnesota Overview Motivation & Problem Definition Related Work & Contribution Proposed Approaches Evaluation Conclusion & Future Work

3. 3Sangho Kim, University of Minnesota Motivation Motivation & Problem Definition Related Work & Contribution Proposed Heuristics Evaluation Conclusion & Future Work Contraflow increases capacity by reversing the direction of roads Hurricane evacuation Terrorist attack evacuation Major sporting events Highway reconstruction Reversible lane 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. 4Sangho Kim, University of Minnesota Motivation (cont.) Motivation & Problem Definition Related Work & Contribution Proposed Approaches Evaluation Conclusion & 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." 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]. 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 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 ?

5. 5Sangho Kim, University of Minnesota Motivation (cont.) Motivation & Problem Definition Related Work & Contribution Proposed Heuristics Evaluation Conclusion & 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: 2 17 = 131,072 –Feasible configurations: 89,032 –# of configurations with min evacuation time: 346 (0.26%) –If three types are allowed (↓↓, ↓↑ or ↑↑), 3 17 > 100 million.

6. 6Sangho Kim, University of Minnesota Problem Definition 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 Motivation & Problem Definition Related Work & Contribution Proposed Approaches Evaluation Conclusion & Future Work

7. 7Sangho Kim, University of Minnesota Simple Contraflow Example Motivation & Problem Definition Related Work & Contribution Proposed Approaches Evaluation Conclusion & Future Work A B D E (1,2)(1,2) (1,2)(1,2) (1,4)(1,4) (1,2)(1,2) (1,3)(1,3) (1,2)(1,2) (4,1)(4,1) (4,1)(4,1) {40,40} {0,10} {0,∞}{0,∞} C (1,3)(1,3) (1,3)(1,3) (travel time, edge capacity) {initial occupancy, node capacity} {20,20} Evacuation Time: 22 A B D E (1,4)(1,4) (1,5)(1,5) (1,5)(1,5) (4,2)(4,2) {40,40} {0,10} {0,∞}{0,∞} C (1,7)(1,7) {20,20} Evacuation Time: 11 A B D E (1,4)(1,4) (1,5)(1,5) (1,5)(1,5) (4,2)(4,2) {40,40} {0,10} {0,∞}{0,∞} C (1,7)(1,7) {20,20} Evacuation Time: 14

8. 8Sangho Kim, University of Minnesota Overview Motivation & Problem Definition Related Work & Contribution Proposed Approaches Evaluation Conclusion & Future Work

9. 9Sangho Kim, University of Minnesota Related Works 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 83 rd TRB, 2004. / “Tabu-based heuristic for optimization of network evacuation contraflow”, presented at 85 rd 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 Motivation & Problem Definition Related Work & Contribution Proposed Approaches Evaluation Conclusion & Future Work

10. 10Sangho Kim, University of Minnesota Our Contribution Motivation & Problem Definition Related Work & Contribution Proposed Approaches Evaluation Conclusion & 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. 11Sangho Kim, University of Minnesota Overview Motivation & Problem Definition Related Work & Contribution Proposed Approaches –Proposed Approaches –Design Decision Evaluation Conclusion & Future Work

12. 12Sangho Kim, University of Minnesota Proposed Approach 1 Integer Programming Motivation & Problem Definition Related Work & Contribution Proposed Approaches Evaluation Conclusion & 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. 13Sangho Kim, University of Minnesota Motivation & Problem Definition Related Work & Contribution Proposed Approaches Evaluation Conclusion & Future Work Proposed Approach 3 Greedy Congestion Index –CongestionIndex(e) = FlowHistory(e) / (Capacity(e) x EvacuationTime) Degree of Contraflow (DoC) –DoC(G reconfigured ) = 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(G original, Doc) 1. run route planner to produce FlowHistory and Evac.Time on G orignal ; 2. for all edge e in G orignal, CongestionIndex(e) = FlowHistory(e) / (Capacity(e) x Eva.Time); 3. sort edges by CongestionIndex(e) in descending order; 4. G reonfigured = G orignal ; 5. for each (i;j) in the first DoC% edges in the sorted edge set, G reconfigured.flip((j;i)); 6. return G reonfigured ;

14. 14Sangho Kim, University of Minnesota A B D E 34% 39% 29% 59% 95% 0% 82% C 14% 89% Motivation & Problem Definition Related Work & Contribution Proposed Approaches Evaluation Conclusion & Future Work Sorted (DoC == 60%) A B D E C Final Configuration A B D E (1,2) (1,3) (1,2) (4,1) {40,40} {0,10} {0,∞} C (1,2) (1,3) {0,10}{20,20} Flow History & Evac. Time (22) from Route Planner Proposed Approach 3 Greedy Example (travel time, edge capacity) EdgeCI (%) 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 Congestion Index % A B D E 15 17 19 26 42 0 0 18 C 6 59

