TR-C2026

Slides for the paper "Combinatorial reconfiguration for perimeter contraflow planning of urban evacuation network" in Transportation Research Part C: Emerging Technologies, 192, 105875 (2026)

Transcript

1. Combinatorial reconfiguration for perimeter contraflow planning of urban evacuation network Satoki Masuda, Eiji Hato Transportation Research Part C: Emerging Technologies, 192, 105875.
2. In the future, the search for adaptive strategies should be extended to more complex, two-dimensional transportation systems. … an evacuation strategy of this type should take into account that people can change routes and may not utilize the network efficiently. So, Stella K., and Carlos F. Daganzo. "Managing evacuation routes." Transportation research part B: methodological 44.4 (2010): 514-520.
3. Background: urban flood evacuation 3 1. Spatial heterogeneity of risk → Spatial imbalance in evacuation traffic demand Contraflow (lane reversal): Reverses lane direction from high-risk to low-risk areas to facilitate evacuation. ◦ Increases outbound capacity toward low-risk areas. ◦ Restricts inbound traffic to high-risk areas. 2. Long lead time for evacuation (In Tokyo, evacuation planning starts 48 hours before typhoon landfall.) In the early stage of evacuation, the actual occurrence of a disaster is uncertain. → Traffic control should be implemented gradually in stages. Shelter River High risk Low risk
4. Literature review 4 Online control, e.g., Ramp metering, routing So & Daganzo (2010): InFO control policy Cui+ (2025): Reinforcement learning • Weather • Traffic • Demand Controller Evacuation bus routing Environment × High control cost ← reactive × Implementation challenges Proactive strategic planning of traffic control Offline planning, e.g., Shelter location allocation, staged evacuation Yi+ (2017): Staged evacuation order Enumerate all transition paths and evaluate by DTA → Impossible as transition paths become large. Policy-maker • Traffic • Demand Planning Evacuation order Optimal order Users / Evacuees Users interactively respond to the planned policy. → Information paradox (time inconsistency) So, S. K., & Daganzo, C. F. (2010). Managing evacuation routes. Transportation research part B: methodological, 44(4), 514-520. Cui, Y., Feng, K., Ma, W., & He, B. (2025). Reinforcement learning for optimizing hurricane evacuation decisions: Hurricane Irma case study. Transportation Research Part D: Transport and Environment, 104882. Yi, W., Nozick, L., Davidson, R., Blanton, B., & Colle, B. (2017). Optimization of the issuance of evacuation orders under evolving hurricane conditions. Transportation Research Part B: methodological, 95, 285-304.
5. Reconfiguration of disaster traffic control 𝑡! Demand 5 𝑡" 𝑡# Evacuation Non-evacuation 6:00 12:00 18:00 Urban road network 6:00 12:00 Typhoon landfall 𝑡 Pre-determined contraflow plan by government Contraflow link Staged deployment Uncongested 6:00 Congested 0:00 8:00 10:00 12:00 Congestion of non-evacuation traffic Simultaneous control = No flexibility Gridlock Optimal reconfiguration from normal to disaster traffic control with efficient algorithm
6. Modeling evacuation traffic using Macroscopic Fundamental Diagram 6 Horizontal congestion Vertical congestion 𝑁! 𝑁 interaction " boundary link 𝑁$ 𝑁# shelter Evacuation traffic Non-evacuation traffic 𝑁 ! : Moving to other zones 𝑁 !,&'() : Moving to other zones 𝑁 " : Moving within destination zones 𝑁 ",&'() : Moving within the zone 𝑁 # : Searching for shelters 𝑁 * : Reaching their destination 𝑁 $ : Completed evacuation
