Focusing on What Really Matters: Irrelevance Pruning in M&S

Transcription

1 Focusing on What Reay Matters: Irreevance Pruning in M&S Ávaro Torraba, Peter Kissmann Saarand University, Germany SoCS 2015, June 11 Session with ICAPS 2015 Torraba, Kissmann From Dominance to Irreevance Pruning SoCS / 16

2 Motivation: Irreevance Pruning Last Tuesday: h 2 -based preprocessor Simpify the task in a preprocessing step Remove operators that cannot possiby beong to any pan Very usefu!!!! Today: Can we simpify the tasks even further? Torraba, Kissmann From Dominance to Irreevance Pruning SoCS / 16

3 Motivation: Irreevance Pruning Last Tuesday: h 2 -based preprocessor Simpify the task in a preprocessing step Remove operators that cannot possiby beong to any pan Very usefu!!!! Today: Can we simpify the tasks even further? A B C D I T G I E G A B C D E (Truck) (Package) Torraba, Kissmann From Dominance to Irreevance Pruning SoCS / 16

4 Motivation: Irreevance Pruning Last Tuesday: h 2 -based preprocessor Simpify the task in a preprocessing step Remove operators that cannot possiby beong to any pan Very usefu!!!! Today: Can we simpify the tasks even further? A B C D I T G I E G A B C D E (Truck) (Package) Torraba, Kissmann From Dominance to Irreevance Pruning SoCS / 16

5 Merge-and-Shrink Heuristic An admissibe abstraction heuristic for cost-optima panning 1 Start with the projection over variabes: v 1, v 2, v 3, v 4 2 Merge: repace Θ i and Θ j by their product 3 Shrink: repace Θ i by its abstraction α(θ i ) L Θ 1 Θ 2 Θ 3 Θ 4 Torraba, Kissmann From Dominance to Irreevance Pruning SoCS / 16

6 Merge-and-Shrink Heuristic An admissibe abstraction heuristic for cost-optima panning 1 Start with the projection over variabes: v 1, v 2, v 3, v 4 2 Merge: repace Θ i and Θ j by their product 3 Shrink: repace Θ i by its abstraction α(θ i ) L Θ 1 Θ 2 Θ 3 Θ 4 Torraba, Kissmann From Dominance to Irreevance Pruning SoCS / 16

7 Merge-and-Shrink Heuristic An admissibe abstraction heuristic for cost-optima panning 1 Start with the projection over variabes: v 1, v 2, v 3, v 4 2 Merge: repace Θ i and Θ j by their product 3 Shrink: repace Θ i by its abstraction α(θ i ) L Θ 1 Θ 2 Θ 3 Θ 4 Torraba, Kissmann From Dominance to Irreevance Pruning SoCS / 16

8 Merge-and-Shrink Heuristic An admissibe abstraction heuristic for cost-optima panning 1 Start with the projection over variabes: v 1, v 2, v 3, v 4 2 Merge: repace Θ i and Θ j by their product 3 Shrink: repace Θ i by its abstraction α(θ i ) L α 1,2 α 3,4 Torraba, Kissmann From Dominance to Irreevance Pruning SoCS / 16

9 Merge-and-Shrink Heuristic An admissibe abstraction heuristic for cost-optima panning 1 Start with the projection over variabes: v 1, v 2, v 3, v 4 2 Merge: repace Θ i and Θ j by their product 3 Shrink: repace Θ i by its abstraction α(θ i ) L α 1,2 α 3,4 Torraba, Kissmann From Dominance to Irreevance Pruning SoCS / 16

10 Simuation-Based Dominance Pruning Labe-dominance simuation (Torraba and Hoffmann, IJCAI 2015): 1 Use M&S to compute a partition of the probem: {Θ 1,..., Θ k } 2 Compute abe-dominance simuation reation: { 1,..., k } Labe dominance: dominates in Θ i if for any s t exists s t s.t. t t State dominance s t: For any s s, exists t t t c( ) c() dominates in the rest of the probem 3 In A, prune any s s.t. s t, g(s) g(t) for some t t s.t.: Torraba, Kissmann From Dominance to Irreevance Pruning SoCS / 16

11 Merge-and-Shrink Framework (Sievers et a. 2014) Θ 1 Θ 2 Θ 3 Θ 4 Goba Θ Torraba, Kissmann From Dominance to Irreevance Pruning SoCS / 16

12 Merge-and-Shrink Framework (Sievers et a. 2014) FDR task: V, O, I, G v 1 v 2 v 3 v 4 State space Torraba, Kissmann From Dominance to Irreevance Pruning SoCS / 16

13 Merge-and-Shrink Framework (Sievers et a. 2014) Θ 1 Θ 2 Θ 3 Θ 4 Goba Θ M&S: Framework for transformation of panning tasks Operation Merge Shrink Exact Labe Reduction Bisimuation shrinking Reachabiity pruning Torraba, Kissmann From Dominance to Irreevance Pruning SoCS / 16

14 Merge-and-Shrink Framework (Sievers et a. 2014) Θ 1 Θ 2 Θ 3 Θ 4 Goba Θ M&S: Framework for transformation of panning tasks Operation Merge Shrink Exact Labe Reduction Bisimuation shrinking Reachabiity pruning Transformation to goba LTS None Abstraction Change abes Preserves h Keeps reachabe/sovabe part Torraba, Kissmann From Dominance to Irreevance Pruning SoCS / 16