15. 15Sangho Kim, University of Minnesota Motivation & Problem Definition Related Work & Contribution Proposed Approaches Evaluation Conclusion & Future Work 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_flow new > max_flow old ) 2. find min-cut of G; 3. flip edges across min-cut toward destination; 4. max_flow old = max_flow new ; 5 max_flow new = max_flow(G); 6. return G;

16. 16Sangho Kim, University of Minnesota Motivation & Problem Definition Related Work & Contribution Proposed Approaches Evaluation Conclusion & Future Work Proposed Approach 4 Min-cut Max-flow Example Final Configuration A B D E (2)(2) (2)(2) (4)(4) (2)(2) (3)(3) (2)(2) (1)(1) (1)(1) C (3)(3) (3)(3) (edge capacity) A B D E (2)(2) (2)(2) (4)(4) (2)(2) (5)(5) (2)(2) C (3)(3) (3)(3) A B D E (2)(2) (2)(2) (5)(5) C (7)(7) (5)(5) (2)(2) A B D E (2)(2) (2)(2) (5)(5) C (7)(7) (5)(5) (2)(2) Max Flow = 4 Max Flow = 5 Max Flow = 7

17. 17Sangho Kim, University of Minnesota Design Decision 1 Overload Degree & Dominance Zone Overload Degree = # of Evacuees / Bottleneck Capacity w/o Contraflow Motivation & Problem Definition Related Work & Contribution Proposed Approaches Evaluation Conclusion & Future Work 0 1 SmallLargeInfinite No contraflow needed Integer Programming Greedy Min-cut Max-flow Overload DegreeNo Overload SmallLargeInfinite Use of Route Planner IterativeOne-timeNone Result Quality OptimalNo Contraflow Needed Integer Programming HeuristicGreedy Min-cut Max-flow S0V2 V1 V3 V5 V4 V6 V8 V7 V9 V11 V10 V12 T13 10 9 9 9 9 99 88 9 9 4 4 8 8 2 2 5 5 6 6 11 8 8 9 9 2 2 7 7 11 11 6 6 6 8 6 12 4 10 8 8 12 1 1 Bottleneck Capacity w/o Contraflow = 22

18. 18Sangho Kim, University of Minnesota Design Decision 2 Choice of Route Planner Motivation & Problem Definition Related Work & Contribution Proposed Approaches Evaluation Conclusion & 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. 19Sangho Kim, University of Minnesota Design Decision 3 Domain Knowledge Motivation & Problem Definition Related Work & Contribution Proposed Approaches Evaluation Conclusion & 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 CapacityTravel time# of EvacueesCongestion Greedy √√√√ IP √√√ Min-cut Max-flow √

20. 20Sangho Kim, University of Minnesota Overview Motivation & Problem Definition Related Work & Contribution Proposed Approaches Evaluation –Analytical Evaluation –Experimental Evaluation Conclusion & Future Work

21. 21Sangho Kim, University of Minnesota Motivation & Problem Definition Related Work & Contribution Proposed Approaches Evaluation Conclusion & Future Work –n vertices and m edges in original network; C = max edge weight –T: time horizon in G T ; 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(n 3 p 3 log(npC)) Heuristic Route Planner: CCRP –O(p (m + 2Cn))  GREEDY w/ CCRP is faster than GREEDY w/ CS Analytical Evaluation Choice of Route Planner

22. 22Sangho Kim, University of Minnesota Motivation & Problem Definition Related Work & Contribution Proposed Approaches Evaluation Conclusion & Future Work –n vertices and m edges in original network; C = max edge weight –T: time horizon in G T ; p: occupancy; T ≈ p The MIN-CUT is faster than GREEDY w/ CCRP if p > 9nlog 3 n / (3 + 2C)n Analytical Evaluation GREEDY vs. MIN-CUT

23. 23Sangho Kim, University of Minnesota Experimental Evaluation Experiment Design Motivation & Problem Definition Related Work & Contribution Proposed Approaches Evaluation Conclusion & Future Work

24. 24Sangho Kim, University of Minnesota 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 41 40 42 33 35 36 43 44 37 8 17 15 47 Motivation & Problem Definition Related Work & Contribution Proposed Approaches Evaluation Conclusion & Future Work Experimental Evaluation Exp. Setup and Dataset 1

25. 25Sangho Kim, University of Minnesota Motivation & Problem Definition Related Work & Contribution Proposed Approaches Evaluation Conclusion & Future Work Experimental Evaluation Dataset 2 Network Generator Software 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.5117,643111287113 1148,007277674119 2269,6355621443112 St. Paul CBD.553,93815336967 184,67824760879 2139,994402103386 Mall of America.58,8783255110 127,40684159103 243,68917038152

