PASAR - Planning as Satisﬁability with Abstraction Reﬁnement · INSTITUT FUR THEORETISCHE...

INSTITUT FUR THEORETISCHE INFORMATIK

PASAR - Planning as Satisfiability with AbstractionRefinement12th Annual Symposium on Combinatorial SearchNils Froleyks (Speaker), Tomas Balyo, Dominik Schreiber | July 17, 2019

KIT – University of the State of Baden-Wuerttemberg and National Research Centre of the Helmholtz Association

www.kit.edu

http://www.kit.edu

Planning as Satisfiability withAbstraction Refinement

A B C

Find a valid sequence of actions from some initial world stateto a desired goal state.

Introduction Algorithm Sparsification Evaluation I Step Skipping Evaluation II Appendix

Nils Froleyks, Tomas Balyo, Dominik Schreiber – PASAR July 17, 2019 2/28


A B C


(World) State: Consistent set of boolean atoms:at(T1,A), at(T2,B), at(P1,B), at(P2,B),empty(T1), empty(T2), road(A,B), road(B,C)




A B C


pickup(T2,P1,B)requires empty(T2), at(T2,B), at(P1,B)deletes at(P1,B), empty(T2) adds in(P1,T2)




A B C


Goal g: Set of Atoms that must hold,e.g. at(P1,C) and at(P2,C)




A B C


Plan π = 〈 pickup(T2,P1,B)




A B C


Plan π = 〈 pickup(T2,P1,B), move(T2,B,C)




A B C


Plan π = 〈 pickup(T2,P1,B), move(T2,B,C), drop(T2,P1,C)




A B C


Plan π = 〈 pickup(T2,P1,B), move(T2,B,C), drop(T2,P1,C),move(T1,A,B)




A B C


Plan π = 〈 pickup(T2,P1,B), move(T2,B,C), drop(T2,P1,C),move(T1,A,B), pickup(T1,P2,B)




A B C


Plan π = 〈 pickup(T2,P1,B), move(T2,B,C), drop(T2,P1,C),move(T1,A,B), pickup(T1,P2,B), move(T1,B,C)




A B C


Plan π = 〈 pickup(T2,P1,B), move(T2,B,C), drop(T2,P1,C),move(T1,A,B), pickup(T1,P2,B), move(T1,B,C),drop(T1,P2,C) 〉




n := 0 →Actions →

Initial state →Goal(s) →

UNSAT:n++ SAT:

1 -2 3 -4 5. . .

(1 ∨ 2)∧(2 ∨ 3 ∨ 7)∧. . .

1. a42. a63. a3. . .

Plan

SATSolver

Decode

Encodefor n steps

[Kautz and Selman, 1992]






UNSAT:n++ SAT:

1 -2 3 -4 5. . .

(1 ∨ 2)∧(2 ∨ 3 ∨ 7)∧. . .

1. a42. a63. a3. . .

Plan

SATSolver

Decode

Encodefor n steps

[Kautz and Selman, 1992]






1. a6, a42. a3, . . .3. a6. . .

1. a42. a63. a3. . .

UNSAT:n++ SAT:

1 -2 3 -4 5. . .

AbstractPlan

Failure:Counterexample

(1 ∨ 2)∧(2 ∨ 3 ∨ 7)∧. . .

Success

Plan

(1 ∨ 2)∧(2 ∨ 3 ∨ 7)∧(5 ∨ 6) ∧ . . .

SATSolver

Decode

Refine

FixAbstract Plan

Encodefor n steps






1. a6, a42. a3, . . .3. a6. . .

1. a42. a63. a3. . .

UNSAT:n++ SAT:

1 -2 3 -4 5. . .

AbstractPlan


(1 ∨ 2)∧(2 ∨ 3 ∨ 7)∧. . .

Success

Plan

(1 ∨ 2)∧(2 ∨ 3 ∨ 7)∧(5 ∨ 6) ∧ . . .

