Models of Robustness in Scheduling and Temporal Planning

Models of Robustness in Scheduling andTemporal PlanningICAPS DC 2017

Jing Cui | Supervisor: Patrik Haslum

Australian National University & DATA61, CSIRO{cui.jing|patrik.haslum}@anu.edu.au

www.data61.csiro.au June, 18st, 2017

Outline

Optimising Simple Temporal Problems with Uncertainty under Dynamic ControllabilityIllustrative Example – Evacuation PlanningBackground – Dynamic Controllability of STPUOptimisation of STPU under Dynamic ControllabilityApplications

Dynamic Controllability of CCTPUIllustrative Example IIBackground – CCTPUMotivationModel with AssumptionsApproach – algorithm structureResult

Summary

2 | Models of Robustness in Scheduling and Temporal Planning | Jing Cui | Supervisor: Patrik Haslum

Outline



Summary


What is STPU?Illustrative Example – Evacuation Planning

Copyright 2013-2014. NICTA. All rights reserved.4 | Models of Robustness in Scheduling and Temporal Planning | Jing Cui | Supervisor: Patrik Haslum

What is STPU?Illustrative Example – Evacuation Planning

GRegion A

Region B

Copyright 2013-2014. NICTA. All rights reserved.5 | Models of Robustness in Scheduling and Temporal Planning | Jing Cui | Supervisor: Patrik Haslum

BackgroundDynamic Controllability of STPU

Simple Temporal Problems with Uncertainty (STPU) (Vidal & Fargier, 1999)

• Consists of Timepoints and Temporal Links• E = C(Contingent) ∪ R(Requirement).• Each link eij : Lij ≤ tj − ti ≤ Uij .

An STPU of the evacuation planning problem

Evacuate A A arrives at G A passes G

Evacuate B B arrives at G B passes G

Start Blocked G

[50, 70] [30, 35]

[25, 30] [30, 35][−5, 5]

[130, 140]

[0, + inf][0, + inf]

[0, + inf]

[0, + inf]



Dynamic Controllability (DC) (Vidal & Fargier, 1999)

• A dynamic strategy satisfying all constraints• Decide the FUTURE controllable nodes, based on observations of the FINISHEDuncontrollable nodes (prehistory).

An example of dynamic strategy


Evacuate B B arrives at G

[50, 70] [30, 35]

[25, 30] [−5, 5]

Timeline T T + [30, 35]T + 5 T + [30, 35]

diff[−5, 5]



DC Checking algorithms:

• Morris, Muscettola and Vidal (2001)I Reduction RulesI O(n4) (Morris, 2006)I O(n3) (Morris, 2014)

• Other AlgorithmsI Fast IDC (Stedl and Williams, 2005)I Efficient IDC (Nilsson, Kvarnstrom

and Doherty, 2014)

DC Reduction example: precede case (lCB ≥ 0)

A B

C

[lAB, uAB][lAC , uAC ]

[lCB, uCB]

[lAB, uAB]

[lAB, uAB]

[uAC − uBC , lAC − lBC ]MOTIVATION

• current research: DC or not• How far? DC→ not DC






and Doherty, 2014)


A B

C


[lCB, uCB]

[lAB, uAB][lAB, uAB]

[uAC − uBC , lAC − lBC ]

MOTIVATION







and Doherty, 2014)


A B

C


[lCB, uCB]

[lAB, uAB][lAB, uAB]

[uAC − uBC , lAC − lBC ]MOTIVATION



ModelOptimisation of STPU under Dynamic Controllability

max fobj(lij , uij | eij ∈ E )s.t. Lij ≤ lij ≤ uij ≤ Uij

N(lij , uij | eij ∈ E ) is DCapplication-specific side constraints

• Variables: lij , uij

• Constraints: the STNU is dynamically controllable(1) guarantee the solutions are dynamically controllable(2) a disjunctive linear constraint model(3) can be used to analyse robustness

(Jing Cui, Peng Yu, Cheng Fang, Patrik Haslum, Brian C. Williams. "OptimisingBounds in Simple Temporal Networks with Uncertainty under Dynamic ControllabilityConstraints". ICAPS 2015.)


