Funded by ERA-NET Transport III Flagship Call 2013 “Future Travelling”

Adaptive Public Transit Network DesignAndrey Shabalov1, Eran Ben-Elia2, Itzhak Benenson1

1Dept of Geography and Human Environment, Tel-Aviv University2Ben-Gurion University of the Negev

bennya@post.tau.ac.il

Outline

• The variety of Transit Network Design Methods• Mobile phone data – types and availability• Trajectory clustering• From “Bugs” to Buses• State-of-the-Art of the SMART-PT project

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Methods of Public Transit Network Design (TND)

• Exact: linear, integer and mixed integer programming

• Heuristics and meta-heuristics:– Specific and ad hoc heuristics, often greedy– Neighborhood search - Simulated annealing, tabu search– Evolutionary search and Genetic algorithms– Hybrid algorithms

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TND State-of-the-art

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Author (Year) Solution Application

Chakroborty and Dwivedi (2002) Genetic Algorithm Examples

Chien and Spasovic (2002) Optimization model, partial derivatives Example

Chen and Yang (2004) Genetic Algorithm + Simulation Example

Fan and Machemehl (2004) Decomposition & Heuristic Examples

Gao et al. (2004)Bi-level programming, restricted network equilibrium approach, variational inequality

Example

Chiou (2005) Gradient-based method Examples

Yang et al. (2007) Ant colony optimization Examples

Fan and Machemehl (2008) Tabu search Example

Szeto and Wu (2011) Genetic Algorithm Tin Shui Wai, Hong Kong

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TND State-of-the-art

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Author (Year) Solution Application

Szeto and Jiang (2012) Artificial bee colony Tin Shui Wai, Hong Kong, Winnipeg, Canada

Chew et al. (2013) Genetic Algorithm Benchmark

Yan et al. (2013) Simulated annealing Examples

Kim and Schonfeld (2014) Probabilistic analytical model Examples

Nayeem et al. (2014) Genetic Algorithm Yubei, China, Brighton and Cardiff, UK

Nikolic and Teodorovic (2014) Artificial bee colony Benchmark

Neumann (2014) Genetic Algorithm Nelson Mandela Bay Area Municipality + Examples

Nourinejad and Roorda (2015)

Binary integer programming and dynamic auction-basedmulti-agent optimization

Example

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Short description of mobile phone geo-data• Cellular cell consists of several, usually 3, antennas, each serving “Pizza”, ~ 60o

sector. Typically, antenna’s service radius is several kilometers

• The network of antennas is optimized to minimize the overlap between antennas’ pizzas

• Depending on antennas’ capacity and loads, your steady phone can be switched between antennas. Once an hour, the network initiates connection with your phone

• Strength of the phone signal enables estimating the “Banana” - range of distances between the phone and antenna. Precision of the distance estimate is essentially higher for the 4th generation and lower for the phones of 3rd and 2nd.

• WiFi connection, in case the phone GPS is activated, is exactly geo-located

In what follows, we assume that phone location data are available at a banana or GPS precision

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The TND methods depend on the type of travel data

Existing methods SMART-PT

TripsPresented by the OD-matrix Ceder (2003), Fan (2006), Barra (2008)

Individual trajectories obtained from geo-located mobile phones

StopsPre-defined setNikolic & Teodorovic (2013), Nayeem et. al. (2014), Neumann (2014), Zhao et. al. (2015)

Generated based on observed activities

GA is applied

To given set of individual trip plans Fan & Machemehl (2011), Szeto & Wu (2011), Cipriani et al. (2012), Nayeem et al. (2014)

For establishing coevolving transit network and individual trip plans

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The SMART-PT ideaAdaptive clustering of individuals’ plans• Given: Set of travellers, each with its own trajectory of

daily activities

Example: Home-work tripsAgent 1: Leave home at at and travel to work at to be there at

Agent 2: Leave home at at and travel to work at to be there at

…….• Adaptively modify and synchronize travelers’

trajectories/activities for sharing travels

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Co-synchronization of individual plans and rides

• Travelers start separately, each with its own “taxi”

• Individual taxi is costly, it’s worth to rideshare – this will decrease costs

• To share rides, travelers synchronize their plans minimizing personal cost

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Modify plan to share rides

Modify clusters of trajectories

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Similar approach was recently applied in M. Nourinejad, M. J. Roorda, 2015 Agent based model for dynamic ridesharing, Transportation Research C, doi:10.1016/j.trc.2015.07.016

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Ways to synchronize agents space-time plans

• Shift start and end times of activities• Introduce walks• Establish meeting point for shared rides (Bus stops)• Adapt transit vehicles capacity• Establish Headways and Schedule