7. Optimal reconfiguration problem max *!"#$…*!%&$ 𝑧' or 𝑧( 7 Demand 𝑧# : Minimize total travel time after reconfiguration 𝑡% 𝑧( 𝑡$ 𝑧' 𝑧( : Minimize total travel time during reconfiguration 𝑡 Decision variables: 𝑋) (contraflow configurations at time 𝜏) subject to (MFD-based traffic dynamics) 𝑋! ∈ ℱ 𝑋!"# , ∀𝜏 ∈ {𝜏$ + 1, … , 𝜏% − 1} Adjacency relation 𝑥&' 𝜏 + 𝑥'& 𝜏 ≤ 1, ∀𝑖 ∈ 𝑅, 𝑗 ∈ Γ& , ∀𝜏 ∈ 𝜏$ + 1, … , 𝜏% − 1 Topological constraints 𝑋!$ = 𝑆, Initial ( 𝑋!+ = 𝑇 𝑥&' 𝜏 ∈ 0, 1 , ∀𝑖 ∈ 𝑅, 𝑗 ∈ Γ& , ∀𝜏 ∈ 𝜏$ + 1, … , 𝜏% − 1 ) and target ( ) configurations Binary decisions (where to activate) Graphically, the problem is to find the optimal path of contraflow configurations in the solution space from 𝜏 = 𝑡% to 𝜏 = 𝑡$ . 𝑡&
8. Solution method using the Cross-Entropy Method 8 Cross-Entropy Method: A sampling-based heuristics for hard optimization problems. Sampling Evaluation Probability update Generate reconfiguration paths from a probability distribution. Evaluate the objective value of each path with the traffic simulation. Update the sampling probabilities based on the performance of sampled paths. contraflow configuration solution space 𝑡 = 𝑡- Issue: When the feasible solution space becomes small due to constraints, the sampling efficiency deteriorates. 𝑡 = 𝑡,
9. A method of sampling-space restriction using the ZDD 9 Idea: If all feasible configurations can be enumerated in advance, then sampling can be restricted to the feasible solution space. Requirements: • Efficiently enumerate and store sets of feasible configurations. • Perform high-speed set operations representing adjacency relations. Sampling-space restriction Zero-suppressed binary Decision Diagram (ZDD): A data structure that efficiently enumerates and stores sets of sets and performs fast set operations. 𝑒! 0 𝑒, 𝑒" 𝑒( 0 𝑒" 1 𝑒# 𝑒' Original network Zerosuppression 1 0 𝑒# 𝑒# 1 0 𝑒# 1 0 1 0 1 0 1 0 1 0 0 0 1 1 1 {𝑒! , 𝑒# }{𝑒! , 𝑒" }{𝑒! , 𝑒" , 𝑒# } Binary decision tree representing solution space 𝑒# 0 Merging 𝑒" 1 0 {𝑒# } 0 𝑒! 0 1 0 1 0 1 𝑒" 1 1 𝑒# 1 1 0 𝑒# 0 𝑒! 1 0 1 1 0 ZDD
10. Algorithm of sampling-space restriction 10 1. Forward search 1. Construct ZDD 𝒞 satisfying the topological constraints. 2. Initialize the set of feasible configurations: 𝒵 !. = 𝑆 ) 𝒵 ).' 𝒵 𝒞 𝑇 3. Iterate from 𝜏 = 𝜏$ + 1 to 𝜏% • Enumerate states reachable from 𝒵 !"# using ZDD operations 𝑆 • Intersect with constraint set 𝒞 to obtain 𝒵 ! . • Utilize high-speed set operations enabled by ZDD. 4. Check whether the target configuration 𝑇 is reached. 2. Backward search 1. Start from the target configuration 𝑇 and proceed backward. 2. At each step, enumerate states reachable from 𝒵 -!.# using ZDD operations to obtain 𝒵 -! 3. Intersect 𝒵 -! with the forward search results 𝒵 ! to extract the feasible set of transitions. → Enumerate all feasible configurations within sampling space. 𝑇 𝑆 𝒵 -)
11. Computational efficiency of sampling-space restriction 11 Comparison: Proposed sampling algorithm vs. naïve sampling. # links 10 20 30 40 50 60 Method of sampling-space restriction ZDD construction [s] Sampling [s] 0.001 0.370 0.002 0.387 0.006 0.671 0.009 1.243 0.460 5.895 20 sec. 2.641 7.115 Naïve sampling Sampling-space restriction Naïve sampling • Sample from the feasible space • Sample from the whole space 0.180 0.642 1.808 4.886 13.07 33.26 • ZDD sampling is 2.7–4.7 times faster than naive sampling. • Check feasibility • Repeat until the feasible path is found. • A 20-second difference per iteration = a 10-minute reduction in total computation time (when repeated 30 times in the optimization algorithm)
12. Computational efficiency of ZDD 12 Comparison: • Proposed algorithm with ZDD • Proposed algorithm without using ZDD (BFS algorithm) NS: computation did not complete within 1 hour Feasible configuration • Feasible reconfiguration paths are enumerated in about 0.01 seconds using ZDD. • The pure BFS approach fails to scale beyond 2 steps.