SATSolver

Decode

Refine

FixAbstract Plan

Encodefor n steps



Encoding

State variable istp and action variable dot

a for each step t = 0 . . . n

1 Initial state

O(|P|)

2 Goal conditions

O(|P|)

3 Preconditions are satisfied at step t

O(n · |A| · |E |)

4 Effects hold at step t + 1

O(n · |A| · |E |)

5 Frame axioms (state doesn’t change arbitrarily)

O(n · |P|)

6

Interference

O(n · |A|2)

Sequential, ∀-step

nothing⇒ abstraction (∃-step)



Interference

A B C

1 {pickup(T2,P1,B), pickup(T2,P2,B),move(T2,B,C)}

2 {drop(T2,P1,C), drop(T2,P2,C)}



Interference

A B C

empty(T2)

at(T2, B)

move

T2, B, Cpickup

T2, P2, B

pickup

T2, P1, B



Disabling graphsV = Actions

(A,B) ∈ E ⇔ A requires a precondition that is deleted by B



Interference

A B C

empty(T2)

at(T2, B)

move

T2, B, Cpickup

T2, P2, B

pickup

T2, P1, B



∀-step [Rintanen et al., 2006]

Interference (A,B)⇒ A ∨ B



Encoding



1 Initial state O(|P|)2 Goal conditions O(|P|)3 Preconditions are satisfied at step t O(n · |A| · |E |)4 Effects hold at step t + 1 O(n · |A| · |E |)5 Frame axioms (state doesn’t change arbitrarily) O(n · |P|)6 Interference O(n · |A|2)

Sequential action execution or ∀-step encoding

Abstraction: Nothing (∃-step)



Encoding



1 Initial state O(|P|)2 Goal conditions O(|P|)3 Preconditions are satisfied at step t O(n · |A| · |E |)4 Effects hold at step t + 1 O(n · |A| · |E |)5 Frame axioms (state doesn’t change arbitrarily) O(n · |P|)6 Interference O(n · |A|2)

Sequential action execution or ∀-step encodingAbstraction: Nothing (∃-step)



Fix Abstract Plan



1. a6, a42. a3, . . .3. a6. . .

1. a42. a63. a3. . .

UNSAT:n++ SAT:

1 -2 3 -4 5. . .

AbstractPlan


(1 ∨ 2)∧(2 ∨ 3 ∨ 7)∧. . .

Success

Plan

(1 ∨ 2)∧(2 ∨ 3 ∨ 7)∧(5 ∨ 6) ∧ . . .

SATSolver

Decode

Refine

FixAbstract Plan

Encodefor n steps



Fix Abstract Plan

S0 S1

A0

Si Si+1

Ai

... Sk−1 Sk

Ak−1

...Ak−2

Si Si+1Si Si+1...

Ai+1

1 Order actionsTopological ordering of disabling graph

2 ReplanGBFS from si to si+1

Small timeout3 Refine

Action set is a counter exampleRefine Abstraction



Trucking – Order

A B C

empty(T2)

at(T2, B)

move

T2, B, Cpickup

T2, P2, B

pickup

T2, P1, B





Trucking – Replan

A B C

A B C





Trucking – Refine

A B C

empty(T2)

at(T2, B)

move

T2, B, Cpickup

T2, P2, B

pickup

T2, P1, B



Add all edges→ ∀-step semantics

Mutex reduction: DFS back edges



Sparsification

A B C

A B C

1 {deliver(T2,P1,B,C), deliver(T2,P2,B,C)}

Planning problem is overdefined

⇒ Plan sparsification



Sparsification

Plan sparsification

Greedy Action elimination algorithm [Nakhost and Muller, 2010]



Sparsification

Ak−1

Plan sparsification




Sparsification

. . .

A0 Ak−1Ak−2

Plan sparsification




Sparsification

A0 Ak−1Ak−2

. . .

Plan sparsification




Sparsification

A B C

A B C

1 {deliver(T2,P1,B,C), deliver(T2,P2,B,C)}



Implementation Details

Fast Downward to ground to SAS+ [Helmert, 2006]

IPASIR generic interface for incremental SAT solving [Balyo et al., 2016]

We chose Glucose [Audemard and Simon, 2009]



Evaluation I

Benchmarks from the satisficing and optimal tracks of IPC 2014 and2018

Up to 5 minutes of total run time

State space search limited to 0.2 secondsCompetitors:

∀-Step encoding using our translationPASAR-Order only orderingPASAR-Replan ordering and replan