Applications

• Relaxing Over-Constrained Problems• Minimising Flexibility• Dynamic Controllability with Chance Constraints• Robustness with Non-Probabilistic Uncertainty

<=0.2 <=0.4 <=0.6 <=0.8 <=1 Feasible

Improvement from SC to DC

% P

roble

ms

010

20

30

40

RESULT: Compare DC with SC

• Dynamic Controllability has moreflexibility than strong controllability• 12% cases are not feasible in SCbut feasible in DC


Outline



Summary


What is CCTPU?Illustrative Exmaple – Evacuation Planning

GRegion A

Region B

Copyright 2013-2014. NICTA. All rights reserved.

G ′


What is CCTPU?Illustrative Exmaple – Evacuation Planning

GRegion A

Region B

Copyright 2013-2014. NICTA. All rights reserved.G′


BackgroundCCTPU

Controllable Conditional Temporal Problem with Uncertainty (CCTPU)

• STPU with controllable discrete variables (Yu and Williams, 2014)• assignments for variables attached to links


Evacuate B B arrives at G B passes G

Start Blocked G

Blocked G’

[50, 70] [30, 35]

[0, 5]

[130, 140]

[40, 50]

B arrives at G’ B passes G’

[25, 30]c = G

[30, 35]c = G[30, 40]c = G ′ [50, 60]c = G ′

[90, 110]


BackgroundCCTPU

a dynamically controllable STPU with fixed assignments

Evacuate A A arrives G Evacuate BB Arrives

G/G’B passes

G/G’

[50,70] [0,5] [25,30]G[30, 40]G ′

[30,35]G[50, 60]G ′

[0,130]G,[0,170]G ′

[90,110]G ′

Timeline

T = 0

A(c)

c = G

c = G ′

a arrives G(G)

a arrives G(G’)

evacuate B(G)

evacuate B(G ′)

arrive (G)

arrive (G ′)

pass (G)

pass (G ′)

[50,70]

[50,70]

[0,5]

[0,5]

[25,30]

[30,40]

[30,35]

[50,60]

[115,140][85, 110] [135, 170]


BackgroundCCTPU



G/G’B passes

G/G’

[50,70] [0,5] [25,30]G[30, 40]G ′

[30,35]G[50, 60]G ′

[0,130]G,[0,170]G ′

[90,110]G ′

Timeline

T = 0

A(c)

c = G

c = G ′

a arrives G(G)

a arrives G(G’)

evacuate B(G)

evacuate B(G ′)

arrive (G)

arrive (G ′)

pass (G)

pass (G ′)

[50,70]

[50,70]

[0,5]

[0,5]

[25,30]

[30,40]

[30,35]

[50,60]

[115,140][85, 110] [135, 170]


BackgroundCCTPU



G/G’B passes

G/G’

[50,70] [0,5] [25,30]G[30, 40]G ′

[30,35]G[50, 60]G ′

[0,130]G,[0,170]G ′

[90,110]G ′

Timeline

T = 0

A(c)

c = G

c = G ′

a arrives G(G)

a arrives G(G’)

evacuate B(G)

evacuate B(G ′)

arrive (G)

arrive (G ′)

pass (G)

pass (G ′)

[50,70]

[50,70]

[0,5]

[0,5]

[25,30]

[30,40]

[30,35]

[50,60]

[115,140][85, 110] [135, 170]


Dynamic Controllability of CCTPUMOTIVATION

MOTIVATION

• postponing decisions allows more flexibility (fully dynamical controllability)I dynamically controllable temporal schedulingI dynamically controllable decisions on variables


G/G’B passes

G/G’

[50,70] [0,5] [25,30]G[30, 40]G ′

[30,35]G[50, 60]G ′

[0,130]G,[0,170]G ′

[90,110]G ′

A(c)


Dynamic Control of CCTPUFULLY DYNAMIC EXECUTION STRATEGY


G/G’B passes

G/G’

[50,70] [0,5] [25,30]G[30, 40]G ′

[30,35]G[50, 60]G ′

[0,130]G,[0,170]G ′

[90,110]G ′

Timeline

T = 0 DT (c)

A(c)

c = G

c = G ′

prehistory ≤ 65

prehistory≥ 55

evacuate B(G)

evacuate B(G ′)

arrive (G)

arrive (G ′)

pass (G)

pass (G ′)

