Combinatorial reconfiguration problem based on MFD for evacuation management under disasters Sep. 3, 2024 Department of Civil Engineering, The University of Tokyo Satoki Masuda Eiji Hato TRC-30@Crete. Session: Perimeter Control 

Background In disaster situations, congestion of evacuation vehicles is a big problem. → failure to evacuate before a disaster, stopping evacuation 2 2019.10.13 https://www.nikkei.com/article/DGXMZO64877960S0A011C2CC1000/ In 2019, evacuation from a large typhoon caused a traffic jam over 10 km. Some people gave up evacuating due to the heavy congestion. https://en.wikipedia.org/wiki/Hurricane_Rita_evacuation Hurricane Rita 

Literature on emergency traffic management Demand-side management Phased/staged evacuation with evacuation order • Encouraging those in high-risk areas to evacuate earlier • Discouraging those in low-risk areas to evacuate 3 Time # evacuees temporal dispersion No control Time # evacuees spatial dispersion No control distant area close area disaster × Effectiveness depends on the compliance rate. × Uncertainty in people’s evacuation behavior 

Literature on emergency traffic management Supply-side management • Contraflow / lane reversal (Kim et al., 2008) • Dynamically change directions of traffic. • Applied during hurricane evacuation in the U.S. • Intersection/ramp control (So and Daganzo, 2010) • Control inflow at intersections to avoid congestion. 4 !! (#) High risk Low risk inflow × Labor- and resource-intensive × Difficulty in coordinating each control in a large network 

This study Supply-side management + MFD 1. Prediction Predict dynamic OD and congestion propagation based on MFD 2. Perimeter control Control boundary flow to minimize total travel time. 5 Edited Yildirimoglu et al. (2014) ○ Fewer control points (reliability ↗) ○ Simpler operation ○ Lower computational cost of forecasting and control We consider the optimal set of boundary links where contraflow are implemented (discrete optimization). Contraflow 

Model framework We propose 1. Supply-side management of emergency traffic using MFD. 6 t = T … Traffic control during a disaster … Origin Shelter t = 1 t = 2 t = T … Evacuation departure and destination choice model Opt. Trip OD Network transmission model Evacuation SP survey Estimation Multi-region MFD dynamics Combinatorial optimization 

Prediction of people’s evacuation behavior Evacuation departure time and destination choice = route choice on a time-extended network → Discounted recursive logit model (Oyama and Hato, 2017) 7 Utility function： ! "!"# "! = % "!"# "! ; ' + max Ε - $%! & .$'!! "$"# "$ Expected future utility instantaneous utility Shelter B Shelter A Home Time to disaster … Origin Shelter t = 1 t = 2 t = T … 

Parameter estimation by SP survey 8 Small utility in areas with large inundation depths Utility of staying home is large, but relatively small for residents on lower floors of inundation area Choose shelters close to home when there is not enough time before disaster 

Network transmission model (Kim et al., 2018) (1/6) 9 Region A Region B 1) Predict evacuees’ departure time and destination using the estimated model = trip OD of each agent 

Network transmission model (Kim et al., 2018) (2/6) 10 2) Calculate the outflow from Region A based on the accumulation in Region A Region A Region B If the accumulation is high and congested, outflow from the region is limited. → Consider congestion in Region A ？ outflow 1) Predict evacuees’ departure time and destination using the estimated model = trip OD of each agent accumulation acceptable inflow 

Network transmission model (Kim et al., 2018) (3/6) 11 3) Calculate the maximum link capacity between Region A and B Region A Region B Small boundary link capacity between regions limits the outflow from Region A → Consider bottlenecks such as bridges outflow boundary link capacity ？ 2) Calculate the outflow from Region A based on the accumulation in Region A 1) Predict evacuees’ departure time and destination using the estimated model = trip OD of each agent accumulation acceptable inflow 

