data-driven dynamic robust resource allocation for ... · • coordination and resource allocation...
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Fei Miao Postdoc, Electrical and Systems Engineering
University of Pennsylvania
Data-Driven Dynamic Robust Resource Allocation for Efficient Transportation
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Cyber-Physical Systems Tightintegra+onofcommunica+onandcomputa+on
systemswithcontrolofphysicalworld
BuildingAutoma+on
IndustrialAutoma+onandAdvancedManufacturing
Transporta+on&Autonomousvehicles SmartCi+es
MedicalDevicesandSystems
SmartGrids
ScienceofCPS
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Internet of Things
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A Growing Field : CPS
2010
2013
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Smart Cities
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Challenges of CPS
Automo+veAgriculture
Civil
Aeronau+cs
Materials
Energy
Manufacturing
Smart&ConnectedCommuni+es
CPSCore
Safety
Verifica-on
Privacy
HumanintheLoop
Control
IoT
NetworkingDataAnaly-cs
DesignAutonomy
Medical
Security
Informa-onManagement
Real--meSystems
5
Applica+onSectors
Data-Driven Control, Optimization of CPS
Growing complexity and dynamics: scale, uncertainty, heterogeneous…
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Data to information Machine learning Statistical method
Minimize cost or Maximize profit Optimization
Information to Action Control
Application Transportation systems Energy networks Manufacturing …....
Demand response of smart grid
Energy dispatch of smart building
Intelligent transportation systems: integration research challenges unsolved
Domain: Transportation Systems
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SmartParking
9.4 9.7 10.01 10.33 10.66 11
0 2 4 6 8
10 12
2009 2010 2011 2012 2013 2014
Revenue of US taxi services increases
Self-drivingcar
State of the Art – The Dark Side…
=20 ×
Cruising Mileage
Idle: 300 million miles/year
New York City
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Previous Work
• Urban traffic, demand modeling – Spatial and temporal patterns in speed prediction: [P. Jaillet et al., 2014] – Infer traffic condition based on taxi trip dataset: [Work et al., 2015]
• Coordination and resource allocation in smart transportation – Smart parking: [Geng and Cassandras, 2013] – Bike redistribution and incentives in sharing:[Morari et.al, 2014] – Mobility-on-demand systems: autonomous vehicles/robotics Minimize re-balancing number; with future demand : [Pavone et.al, 2014, 2015] Dynamic on-demand ride-sharing [Frazzoli, et al., 2016] Evaluation metric: number of vehicles needed; simulated waiting time
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Novelty of my work Brings data-driven optimization to system-wide efficient transportation
Motivation: Efficient Transportation
On demand ridesharing service • Greedy, increase human satisfaction myopically
• Optimal vehicle allocating with accurate, known demand distributions
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No system-level optimal, proactive resource allocation DataàPredicted demand àImproved system performance?
High Demand
Low Supply
Problem and Goal
Real-Time Control
Pickup & Delivery
Vehicle Mobility
Predicted Demand
Storage/Dispatch Center
Cellular Ratio
GPS
Occupancy status
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System-level balanced supply-demand ratio (fair service) with least total idle distance
Local controller: heuristic, greedy, matching, etc. Hierarchical
Challenges: scale, uncertainty Conflict of interests Limited resource Customers: reach destination soon System optimal: minimum idle
Contributions Outline: Data-Driven Control, Optimization of CPS
Large-scale dynamic decision, receding horizon control Demand predicted from historical and real-time sensing data
Uncertain demand: computationally tractable, probabilistic cost guarantee 1.Robust optimization for the worst-case resource allocation cost 2.Distributionally robust optimization for the expected cost
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Contributions Outline: Data-Driven Control, Optimization
• Reduce idle mileage of ride-sharing service • Considering both current and predicted future demand
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Large-scale dynamic decision, receding horizon control Demand predicted from historical and real-time sensing data
Receding Horizon Control Hierarchical Vehicle Dispatch
Spatial-temporal data à demand, mobility e.g. Poisson, vector time series
Dynamically optimize: time t, consider dispatch costs of (t,…, t+τ), execute decision for t 1.Update sensing data, demand prediction 2. System-level: balanced supply towards demand with minimum total idle distance 3.Send decisions to vehicles, local dispatcher t = t+1
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Spatial Urban Regions
Temporal Hourly Windows
One region, local dispatcher
n regions, optimization
Objective #1: Fair Service à Balanced Supply
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rkiPredicted demand�
Decision variables : number of vacant vehicles from region i to j Xkij > 0
Supply �original number of vacant vehicles before dispatch (GPS): Lik
• Goal: Fair service, similar average waiting time
• Local supply/demand ratio close to global level: penalty difference
Local s/d ratio Global s/d ratio (city)
Region 1 r1 L1
X23
X13 X24
Wij=Wji
Region 2 r2 L2
Region 3 r3 L3
Region 4 r4 L4
JE =⌧X
k=1
nX
i=1
��������
nPj=1
Xkji �
nPj=1
Xkij + Lk
i
rki� Nk
nPj=1
rkj
��������
Objective #2: Minimum Cost: Total Idle Distance
• Total idle distance to meet demand
4/6/15, 3:32 PMCable Car Museum, Mason Street, San Francisco, CA to Montgomery St. - Google Maps
Page 1 of 2https://www.google.com/maps/dir/Cable+Car+Museum,+Mason+Street,+…ff7491:0xb04336aed684aa9f!2m2!1d-122.401407!2d37.789256!3e0!5i2
Directions from Cable Car Museum, Mason Street, San Francisco, CA to Montgomery St.
