Constraint-based Approaches for Balancing Bike Sharing Systems

Constraint-based Approaches for Balancing
Bike Sharing Systems
Luca di Gaspero1 , Andrea Rendl2 and Tommaso Urli1
DIEGM, University of Udine,
Via Delle Scienze, 206 - 33100 Udine, Italy
{luca.digaspero|tommaso.urli}@uniud.it
Dynamic Transportation Systems, Mobility Department,
Austrian Institute of Technology
Giefinggasse 2, 1210 Vienna, Austria
[email protected]
in cooperation with TU Vienna - Algorithms and Data Structures Group
funded by the Austrian Federal Ministry of Transport, Innovation and Technology (BMVIT)
CP-2013, September 17, 2013
Bike Sharing Systems
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Unbalanced Bike Stations
stations are located all over the city
load of bikes varies strongly between stations
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Balancing Bike Stations
station load becomes unbalanced over time
bikes need to be re-distributed
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Applied Research Project
Project Partners
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Austrian Institute of Technology (AIT)
TU Vienna, ADS Group
Citybike Wien/Vienna
Energie- und Umweltagentur NÖ (environemental agency)
cooperation with Luca di Gaspero and Tommaso Urli from
the University of Udine, Italy
Project aim: develop a decision support system for
balancing bike sharing systems
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17.9.2013
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Applied Research Project
Project Partners
•
•
•
•
Austrian Institute of Technology (AIT)
TU Vienna, ADS Group
Citybike Wien/Vienna
Energie- und Umweltagentur NÖ (environemental agency)
cooperation with Luca di Gaspero and Tommaso Urli from
the University of Udine, Italy
Project aim: develop a decision support system for
balancing bike sharing systems
L. di Gaspero, A. Rendl, T. Urli |
17.9.2013
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Balancing Bike Sharing Systems Problem (BBSS)
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Balancing Bike Sharing Systems Problem (BBSS)
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Static BBSS: Problem Parameters
bike stations S = {1, . . . , S}
• capacity Cs
• load bs
• target load ts (demand)
fleet of vehicles V = {1, . . . , V }
• capacity cv
• depot D
• time budget t̂
travel time matrix travelTimeu,v with u, v ∈ S ∪ D
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Static BBSS
Find a tour with loading instructions for each vehicle,
considering:
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vehicle capacity
station capacities
time budget
vehicles start and end their tours empty at the depot
a vehicle does not visit a station more than once
objective: minimal deviation from the target loads and
minimal travel time
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Static BBSS
Find a tour with loading instructions for each vehicle,
considering:
•
•
•
•
•
vehicle capacity
station capacities
time budget
vehicles start and end their tours empty at the depot
a vehicle does not visit a station more than once
objective: minimal deviation from the target loads and
minimal travel time
L. di Gaspero, A. Rendl, T. Urli |
17.9.2013
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1
CP Models for BBSS
Routing Model
Step Model
2
Large Neighbourhood Search (LNS)
3
Experimental Results
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Routing Model
Based on Vehicle Routing Problem (VRP) model:
extended graph: start and end depot for each vehicle
successor variables for each station
dummy vehicle visits unvisited stations
service and load variables for loading instructions
vehicle and time variables
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Routing Model
Based on Vehicle Routing Problem (VRP) model:
extended graph: start and end depot for each vehicle
successor variables for each station
dummy vehicle visits unvisited stations
service and load variables for loading instructions
vehicle and time variables
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Routing Model
2 vehicles and 5 stations
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Routing Model: Search Strategy
incrementally construct the tours vehicle by vehicle
successor variables:
• variable selection: the successor of the last variable
• value selection: according to the stations’ utility
• if time budget is consumed for current vehicle, the
successor is set to the next vehicle start depot
service variables:
after setting each successor variable, we search on its
respective service variable
L. di Gaspero, A. Rendl, T. Urli |
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Routing Model: Search Strategy
incrementally construct the tours vehicle by vehicle
successor variables:
• variable selection: the successor of the last variable
• value selection: according to the stations’ utility
• if time budget is consumed for current vehicle, the
successor is set to the next vehicle start depot
service variables:
after setting each successor variable, we search on its
respective service variable
L. di Gaspero, A. Rendl, T. Urli |
17.9.2013
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Routing Model: Search Strategy
incrementally construct the tours vehicle by vehicle
successor variables:
• variable selection: the successor of the last variable
• value selection: according to the stations’ utility
• if time budget is consumed for current vehicle, the
successor is set to the next vehicle start depot
service variables:
after setting each successor variable, we search on its
respective service variable
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Step Model
Based on an AI-planning perspective
route for each vehicle of maximal K stops, starting and
ending at the depot
estimated upper bound for K
service, load and time variables
advantage: direct representation each vehicle’s route
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Step Model
2 vehicles and 5 stations
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Step Model: Search Strategy
construct tour after tour, searching on route and service
variables
route variables: static variable selection, selecing the
station with highest utility (deviation from target)
service variables: after setting each route variable, search
on the service with dynamic max-value selection
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Large Neighbourhood Search (LNS)
given a valid solution
destroy-step: release parts of the solution (large
neighbourhood), fix the remaining variables
repair-step: solve problem with an exact approach to
optimality
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Large Neighbourhood Search (LNS): destroy
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Large Neighbourhood Search (LNS): repair
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LNS Parameters (1/2)
initial solution: first solution from tree search
destruction rate d increases if no improvement can be
made and is reset otherwise
destroy step
Routing model select d · |Ri | stations from each tour Ri for
destruction, and reset successor, service and
vehicle variables
P
Step model select d · i |Ri | visited stations and reset
route and service variables
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LNS Parameters (2/2)
repair step: Branch & Bound with time limit proportional to
the number of free variables
acceptance: the repaired solution is accepted if it
improves the current best solution
restarts: after C iterations with no improvement, a new
initial solution is generated and search is restarted
stopping criterion: timeout
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Experimental Setup
adapted real world instances derived from historical data
LNS parameters are tuned by F-Race (confidence level
0.95 over 150 instances)
we provided our source code and instances to the
recomputation initiative (see Tutorial by Ian Gent and Lars
Kotthoff on Wednesday, 13:30)
CP Solver: Gecode 3.7.3
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Routing versus Step Model: CP and LNS
red: routing model, blue: step model
dotted: pure CP, line: average LNS
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LNS versus State-of-the-Art
state-of-the-art: VNS approach (Raidl et al, 2013)
our approach is competitive but does not beat the
state-of-the-art
advantage of our approach: easily extendable to similar
problem setups
detailed results are in our paper
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Conclusions & Future Work
What to remember form this talk:
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Nice problem: BBSS
routing and step model
Large Neighbourhood Search (LNS)
CP approach is competitve with state-of-the-art
Future Work: dynamic multi-day BBSS
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Constraint-based Approaches for Balancing
Bike Sharing Systems
Luca di Gaspero1 , Andrea Rendl2 and Tommaso Urli1
DIEGM, University of Udine,
Via Delle Scienze, 206 - 33100 Udine, Italy
{luca.digaspero|tommaso.urli}@uniud.it
Dynamic Transportation Systems, Mobility Department,
Austrian Institute of Technology
Giefinggasse 2, 1210 Vienna, Austria
[email protected]
in cooperation with TU Vienna - Algorithms and Data Structures Group
funded by the Austrian Federal Ministry of Transport, Innovation and Technology (BMVIT)
CP-2013, September 17, 2013