[0,5]

[0,5]

[25,30]

[30,40]

[30,35]

[50,60]

[110,130][90, 110] [140, 170]




G/G’B passes

G/G’

[50,70] [0,5] [25,30]G[30, 40]G ′

[30,35]G[50, 60]G ′

[0,130]G,[0,170]G ′

[90,110]G ′

Timeline

T = 0 DT (c)

A(c)

c = G

c = G ′

prehistory ≤ 65

prehistory≥ 55

evacuate B(G)

evacuate B(G ′)

arrive (G)

arrive (G ′)

pass (G)

pass (G ′)

[0,5]

[0,5]

[25,30]

[30,40]

[30,35]

[50,60]

[110,130][90, 110] [140, 170]




G/G’B passes

G/G’

[50,70] [0,5] [25,30]G[30, 40]G ′

[30,35]G[50, 60]G ′

[0,130]G,[0,170]G ′

[90,110]G ′

Timeline

T = 0 DT (c)

A(c)

c = G

c = G ′

prehistory ≤ 65

prehistory≥ 55

evacuate B(G)

evacuate B(G ′)

arrive (G)

arrive (G ′)

pass (G)

pass (G ′)

[0,5]

[0,5]

[25,30]

[30,40]

[30,35]

[50,60]

[110,130][90, 110] [140, 170]


Dynamic Controllability of CCTPUMODEL

Dynamic Controllability of CCTPU

• Making FUTURE Assignments and Scheduling based on PAST observations• Fully Dynamic Strategy: 〈ES, DT 〉, ES :< A, S > and DT : C → V

I A(c) is made at DT (c)

Assumptions

• DT (c) is prior to all links related to c• Prehistory of c consists of e ∈ E definitely finishing before DT (c)• DT (c) is the end point of a contingent link


ApproachAlgorithm Structure

Expanding/Combining Tree

root CCTPU

. . .

. . .

leaf STPU

c1 = dc11c1 = dc12

c1 = dc1n

c2 = dc21c2 = dc22

c2 = dc2n

A(C)

Ec

Ec(dc22)Ec(dc21) Ec(dc2n)

Ec2(dc12)Ec2(dc11) Ec2(dc1n)

ALGORITHM STRUCTURE

• ExpandingI assigning variables inchronological order

I traversing in depth first order• Extracting DC Envelope Ec

I Enumerate ConflictsI Conflict Resolutions (Yu, Fang and

Williams, 2014)

• Aggregating Ec

I Updating Relaxable SetI Combining Ec(d),∀d ∈ D(ci)

• The CCTPU is DC if an Ec coversall uncertainty in its prehistory




root CCTPU

. . .

. . .

leaf STPU

c1 = dc11c1 = dc12

c1 = dc1n

c2 = dc21c2 = dc22

c2 = dc2n

A(C) Ec



ALGORITHM STRUCTURE




Williams, 2014)• Aggregating Ec






root CCTPU

. . .

. . .

leaf STPU

c1 = dc11c1 = dc12

c1 = dc1n

c2 = dc21c2 = dc22

c2 = dc2n

A(C) Ec



ALGORITHM STRUCTURE




Williams, 2014)• Aggregating Ec




Result

infeasible feasible with fixed option

feasible with dynamic option

0

2000

4000

6000

8000

10000

12000

14000

#problems

Fixed Assignment

Dynamic Assignment • Comparedimplementation: DCchecking with fixedassignment• Benchmark: Zipcar(1-8 variables, 1-10options, 11-330 links)(https://github.com/yu-peng/BCDRTestGenerator)


Conclusion

Summary

• Optimisation Model of STPU under dynamic controllabilityI answer How farI robust measures (dynamic controllability vs. strong controllability)

• Formulate Dynamic Controllability of CCTPUI dynamic assignments vs. fixed assignment

* Future: Optimisation Model of CCTPU under dynamic controllability

ICAPS 2017 paper – Dynamic Controllability of CCTPU

• Thursday (June 22nd) 2.20pm, Temporal Planning I• Room: GHC 4401


Documents

Models of Robustness in Scheduling and Temporal Planning