Network transmission model (Kim et al., 2018) (4/6) 12 4) Calculate acceptable inflow into Region B from the accumulation in Region B Region A Region B If the accumulation is high and congested, inflow into the region is limited. → Consider congestion in Region B ？ boundary link capacity outflow 3) Calculate the maximum link capacity between Region A and B 2) Calculate the outflow from Region A based on the accumulation in Region A 1) Predict evacuees’ departure time and destination using the estimated model = trip OD of each agent accumulation acceptable inflow 

Network transmission model (Kim et al., 2018) (5/6) 13 5) Out of outflow from MFD, the capacity of boundary links, and acceptable inflow from MFD, the minimum is the inter-region traffic volume. outflow boundary link capacity 4) Calculate acceptable inflow into Region B from the accumulation in Region B 3) Calculate the maximum link capacity between Region A and B 2) Calculate the outflow from Region A based on the accumulation in Region A 1) Predict evacuees’ departure time and destination using the estimated model = trip OD of each agent accumulation acceptable inflow 

Network transmission model (Kim et al., 2018) (6/6) 14 6) The calculated flow between regions is considered as the capacity of the inter-region transfer, and each agent is moved by the point queue model. 5) Out of outflow from MFD, the capacity of boundary links, and acceptable inflow from MFD, the minimum is the inter-region traffic flow. 4) Calculate acceptable inflow into Region B from the accumulation in Region B 3) Calculate the maximum link capacity between Region A and B 1) Predict evacuees’ departure time and destination using the estimated model = trip OD of each agent 2) Calculate the outflow from Region A based on the accumulation in Region A outflow boundary link capacity accumulation acceptable inflow 

Combinatorial optimization: Genetic Algorithm 1. Set the sets of initial boundary contraflow links. The capacity of contraflow links is increased by 1.5 times, and opposite links’ capacity is reduced by half. 2. Perform the network transmission model and calculate the objective function. objective function: total travel time 3. Set the sets of next contraflow link configuration. 1. Selection of good configurations 2. Mutation 3. Crossover 4. Replacement of the configurations 15 

Model framework We propose 1. Supply-side management of emergency traffic using MFD. 2. Step-by-step implementation of traffic management considering normal and evacuation traffic. 16 Disaster approaching t = 1 t = 2 t = T … … Traffic control in ordinary times Traffic control during a disaster Combinatorial reconfiguration … Origin Shelter t = 1 t = 2 t = T … Evacuation departure and destination choice model Opt. Trip OD Network transmission model Evacuation SP survey Estimation Multi-region MFD dynamics Combinatorial optimization 

Model framework We propose 1. Supply-side management of emergency traffic using MFD. 2. Step-by-step implementation of traffic management considering normal and evacuation traffic. 17 Disaster approaching t = 1 t = 2 t = T … … Traffic control in ordinary times Combinatorial reconfiguration … Origin Shelter t = 1 t = 2 t = T … Evacuation departure and destination choice model Opt. Trip OD Network transmission model Evacuation SP survey Estimation Multi-region MFD dynamics Combinatorial optimization Traffic control during a disaster 

Combinatorial reconfiguration • A field of theoretical computer science that analyzes changes over discrete state spaces. • Given the initial state and the target state, we want to calculate the optimal sequence of the intermediate state under a given transition rule. 18 initial target intermediate 

Combinatorial reconfiguration Is it difficult?? 19 à Yes Contraflow links in ordinary times … … … … … … … … … … … … … Optimal contraflow links during a disaster The number of transition states grows exponentially. → Enumerating all the sequences and finding the best one is difficult due to memory and computational cost. 

From optimization to reconfiguration Why do we consider gradual/step-by-step implementation? → Controlling network all at once under disaster uncertainty leads to disrupted ordinary traffic. ex) On Feb. 2024 in Tokyo, a large-scale highway closure before heavy snow caused congestion of the normal traffic on the local road. → It started snowing 5 hours later than predicted… 20 https://www.ktr.mlit.go.jp/kisha/kisha_01170.pdf https://www.nhk.or.jp/shutoken/newsup/20240208b.html → Need to implement emergency traffic control gradually considering normal and evacuation traffic. 

