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

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

Planning as Satisfiability withAbstraction Refinement

A B C

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

(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)

Introduction Algorithm Sparsification Evaluation I Step Skipping Evaluation II Appendix

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

Planning as Satisfiability withAbstraction Refinement

A B C

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

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

Introduction Algorithm Sparsification Evaluation I Step Skipping Evaluation II Appendix

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

Planning as Satisfiability withAbstraction Refinement

A B C

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

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

Introduction Algorithm Sparsification Evaluation I Step Skipping Evaluation II Appendix

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

Planning as Satisfiability withAbstraction Refinement

A B C

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

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

Introduction Algorithm Sparsification Evaluation I Step Skipping Evaluation II Appendix

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

Planning as Satisfiability withAbstraction Refinement

A B C

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

Plan π = 〈 pickup(T2,P1,B)

Introduction Algorithm Sparsification Evaluation I Step Skipping Evaluation II Appendix

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

Planning as Satisfiability withAbstraction Refinement

A B C

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

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

Introduction Algorithm Sparsification Evaluation I Step Skipping Evaluation II Appendix

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

Planning as Satisfiability withAbstraction Refinement

A B C

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

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

Introduction Algorithm Sparsification Evaluation I Step Skipping Evaluation II Appendix

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

Planning as Satisfiability withAbstraction Refinement

A B C

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

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

Introduction Algorithm Sparsification Evaluation I Step Skipping Evaluation II Appendix

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

Planning as Satisfiability withAbstraction Refinement

A B C

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

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

Introduction Algorithm Sparsification Evaluation I Step Skipping Evaluation II Appendix

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

Planning as Satisfiability withAbstraction Refinement

A B C

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

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)

Introduction Algorithm Sparsification Evaluation I Step Skipping Evaluation II Appendix

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

Planning as Satisfiability withAbstraction Refinement

A B C

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

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) 〉

Introduction Algorithm Sparsification Evaluation I Step Skipping Evaluation II Appendix

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

Planning as Satisfiability withAbstraction Refinement

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]

Introduction Algorithm Sparsification Evaluation I Step Skipping Evaluation II Appendix

Nils Froleyks, Tomas Balyo, Dominik Schreiber – PASAR July 17, 2019 3/28

Planning as Satisfiability withAbstraction Refinement

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]

Introduction Algorithm Sparsification Evaluation I Step Skipping Evaluation II Appendix

Nils Froleyks, Tomas Balyo, Dominik Schreiber – PASAR July 17, 2019 4/28

Planning as Satisfiability withAbstraction Refinement

n := 0 →Actions →

Initial state →Goal(s) →

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

Introduction Algorithm Sparsification Evaluation I Step Skipping Evaluation II Appendix

Nils Froleyks, Tomas Balyo, Dominik Schreiber – PASAR July 17, 2019 5/28

Planning as Satisfiability withAbstraction Refinement

n := 0 →Actions →

Initial state →Goal(s) →

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

Introduction Algorithm Sparsification Evaluation I Step Skipping Evaluation II Appendix

Nils Froleyks, Tomas Balyo, Dominik Schreiber – PASAR July 17, 2019 6/28

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)

Introduction Algorithm Sparsification Evaluation I Step Skipping Evaluation II Appendix

Nils Froleyks, Tomas Balyo, Dominik Schreiber – PASAR July 17, 2019 7/28

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)}

Introduction Algorithm Sparsification Evaluation I Step Skipping Evaluation II Appendix

Nils Froleyks, Tomas Balyo, Dominik Schreiber – PASAR July 17, 2019 8/28

Interference

A B C

empty(T2)

at(T2, B)

move

T2, B, Cpickup

T2, P2, B

pickup

T2, P1, B

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

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

Disabling graphsV = Actions

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

Introduction Algorithm Sparsification Evaluation I Step Skipping Evaluation II Appendix

Nils Froleyks, Tomas Balyo, Dominik Schreiber – PASAR July 17, 2019 8/28

Interference

A B C

empty(T2)

at(T2, B)

move

T2, B, Cpickup

T2, P2, B

pickup

T2, P1, B

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

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

∀-step [Rintanen et al., 2006]

Interference (A,B)⇒ A ∨ B

Introduction Algorithm Sparsification Evaluation I Step Skipping Evaluation II Appendix

Nils Froleyks, Tomas Balyo, Dominik Schreiber – PASAR July 17, 2019 8/28

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 action execution or ∀-step encoding

Abstraction: Nothing (∃-step)

Introduction Algorithm Sparsification Evaluation I Step Skipping Evaluation II Appendix

Nils Froleyks, Tomas Balyo, Dominik Schreiber – PASAR July 17, 2019 9/28

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

Introduction Algorithm Sparsification Evaluation I Step Skipping Evaluation II Appendix