Drive 1.0 mile, 5 min
Cable Car Museum, Mason Street, San Francisco, CA
1. Head south on Mason St toward Washington St
2. Turn left at the 1st cross street onto Washington St
3. Turn right onto Powell St
4. Turn left onto Clay St
5. Turn right onto Montgomery St
6. Turn left onto Market St
Montgomery St.
108 ft
482 ft
328 ft
0.4 mi
0.4 mi
223 ft
Initial position
Dispatched position
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• The distance between region i and region j at time k:
JD =⌧P
k=1
nPi=1
nPj=1
XkijW
kij
W kij
Region 1 r1 L1
X23
X13 X24
Wij=Wji
Region 2 r2 L2
Region 3 r3 L3
Region 4 r4 L4
Decision variables : number of vacant vehicles from region i to j Xkij > 0
System-Level Optimal Vehicle Dispatch
(1)
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Balanced supply Idle distance to meet demand
Supply positive
State dynamics: trip
Sparsity constraint (distance limited)
Computational complexity: polynomial of variable number (τn2) Spatial-temporal granularity
min.X1:⌧ ,L2:⌧
J =⌧X
k=1
(JD(Xk) + �JE(Xk, rk))
=⌧X
k=1
nX
i=1
0
BB@nX
j=1
XkijWij + �
��������
nPj=1
Xkji �
nPj=1
Xkij + Lk
i
rki� Nk
nPj=1
rkj
��������
1
CCA
s.t. (Lk+1)T = (1TnX
k � (Xk1n)T + (Lk)T )P k,
1TnX
k � (Xk1n)T + (Lk)T > 0,
XkijW
kij 6 mkXk
ij ,
Xkij > 0
Experiment: RHC dispatch with Real-Time information
2 4 6 8 10 12 14 16 18 20 22 240
120
240
360
480
600
Time: Hour
Aver
age
tota
l idle
dist
ance
: mile
Idle distance comparison
Dispatch with RT informationDispatch without RT informationNo dispatch
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• System-level vehicle balancing and local shortest path dispatcher • Average demand, GPS vehicle locations Average idle distance 42%
Collection Period 28 days
Number of Taxis 500
GPS Record Number
1,000,000
Experiment: Dispatch with Real-Time Information
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 160.5
0.8
1.1
1.4
1.7
2.0
Region ID
Supp
ly d
eman
d ra
tio
Supply demand ratio under different conditions
Global supply demand ratioDispatch without RT informationDispatch with RT informationNo dispatch
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Collection Period 28 days
Number of Taxis 500
Record Number 1,000,000
• System-level vehicle balancing and local shortest path dispatcher • Average demand, GPS vehicle locations Average supply-demand ratio error 45%
Large error caused by prediction error
Contributions Outline: Data-Driven Control, Optimization of CPS
Uncertain demand: computationally tractable, probabilistic cost guarantee 1.Robust optimization for the worst-case resource allocation cost 2.Distributionally robust optimization for the expected cost
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• Bootstrap (repeated experiments) • Confidence region of H0:mean,
covariance, probability distribution • Closed and convex uncertainty sets
Spatial-temporal data • Partition city map, cluster dataset • Trip/trajectory→ Aggregated demand
Data to Uncertain Demand or Demand Distributions
All dataWeekday
*H. David and H. Nagaraja. Order statistics. Wiley Online Library, 1970. �D. Bertsimas et al, Data-driven robust optimization. Operations Research 2015.
Box:
Second-order-cone (SOC):
Distribution set
rk+1 = fr(I[k�l,k]), rk+1 = rk+1 + �k+1.
rk+1 = fr(I[k�l,k]), rk+1 = rk+1 + �k+1.