13. Case Study 13 • The urban network of Tokyo is divided into 9 zones and 34 boundary links. • The evacuation order is issued 36 hours before landfall (𝑡$ ). • Regular traffic peaks between 42 and 36 hours before landfall (𝑡% ≤ 𝑡 ≤ 𝑡$ ). • One reconfiguration step corresponds to 1 hour. 𝑡% 8000 Normal Evacuation 𝑡& 𝑡$ 250,000 200,000 6000 150,000 4000 100,000 2000 0 300,000 50,000 48 42 36 30 24 18 Time before landfall 12 6 0 0 Cumulative • Evacuation demand: Generated using evacuation departure and destination choice model 10000 Histogram • Normal demand: Public survey data on road traffic
14. Demand setting 14 • The evacuation departure and destination choice model was estimated using bootstrap resampling. • The parameter set at the 95% and 100% percentile (worst-case scenario) was adopted. Non-evacuation OD Evacuation OD Predominant travel direction is east–west. Zones 5 and 6 generate the largest departures Predominant travel direction is north–south. Color scale Red = Dep. > Arr. Blue = Arr. < Dep.
15. Demand scenarios 15 Four demand scenarios that cause gridlock during evacuation periods Max-Max Evacuation: Max Background: 100% Max-90 Evacuation: Max Background: 90% High demand scenarios Max-80 Evacuation: Max Background: 80% 95-Max Evacuation: 95% Background: 100% Low demand scenarios
16. Optimal transition vs. Random transition 𝒛𝟏 : Minimize the total travel time after the reconfiguration 16 Optimal 𝒛𝟐 : Minimize the total travel time during the reconfiguration Random Evaluation metrics: Average travel time during/after the reconfiguration The optimal transition improves traffic compared with a random one. Especially when normal traffic demand is high (up to 18.1% ≈ 17 min.) More normal traffic, more reduction. Max-Max Max-90 Reconfiguration can disrupt traffic, but an optimal transition mitigates the disruption. Max-80 95-Max
17. Optimal transition sequences 7:00 (𝒕𝟎 ) Max-Max 8:00 9:00 10:00 17 11:00 12:00 (𝒕𝒆 ) Contraflow link A robust contraflow pattern across demand scenarios The link 6→5 is activated later. Max-90 = Robust transition pattern Max-80 95-Max Regular traffic demand
18. Performance evaluation with microscopic simulation • A microscopic simulator, SUMO, is used to validate the optimization results of the macroscopic simulator. • 214 links are selected for contraflow. • The capacity of the links is doubled when control is implemented. • Demand is a Max-Max scenario. Without contraflow With contraflow 18
19. 19 Optimal transition vs. Simultaneous activation (no-transition) MFD of the whole network Change rate of link average speed drop drop Time before typhoon landfall Time of simultaneous activation Optimal transition Optimal transition Random transition (worst case) Ensure that the optimal transition outperforms the random transition. Time of simultaneous activation No-transition • The no-transition case shows a large drop in speed at the time of contraflow. → Flow disruption by the abrupt change • Reconfiguration levels the local congestion by control over time.
20. Conclusion The advantage of optimal reconfiguration. • A flexible and adaptable planning scheme. • Random transitions can degrade traffic, but an optimal transition minimizes the impact. • Levels the local congestion by traffic control over the planning horizon. Macro-micro cooperation. • MFD-based model successfully found the effective reconfiguration plan. • Microscopic simulation helps verify the macroscopic plan and evaluate the link-level congestion. Sampling-space restriction speeds up optimization. • A large but constrained solution space makes it difficult to sampling-based heuristics. • A method of sampling-space restriction speeds up computation by using efficient ZDD-based enumeration. 20