Nils Froleyks, Tomas Balyo, Dominik Schreiber – PASAR July 17, 2019 9/28

Fix Abstract Plan

n := 0 →Actions →

Initial state →Goal(s) →

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

Introduction Algorithm Sparsification Evaluation I Step Skipping Evaluation II Appendix

Nils Froleyks, Tomas Balyo, Dominik Schreiber – PASAR July 17, 2019 10/28

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

Introduction Algorithm Sparsification Evaluation I Step Skipping Evaluation II Appendix

Nils Froleyks, Tomas Balyo, Dominik Schreiber – PASAR July 17, 2019 11/28

Trucking – Order

A B C

empty(T2)

at(T2, B)

move

T2, B, Cpickup

T2, P2, B

pickup

T2, P1, B

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

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

Introduction Algorithm Sparsification Evaluation I Step Skipping Evaluation II Appendix

Nils Froleyks, Tomas Balyo, Dominik Schreiber – PASAR July 17, 2019 12/28

Trucking – Order

A B C

empty(T2)

at(T2, B)

move

T2, B, Cpickup

T2, P2, B

pickup

T2, P1, B

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

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

Introduction Algorithm Sparsification Evaluation I Step Skipping Evaluation II Appendix

Nils Froleyks, Tomas Balyo, Dominik Schreiber – PASAR July 17, 2019 12/28

Trucking – Replan

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)}

Introduction Algorithm Sparsification Evaluation I Step Skipping Evaluation II Appendix

Nils Froleyks, Tomas Balyo, Dominik Schreiber – PASAR July 17, 2019 12/28

Trucking – Refine

A B C

empty(T2)

at(T2, B)

move

T2, B, Cpickup

T2, P2, B

pickup

T2, P1, B

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

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

Add all edges→ ∀-step semantics

Mutex reduction: DFS back edges

Introduction Algorithm Sparsification Evaluation I Step Skipping Evaluation II Appendix

Nils Froleyks, Tomas Balyo, Dominik Schreiber – PASAR July 17, 2019 12/28

Trucking – Refine

A B C

empty(T2)

at(T2, B)

move

T2, B, Cpickup

T2, P2, B

pickup

T2, P1, B

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

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

Add all edges→ ∀-step semantics

Mutex reduction: DFS back edges

Introduction Algorithm Sparsification Evaluation I Step Skipping Evaluation II Appendix

Nils Froleyks, Tomas Balyo, Dominik Schreiber – PASAR July 17, 2019 12/28

Trucking – Refine

A B C

empty(T2)

at(T2, B)

move

T2, B, Cpickup

T2, P2, B

pickup

T2, P1, B

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

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

Add all edges→ ∀-step semantics

Mutex reduction: DFS back edges

Introduction Algorithm Sparsification Evaluation I Step Skipping Evaluation II Appendix

Nils Froleyks, Tomas Balyo, Dominik Schreiber – PASAR July 17, 2019 12/28

Sparsification

A B C

A B C

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

Planning problem is overdefined

⇒ Plan sparsification

Introduction Algorithm Sparsification Evaluation I Step Skipping Evaluation II Appendix

Nils Froleyks, Tomas Balyo, Dominik Schreiber – PASAR July 17, 2019 13/28

Sparsification

Plan sparsification

Greedy Action elimination algorithm [Nakhost and Muller, 2010]

Introduction Algorithm Sparsification Evaluation I Step Skipping Evaluation II Appendix

Nils Froleyks, Tomas Balyo, Dominik Schreiber – PASAR July 17, 2019 14/28

Sparsification

Ak−1

Plan sparsification

Greedy Action elimination algorithm [Nakhost and Muller, 2010]

Introduction Algorithm Sparsification Evaluation I Step Skipping Evaluation II Appendix

Nils Froleyks, Tomas Balyo, Dominik Schreiber – PASAR July 17, 2019 14/28

Sparsification

Ak−1

Plan sparsification

Greedy Action elimination algorithm [Nakhost and Muller, 2010]

Introduction Algorithm Sparsification Evaluation I Step Skipping Evaluation II Appendix

Nils Froleyks, Tomas Balyo, Dominik Schreiber – PASAR July 17, 2019 14/28

Sparsification

Ak−1

Plan sparsification

Greedy Action elimination algorithm [Nakhost and Muller, 2010]

Introduction Algorithm Sparsification Evaluation I Step Skipping Evaluation II Appendix

Nils Froleyks, Tomas Balyo, Dominik Schreiber – PASAR July 17, 2019 14/28

Sparsification

Ak−1

Plan sparsification

Greedy Action elimination algorithm [Nakhost and Muller, 2010]

Introduction Algorithm Sparsification Evaluation I Step Skipping Evaluation II Appendix

Nils Froleyks, Tomas Balyo, Dominik Schreiber – PASAR July 17, 2019 14/28

Sparsification

Ak−1

Plan sparsification

Greedy Action elimination algorithm [Nakhost and Muller, 2010]

Introduction Algorithm Sparsification Evaluation I Step Skipping Evaluation II Appendix

Nils Froleyks, Tomas Balyo, Dominik Schreiber – PASAR July 17, 2019 14/28

Sparsification

Ak−1

Plan sparsification

Greedy Action elimination algorithm [Nakhost and Muller, 2010]

Introduction Algorithm Sparsification Evaluation I Step Skipping Evaluation II Appendix

Nils Froleyks, Tomas Balyo, Dominik Schreiber – PASAR July 17, 2019 14/28

Sparsification

. . .