Populationdemand

Publictransit

Adapts to

Adapts to

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Clustering trajectories

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Clustering individual trajectories

Partition and Group • Partitioning: Each trajectory is

partitioned into a set of space-time segments at the points where the behavior of trajectory rapidly changes

• Grouping: Similar segments are grouped into a cluster applying density-based clustering method

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Clustering of trajectories: Partitioning

Input: Set of trajectories , , - number of agentsOutput: Set { of bifurcation points1: Add into the set ; // set starting point2: , ;3: while do4:5:6:/* check if partitioning at the current point increases the MDL cost*/7: if then8: Add into the set ; // include previous point9: , ;10: else11: ; // do not include previous point12: Add into the set ;

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Input: A set of line segments Parameters: – maximal dissimilarity between cluster’s segments, – minimal

number of linesOutput: A set of clusters 1: Set to 0; // initialize2: Mark all the line segments in as unclassified // initialize3: for each do4: if ( is unclassified) then Compute 6: if then7: Assign to ;8: Insert into the queue ;9: ExpandCluster;10: Increase by 1; 11: else12: Mark as a noise;13: Allocate all to its cluster ;14: // check cardinality of the trajectory15: for each do16: if then Remove from the set of clusters;

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Clustering of trajectories: Grouping

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Flowchart of the Algorithm

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Initial set of trajectories T

i ≤ |T|

Partitioning of trajectories

Get a set D of trajectory’s segments

Cluster segments

A set of clusters O

true false

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Illustration of the idea

10 agents

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20 agents

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Illustration of the idea

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10 agents

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Illustration of the idea

5 agents

1 agent

2 agents

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Illustration of the idea

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Noise

Noise

ClustersNoiseClusters

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Illustration of the idea

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Synthetic data: travellers starting their trips 7:00 – 7:15

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Illustration of obtained clusters (20 trajectories, e = 3, MinLns = 3)

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Clustering moving objects

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From Bugs to Buses

• Bugs are constantly moving, carrying travellers from place to place• Bugs want to evolve into buses: to grow to a bus-like capacity, to let

travellers board and alight at constant stops, to move along the same route and according to the same schedule during the entire day

• Initially, bugs start their movement over the road network based on the trajectories obtained from the clustering algorithm

• A Traveler boards a bug when nearby in space-time, and travels with a bug until their trajectories significantly deviate. This increases travellers utility.

• Bug stops for boarding/alighting travelers. This decreases travellers utility• Two bugs can be recombined into two or three others if their trajectories in

space-time essentially overlap.• A bug can produce a child-bug if a sufficient number of travellers want to

continue their trajectory while a sufficiently large subgroup will alight and continue traveling together on another trajectory

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Step 1: Clustering trajectories

5 agents 4 agents

4 agents1 agent

- an agent

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4 trajectories make up a cluster

Cluster of trajectories

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Step 1: Clustering trajectories

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4 agents 4 agents

4 agents1 agent

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Step 1: Clustering trajectories

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Clusters of trajectories

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Step 1: Clustering trajectories

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2 agents

3 agents

3 agents

2 agents

1 agent 2 agents

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Step 1: Clustering trajectories

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Clusters of trajectories become initial genotypes of the bugs

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Step 1: Clustering trajectories

Trajectory cluster

Clusters of trajectories

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Step 2: Bugs start moving along the clusters of step 1

- a traveller

- a bug

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Step 2: Adaptation of travellers plans to bugs

- an agent

- a bug

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- an agent

- a bug

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Step 2: Adaptation of travellers plans to bugs

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- an agent

- a bug

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Step 2: Adaptation of travellers plans to bugs

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Step 3: Bug turns into bus

- an agent

- a bus

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- an agent

- a bus

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Step 3: Bugs turn into buses, more complex example

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Bug’s genotype

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First Stop …

Route

Last Stop Capacity Frequency

Traveler’s genotype

Fitness of a bug Fitness of a traveler

Coding Representations

• maximize the number of satisfied passengers• minimize the total number of transfers• minimize the total travel time of all the

served passenger

• minimize travel cost• minimize travel time

Location 1Time

Location 2Time

Travel Plan

… … Location nTime

Location Arrival/Departure

Bus Stop

Location can be a bus stop

THANKS and visit us @

https://smart-pt.tau.ac.il/

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SMART-PT project, state-of-the-art:1. We have an access to antenna and data-connection data2. No access to “bananas” data yet3. Very recently we have got an access to data-connection records4. Step 1 is implemented and is currently tested5. Steps 2 and 3 are in development6. MATSim implementation of all three steps is in development