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