A0 Ak−1Ak−2

Plan sparsification

Greedy Action elimination algorithm [Nakhost and Muller, 2010]

Introduction Algorithm Sparsification Evaluation I Step Skipping Evaluation II Appendix

Nils Froleyks, Tomas Balyo, Dominik Schreiber – PASAR July 17, 2019 14/28

Sparsification

A0 Ak−1Ak−2

. . .

Plan sparsification

Greedy Action elimination algorithm [Nakhost and Muller, 2010]

Introduction Algorithm Sparsification Evaluation I Step Skipping Evaluation II Appendix

Nils Froleyks, Tomas Balyo, Dominik Schreiber – PASAR July 17, 2019 14/28

Sparsification

A B C

A B C

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

Introduction Algorithm Sparsification Evaluation I Step Skipping Evaluation II Appendix

Nils Froleyks, Tomas Balyo, Dominik Schreiber – PASAR July 17, 2019 15/28

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]

Introduction Algorithm Sparsification Evaluation I Step Skipping Evaluation II Appendix

Nils Froleyks, Tomas Balyo, Dominik Schreiber – PASAR July 17, 2019 16/28

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

Introduction Algorithm Sparsification Evaluation I Step Skipping Evaluation II Appendix

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

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

Introduction Algorithm Sparsification Evaluation I Step Skipping Evaluation II Appendix

Nils Froleyks, Tomas Balyo, Dominik Schreiber – PASAR July 17, 2019 18/28

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

Introduction Algorithm Sparsification Evaluation I Step Skipping Evaluation II Appendix

Nils Froleyks, Tomas Balyo, Dominik Schreiber – PASAR July 17, 2019 19/28

Step Skipping – local

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)}

h(s) =∑j+1

x=i+1 dM(s, sx) · 1.2x

S1... Sk

...� � � �Sx

Sz

Sj+1Si

Sy

Introduction Algorithm Sparsification Evaluation I Step Skipping Evaluation II Appendix

Nils Froleyks, Tomas Balyo, Dominik Schreiber – PASAR July 17, 2019 19/28

Step Skipping – global

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)}

h(s) =∑k

x=2 dM(s, sx) · 1.2x

S1 Sk

Sv

Sw

Sx SySz

Introduction Algorithm Sparsification Evaluation I Step Skipping Evaluation II Appendix

Nils Froleyks, Tomas Balyo, Dominik Schreiber – PASAR July 17, 2019 19/28

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)

Introduction Algorithm Sparsification Evaluation I Step Skipping Evaluation II Appendix

Nils Froleyks, Tomas Balyo, Dominik Schreiber – PASAR July 17, 2019 20/28

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

Introduction Algorithm Sparsification Evaluation I Step Skipping Evaluation II Appendix

Nils Froleyks, Tomas Balyo, Dominik Schreiber – PASAR July 17, 2019 21/28

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

Introduction Algorithm Sparsification Evaluation I Step Skipping Evaluation II Appendix

Nils Froleyks, Tomas Balyo, Dominik Schreiber – PASAR July 17, 2019 22/28

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.

Introduction Algorithm Sparsification Evaluation I Step Skipping Evaluation II Appendix

Nils Froleyks, Tomas Balyo, Dominik Schreiber – PASAR July 17, 2019 23/28

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.

Introduction Algorithm Sparsification Evaluation I Step Skipping Evaluation II Appendix

Nils Froleyks, Tomas Balyo, Dominik Schreiber – PASAR July 17, 2019 24/28

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]

Introduction Algorithm Sparsification Evaluation I Step Skipping Evaluation II Appendix

Nils Froleyks, Tomas Balyo, Dominik Schreiber – PASAR July 17, 2019 25/28

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

Introduction Algorithm Sparsification Evaluation I Step Skipping Evaluation II Appendix

Nils Froleyks, Tomas Balyo, Dominik Schreiber – PASAR July 17, 2019 26/28

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)

Introduction Algorithm Sparsification Evaluation I Step Skipping Evaluation II Appendix

Nils Froleyks, Tomas Balyo, Dominik Schreiber – PASAR July 17, 2019 27/28

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

Introduction Algorithm Sparsification Evaluation I Step Skipping Evaluation II Appendix

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