Vector time series Poisson distribution
Uncertain Demand: Computationally Tractable Approximation
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• Objective not computationally intractable under uncertain demand
• Predicted demand �a closed and convex set (demand at time k: rk ) rc = (r1, r2, . . . , r⌧ ) 2 � 2 R⌧n
Region 1 R1 S1
X23
X13 X24
Wij=Wji
Region 2 R2 S2
Region 3 R3 S3
Region 4 R4 S4
• Decision variables : number of vacant taxis from region i to j Xkij > 0
supply at region i time k, linear of previous decisions Ski = f(X1:k)
JE =⌧X
k=1
nX
i=1
��������
Ski
rki�
nPj=1
Skj
nPj=1
rkj
��������
Uncertain Demand: Computationally Tractable Approximation
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*Theorem: computationally tractable approximation (concave of demand) *Fei Miao et. al, CDC, 2015; Fei Miao et. al, under revision, IEEE TCST 2016
• Predicted demand �a closed and convex set (demand at time k: rk )
rc = (r1, r2, . . . , r⌧ ) 2 � 2 R⌧n
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 11 0
5
10
15mi
smatc
h valu
e Demand and supply mismatch value change with
• Decision variables : number of vacant vehicles from region i to j Xkij > 0
supply at region i time k, linear of previous decisions Ski = f(X1:k)
min.Xk
nPi=1
rki(Sk
i )↵
⌧Pk=1
nPi=1
������rkiSki�
nPj=1
rkj
nPj=1
Skj
������9↵ > 0
JE =⌧X
k=1
nX
i=1
��������
Ski
rki�
nPj=1
Skj
nPj=1
rkj
��������
�
Probabilistic guarantee
• Predicted demand �a closed and convex set (demand at time k: rk )
rc = (r1, r2, . . . , r⌧ ) 2 � 2 R⌧n
min.X1:⌧
J(X1:⌧ , rc)
s.t. Prc⇠P⇤(rc)(f(X1:⌧ , rc) 6 0) > 1� ✏.
min.
X1:⌧max
rc⇠�J(X1:⌧ , rc),
s.t. f(X1:⌧ , rc) 6 0,
Robust optimization problem
Probabilistic Cost Guarantee for Worst-Case by Robust Solutions
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• Probabilistic guarantee for the dispatch cost
*Theorems: robust optimization à Equivalent convex optimization 1. Approximated objective: concave of uncertainties, convex of variables 2. Closed and convex uncertainty set (related toε,first/second order) *Fei Miao et. al, CDC, 2015; Fei Miao et. al, under revision, IEEE TCST 2016
Minimize Expected Cost: Distributionally Robust Optimization (DRO)
• Motivation: Trade-off between the expected and the worst-case costs
• Formulation
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X1:⌧ = {X1, X2, . . . X⌧}rc ⇠ F ⇤, F ⇤ 2 FDemand: ,
Resource allocation decision (spatial-temporal): rc = (r1, r2, . . . , r⌧ ) 2 R⌧n
Stochastic programming min.X1:⌧
Erc⇠F⇤⇥J(X1:⌧ , rc)
⇤
s.t. X1:⌧ 2 Dc.
Distributionally robust optimization min.
X1:⌧max
F2FE⇥J(X1:⌧ , rc)
⇤
s.t. X1:⌧ 2 Dc.
*Theorem: DRO à Equivalent convex optimization 1.Approximated objective: concave of uncertainties, convex of variables 2.Closed and convex set of probability distributions (first/second order) *Fei Miao et. al, accepted, CPSWeek ICCPS 2017.
Applications of Data-Driven DRO Resource Allocation
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supply at region i time k, linear of previous decisions
Resource allocation under demand uncertainties • Autonomous vehicle balancing for mobility-on-demand system • Bicycle balancing: supply-demand ratio at each station is in a range • Hierarchical carpooling framework: global balance, local carpool • Real-time demand response with limited resource
min.