Evaluation I

0 50 100 150 200 250#solved

0

50

100

150

200

250

300tim

e [s

] [188] -Step[229] PASAR-Order[231] PASAR-Replan



Step Skipping

A B C

A B C

A B C

1 {pickup(T2,P1,B),pickup(T2,P2,B),move(T2,B,C)}

2 {drop(T2,P1,C),drop(T2,P2,C)}

S1... Sk

...Si+1 Sj−1...� ? ? ? ?� � �Sj+1Si



Step Skipping – local

A B C

A B C

A B C



h(s) =∑j+1

x=i+1 dM(s, sx) · 1.2x

S1... Sk

...� � � �Sx

Sz

Sj+1Si

Sy



Step Skipping – global

A B C

A B C

A B C



h(s) =∑k

x=2 dM(s, sx) · 1.2x

S1 Sk

Sv

Sw

Sx SySz



Evaluation II

Competitors:∀-Step encoding using our translationPASAR-Order only orderingPASAR-Replan ordering and replanPASAR-Local local step skippingPASAR-Global additionally global step skipping fallbackMadagascar [Rintanen, 2013]

glueMp Madagascar (linear scheduling) with glucoseglueMpC Madagascar (exponential scheduling) with glucoseMp Madagascar (linear scheduling)MpC Madagascar (exponential scheduling)



Evaluation II

0 50 100 150 200 250 300#solved

0

50

100

150

200

250

300tim

e [s

]

[188] -Step[229] PASAR-Order[231] PASAR-Replan[244] PASAR-Local[248] PASAR-Global[206] glueMp[241] glueMpC[306] Mp[317] MpC



Conclusion

Sparkle Planning Challenge (ICAPS 19)

Contributed 22% to the optimal portfolio

3rd most relevant planner

Future Work

More coarse-grained Abstraction with increasing Refinement

Relaxed encodings

Action learning



References I

Audemard, G. and Simon, L. (2009).

Predicting learnt clauses quality in modern SAT solvers.

In Twenty-first International Joint Conference on Artificial Intelligence.

Balyo, T., Biere, A., Iser, M., and Sinz, C. (2016).

SAT Race 2015.

Artificial Intelligence, 241:45–65.

Helmert, M. (2006).

The fast downward planning system.

Journal of Artificial Intelligence Research (JAIR), 26:191–246.

Kautz, H. and Selman, B. (1992).

Planning as Satisfiability.

In Proceedings of the European Conference on Artificial Intelligence, pages359–363.



References II

Nakhost, H. and Muller, M. (2010).

Action elimination and plan neighborhood graph search: Two algorithms for planimprovement.

pages 121–128.

Rintanen, J. (2013).

Planning as satisfiability: state of the art.

https://users.aalto.fi/rintanj1/satplan.html.

Rintanen, J., Heljanko, K., and Niemela, I. (2006).

Planning as satisfiability: parallel plans and algorithms for plan search.

Artificial Intelligence, 170(12-13):1031–1080.



https://users.aalto.fi/rintanj1/satplan.html

Evaluation III

Competitors:∀-Step encoding using our translationPASAR-Order only orderingPASAR-Replan ordering and replanPASAR-Local local step skippingPASAR-Global additionally global step skipping fallbackMadagascar [Rintanen, 2013]

glueMp Madagascar (linear scheduling) with glucoseglueMpC Madagascar (exponential scheduling) with glucoseMp Madagascar (linear scheduling)MpC Madagascar (exponential scheduling)

PASAR-GBFS initial GBFS for 100 secondsLAMA Fast Downward with the LAMA configuration [Helmert, 2006]



Evaluation III

0 100 200 300 400#solved

0

50

100

150

200

250

300tim

e [s

]

[248] PASAR-Global[306] Mp[317] MpC[392] PASAR-GBFS[407] LAMA



Plan Caching

S1... Sk

...Si+1 Sj−1...� ? ? ? ?� � �Sj+1Si

Left cache︸︷︷︸

Right cache︸︷︷︸

Plan from initial stateis known

Order and replan

Reached by stateskipping search

Plan to goal stateis known

Only order(no full state known)



Same Makespan Limit

The abstraction doesn’t represent enough of the problem

When too many abstractions are solved in the same makespan

Add all remaining interferences

⇒ Fallback to ∀-step



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