26. 26Sangho Kim, University of Minnesota Motivation & Problem Definition Related Work & Contribution Proposed Approaches Evaluation Conclusion & Future Work Experimental Evaluation 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

27. 27Sangho Kim, University of Minnesota Motivation & Problem Definition Related Work & Contribution Proposed Approaches Evaluation Conclusion & Future Work Experimental Evaluation 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

28. 28Sangho Kim, University of Minnesota Motivation & Problem Definition Related Work & Contribution Proposed Approaches Evaluation Conclusion & Future Work Experimental Evaluation 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 sec450 sec Runtime

29. 29Sangho Kim, University of Minnesota Motivation & Problem Definition Related Work & Contribution Proposed Approaches Evaluation Conclusion & Future Work Experimental Evaluation 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

30. 30Sangho Kim, University of Minnesota Motivation & Problem Definition Related Work & Contribution Proposed Approaches Evaluation Conclusion & Future Work Experimental Evaluation Monticello Reconfigured N/W Reconfigured Contraflow N/W with 10% Flips

31. 31Sangho Kim, University of Minnesota Motivation & Problem Definition Related Work & Contribution Proposed Approaches Evaluation Conclusion & Future Work Experimental Evaluation GREEDY Result /w Metro Data Minneapolis CBD St. Paul CBD

32. 32Sangho Kim, University of Minnesota Motivation & Problem Definition Related Work & Contribution Proposed Approaches Evaluation Conclusion & Future Work Experimental Evaluation Statistics of GREEDY Results IPGREEDY /w RELAX GREEDY /w CCRP Monticello43%38%36% Minneapolis CBD51% St. Paul CBD42% Mall of America49%50% Average45% Evacuation Time Reduction by Contraflow Mall of America

33. 33Sangho Kim, University of Minnesota Motivation & Problem Definition Related Work & Contribution Proposed Approaches Evaluation Conclusion & Future Work Experimental Evaluation 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

34. 34Sangho Kim, University of Minnesota Overview Motivation & Problem Definition Related Work & Contribution Proposed Approaches Evaluation Conclusion & Future Work

35. 35Sangho Kim, University of Minnesota 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. Motivation & Problem Definition Related Work & Contribution Proposed Approaches Evaluation Conclusion & Future Work

36. 36Sangho Kim, University of Minnesota 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 Motivation & Problem Definition Related Work & Contribution Proposed Approaches Evaluation Conclusion & Future Work

37. 37Sangho Kim, University of Minnesota Q & A ?

38. 38Sangho Kim, University of Minnesota Motivation & Problem Definition Related Work & Contribution Proposed Approaches Evaluation Conclusion & Future Work Proposed Approach 2 Simulated Annealing evac time Global min Plateau Local min network configurations Procedure SimulatedAnnealing 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 * iterations until 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

39. 39Sangho Kim, University of Minnesota Motivation & Problem Definition Related Work & Contribution Proposed Approaches Evaluation Conclusion & Future Work Proposed Approach 4 Min-cut Max-flow Example S0V2 V1 V3 V5 V4 V6 V8 V7 V9 V11 V10 V12 T13 10 9 9 9 9 99 88 9 9 4 4 8 8 2 2 5 5 6 6 11 8 8 9 9 2 2 7 7 11 11 6 6 3 3 4 4 5 5 3 3 12 22 5 5 8 8 1 1 S0V2 V1 V3 V5 V4 V6 V8 V7 V9 V11 V10 V12 T13 10 9 9 9 9 99 88 9 9 4 4 8 8 2 2 5 5 6 6 11 8 8 9 9 2 2 7 7 11 11 6 6 6 8 6 12 4 10 8 8 12 1 1 f = 22 f = 28 S0V2 V1 V3 V5 V4 V6 V8 V7 V9 20 18 99 88 9 9 4 4 8 8 2 2 5 5 6 6 11 8 8 10 9 9 2 2 7 7 11 11 1 1 6 S0V2 V1 V3 V5 V4 V6 V8 V7 V9 20 18 99 88 9 9 4 4 8 8 2 2 5 5 6 6 11 8 8 10 9 9 2 2 7 7 11 11 1 1 6 V11 V10 V12 T13 10 6 6 6 8 6 12 4 10 8 8 12 f = 30 V11 V10 V12 T13 10 6 6 6 8 6 12 4 10 16 24 f = 44

40. 40Sangho Kim, University of Minnesota Experimental Evaluation Framework Motivation & Problem Definition Related Work & Contribution Proposed Approaches Evaluation Conclusion & Future Work Route Planner Greedy Original Evacuation Network (with Source, Destination Vertices) Flow History Reconfigured Network Termination Condition Satisfied? Evacuation Time as Objective Function Final Evacuation Time No Yes IP /w CPLEX Perturbed Network Min-cut Max-flow