How to solve? What is ZDD? • ZDD is a data structure that compactly compresses a family of sets. • Consider a network with & links and a subset of graphs using those links. • Consider representing a subset of graphs on a computer. 21 … Data compression using Zero-suppressed binary Decision Diagrams (ZDD) 

What is ZDD? • Consider representing a subset of graphs on a computer (a, b, c, and d are the names of links.) 22 a b b c c c c d d d d d d d d 0 0 0 1 1 0 0 0 0 1 0 0 1 0 0 1 2N terminal nodes to represent whether each link is included in the sets. 1 0 Binary tree a b b c c d 0 1 1 0 node reduction ZDD The same representation of the set, but less memory usage e.g.) Preserving paths connecting the diagonal vertices of an 8×8 grid requires 11 TB with a binary tree, but only 168 KB with ZDD. 

How to solve? • ZDD enables efficient operations on compressed sets, such as union, intersection, and addition of new items. 23 https://github.com/takemaru/graphillion You can construct your own ZDD with a Python package, “Graphillion.” Control links in ordinary times … … … … … … … … … … … … … a b b c c d 0 1 1 0 ZDD Compact representation of graph set Add/remove a new item and make a new graph set → Fast 

… … … … … … … … … … … … … Solution algorithm 1. Link weight is set based on importance in normal traffic. 2. Transition the graph from the initial state until the target state is found. Save the graph sets as ZDD. ※ Transition rule: add one link & remove one link 3. Transition the graph backward from the target state. The transition destination must be intersection with the graph set in step 1. 4. If multiple transitions exist, the state maximizing the sum of the contraflow links’ weight is chosen. 24 • Shortest transition • Max. the weights (= convenience for the normal traffic) Contraflow links in ordinary times target state target state construction, union, intersection of ZDD = Fast 

Case study in Tokyo Koto City, Tokyo = densely populated urban area 25 10km 6km 540,000 people Koto City 

Case study in Tokyo Flood risk: The inundation depth and duration could exceed 10 meters and two weeks. 26 Arakawa river Koto City 

Case study in Tokyo • Koto City, Tokyo • Calculation time for one run (878,260 agents, 5528 nodes, 12799 links) Microscopic simulation: > 1 hours Network transmission model: 1.2 [sec] 27 Arakawa river Koto City 1km N 1 2 3 4 5 6 7 8 9 

1km N 1 2 3 4 5 6 7 8 9 Result of optimization Optimal contraflow links 28 low-risk regions high-risk regions • Promoting inflow to all regions is not optimal. • The result is intuitive, evacuating people from high-risk to low-risk regions. 

Optimal contraflow links No contraflow Link Number Queue length of boundary links • Total queue length: 2579 (No contraflow) à 1736 (Optimal contraflow links) The queue length in the peak demand is decreased by contraflow The boundary link from region 5 to 6 (bottleneck) Result of optimization 29 

Result of combinatorial reconfiguration • The weights of contraflow links at normal time are set to 1, otherwise -1. 30 t = 5 Evacuation performance (queue length if the contraflow links are kept for all steps) 2112 1923 1913 1878 1736 improve Convenience for the normal traffic (sum of the link weight) 5 4 3 1 -1 decrease add remove • The transition sequence gradually prioritizes evacuation performance (“queue”) to the convenience for the normal traffic (“weight”). 

Conclusion • Emergency traffic management requires 31 • a simple, not link-based, control method • accurate prediction of evacuation behavior • gradual implementation of the emergency control under uncertainty à Simulation-based optimization using MFD à Evacuation departure and destination choice using a recursive logit model à ZDD-based solution for combinatorial reconfiguration • Expanding boundary capacity by contraflow can eliminate congestion at the bottleneck in a peak time. • Combinatorial reconfiguration gradually implement the optimal contraflow plan, balancing between the normal traffic and evacuation performance. 

June 22 (Mon.) – June 27 (Fri.) of 2025 The 12th Triennial Symposium on Transportation Analysis conference (TRISTAN XII) ➔ Submission site is now open ! The deadline of extended abstract is October 15, 2024. https://tristan2025.org/ Michel Bierlaire EPFL Thank you !