X1:⌧ ,S1:⌧max
F2FE"
⌧X
k=1
JD(Xk
) + �nX
i=1
rki(Sk
i )↵
!#
s.t. X1:⌧ , S1:⌧ 2 Dc
Metric of service quality (d/s ratio related) Allocation cost
Ski = f(X1:k)
(3)
Evaluations: Robust VS Non-Robust Solutions
0 60 120 180 2400
20%
40%
60%
Demand supply ratio error range
Perc
enta
ge
Demand supply ratio error comparison
Robust solutionsNon−robust solutions
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Cross-validation Second-order-cone uncertainties Probabilistic guarantee 1-ε=0.75 The average demand supply ratio error reduced by 31.7%
The average total idle distance Robust VS non-robust: ê10.13%
0.7 0.8 0.9 1 1.1 1.2 1.3x 105
0
25%
50%
75%
Total idle distance range
Perc
enta
ge
Total idle distance comparison
Robust solutionsNon−robust solutions
Collection Period 4 years Data Size 100 GB Trip number 700 million
Evaluation: Average Costs of (distributionally) Robust Solutions
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 117
8
9
10x 104 Average cost comparison of DRO and RO
ϵ
Aver
age
cost
SOCBoxNRDRO
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SOC: second-order-cone uncertainty set Box: range of demand at each region Compared with non-robust (NR) solutions (100GB NYC taxi data) The average total idle driving distance is reduced by 10.05%
Dynamic Region Partition with DRO to Reduce Cost
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• [Quad-tree region partition, uncertainty set of demand probability distributions, distributionally robust vehicle balancing] VS [static grid, non-robust model]
à total idle distance 60 million miles, 8 million dollars gas consumption/year • Compared with total idle distance of original data: 55%
Region Division Grid Idle Mile Quad-Tree Idle Mile Change Rate t=1 hour 13.1%
T=30 minutes 20.0%
7.63⇥ 104 6.62⇥ 104
6.84⇥ 104 5.47⇥ 104
Summary of Contributions in Data-Driven CPS
• Learn demand from data; real-time, hierarchical decision-making
• Transportation efficiency Fei Miao et.al, ICCPS15 best paper finalist
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Computationally tractable, probabilistic guarantee under model uncertainties
Fei Miao et.al, ICCPS17;CDC15,TCST16
Automo+ve Agriculture
Civil
Aeronau+cs
Materials
Energy
Manufacturing
Smart&ConnectedCommuni+e
s
CPSCore
Safety
Verifica-on
Privacy
HumanintheLoop
Control
IoT
NetworkingDataAnaly-c
s
DesignAutonomy
Medical
Security
Informa-onManagement
Real--meSystems
Challenges with growing complexity and dynamics: scale, uncertainty
Future work of CPS Safety and Security
Automo+veAgriculture
Civil
Aeronau+cs
Materials
Energy
Manufacturing
Smart&ConnectedCommuni+es
CPSCore
Safety
Verifica-on
Privacy
HumanintheLoop
Control
IoT
NetworkingDataAnaly-cs
DesignAutonomy
Medical
Security
Informa-onManagement
Real--meSystems
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Applica+onSectors
Challenges: Safety, Security and Resilience
• With integration of communication, computation and control, cyber attacks can cause disasters in the physical world
• Knowledge of physical system dynamics helpful for security, resilience
33FeiMiao Connected vehicles
CPS Security: Coding for Stealthy Data Injection Attacks Detection
• Problem: Stealthy Data Injection Attacks -Attacker is smarter with the system model knowledge: inject data to communication channel, drive system to unstable state and pass detectors.
-Communication cost for encrypted messages is too large
• Goal: A low cost technique to detect stealthy data injection attacks
Estimator
Detector
Controlleruk
uk-1
.
.
.yk=Cxk+vk
Xk+1=Axk+Buk+wk
LTI S1
S2
Sp
a1
am
Attacker
change yk
to yk'
yk/yk'
.
.
.
yak
y'k=Cxk+yak+vk
a2
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Coding Schemes for Stealthy Data Injection Attacks Detection
Low cost: no extra bytes to communicate after coding *Research Contributions -Analyze sufficient conditions of feasible, low cost coding -Design an algorithm to calculate a feasible Σin real-time -Time-varying coding when the attacker can estimate Σ
*Fei Miao et.al, TCNS 2016. (funded by DARPA)
yk = Cxk + vk
Yk = ⌃(Cxk + vk)
Y
0k = ⌃(Cxk + vk) + y
ak
Estimator decode y0k = ⌃�1Y 0
k = yk + ⌃�1yak
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Dynamic Stochastic Game for Resilient Systems
36
Linear time invariant system
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• Problem: When an attack happens? What type of attack? Not known! Higher attack detection rate, higher investment cost in security in general *Contributions: dynamic stochastic game for an optimal switching policy between subsystems to balance security overhead and control cost
*Fei Miao et.al, CDC 2013,2014; journal version submitted to Automatica (funded by DARPA)
New York�37
• Agenda: safety, efficiency, security for CPSs with focus on smart cities, autonomous transportation systems
• Contributions: data-driven CPSs, CPSs/Smart Cities security
• Future work -Hierarchical decision making based on heterogeneous data information
-Design incentive mechanisms (e.g., dynamic pricing) of users and suppliers for social optimal behavior -Safety assurance of coordinated control of connected autonomous vehicles
-Security and resiliency of smart cities infrastructure with physical dynamics knowledge, distributed sensor networks