15 Merge-and-Shrink Framework (Sievers et a. 2014) Θ 1 Θ 2 Θ 3 Θ 4 Goba Θ M&S: Framework for transformation of panning tasks Operation Merge Shrink Exact Labe Reduction Bisimuation shrinking Reachabiity pruning Subsumed transition pruning Transformation to goba LTS None Abstraction Change abes Preserves h Keeps reachabe/sovabe part Preserves h Torraba, Kissmann From Dominance to Irreevance Pruning SoCS / 16

16 Pan Preserving Transformations of Panning Tasks Pan preserving Π Π Pan preserving: 1 Does not add any new optima pan to the task 2 At east one optima pan for the origina task is preserved (h (I)) Unreachabe/dead-end pruning is pan preserving In this paper: subsumed transition pruning remove transitions from M&S transition systems gobay h-preserving (h (s) for every s) Torraba, Kissmann From Dominance to Irreevance Pruning SoCS / 16

17 Subsumed Transition Pruning Definition (Subsumed transition) s i t i is subsumed by s i t i if: 1 t i t i and 2 c( ) c() and 3 dominates in a Θ j for j i. Thm: Remove subsumed transitions is gobay h-preserving Torraba, Kissmann From Dominance to Irreevance Pruning SoCS / 16

18 Subsumed Transition Pruning Definition (Subsumed transition) s i t i is subsumed by s i t i if: 1 t i t i and 2 c( ) c() and 3 dominates in a Θ j for j i. Thm: Remove subsumed transitions is gobay h-preserving A B C D I E G Torraba, Kissmann From Dominance to Irreevance Pruning SoCS / 16

19 Subsumed Transition Pruning Definition (Subsumed transition) s i t i is subsumed by s i t i if: 1 t i t i and 2 c( ) c() and 3 dominates in a Θ j for j i. Thm: Remove subsumed transitions is gobay h-preserving I A B E C D G I A is subsumed by I E G D is subsumed by G E Torraba, Kissmann From Dominance to Irreevance Pruning SoCS / 16

20 Subsumed Transition Pruning Definition (Subsumed transition) s i t i is subsumed by s i t i if: 1 t i t i and 2 c( ) c() and 3 dominates in a Θ j for j i. Thm: Remove subsumed transitions is gobay h-preserving I A B E C D G I A is subsumed by I E G D is subsumed by G E A, B, C, D become unreachabe Torraba, Kissmann From Dominance to Irreevance Pruning SoCS / 16

21 Exampe: Subsumed Transition Pruning Θ 1 : Θ 2 : s 1 s 2 t 1 t 2 Θ 1 Θ 2 : (s 1, s 2 ) (s 1, t 2 ) (t 1, s 2 ) (t 1, t 2 ) Torraba, Kissmann From Dominance to Irreevance Pruning SoCS / 16

22 Exampe: Subsumed Transition Pruning Θ 1 : Θ 2 : s 1 s 2 t 1 t 2 Θ 1 Θ 2 : (s 1, s 2 ) (s 1, t 2 ) (t 1, s 2 ) (t 1, t 2 ) s 1 t 1 is subsumed by s 1 t 1 Torraba, Kissmann From Dominance to Irreevance Pruning SoCS / 16

23 Exampe: Subsumed Transition Pruning Θ 1 : Θ 2 : s 1 s 2 t 1 t 2 Θ 1 Θ 2 : (s 1, s 2 ) (s 1, t 2 ) (t 1, s 2 ) (t 1, t 2 ) s 1 t 1 is subsumed by s 1 t 1 s 2 t 2 is subsumed by s 2 t 2 Torraba, Kissmann From Dominance to Irreevance Pruning SoCS / 16

24 Exampe: Subsumed Transition Pruning Θ 1 : Θ 2 : s 1 s 2 t 1 t 2 Θ 1 Θ 2 : (s 1, s 2 ) (s 1, t 2 ) (t 1, s 2 ) (t 1, t 2 ) s 1 t 1 is subsumed by s 1 t 1 s 2 t 2 is subsumed by s 2 t 2 Don t remove a transition if the abe dominance changes! Torraba, Kissmann From Dominance to Irreevance Pruning SoCS / 16

25 Taking Advantage of Pan-Preserving Transformations 1 Search task Π instead of Π impementation overhead (future work) Torraba, Kissmann From Dominance to Irreevance Pruning SoCS / 16

26 Taking Advantage of Pan-Preserving Transformations 1 Search task Π instead of Π impementation overhead (future work) 2 Remove dead operators: after subsumed transition and unreachabiity pruning Torraba, Kissmann From Dominance to Irreevance Pruning SoCS / 16

27 Taking Advantage of Pan-Preserving Transformations 1 Search task Π instead of Π impementation overhead (future work) 2 Remove dead operators: after subsumed transition and unreachabiity pruning 3 M&S heuristics: If Θ is a pan-preserving transformation of Θ, abstractions of Θ are not admissibe for Θ Torraba, Kissmann From Dominance to Irreevance Pruning SoCS / 16

28 Taking Advantage of Pan-Preserving Transformations 1 Search task Π instead of Π impementation overhead (future work) 2 Remove dead operators: after subsumed transition and unreachabiity pruning 3 M&S heuristics: If Θ is a pan-preserving transformation of Θ, abstractions of Θ are not admissibe for Θ It s not a bug, it s a feature!!! ess expanded states gobay admissibe (preserve h in at east one optima pan) A returns optima soutions Subsumed transition pruning + unreachabiity anaysis must be appied before any shrinking (except bisimuation) Torraba, Kissmann From Dominance to Irreevance Pruning SoCS / 16

29 Simiarity Shrinking Shrink s, t iff s t and t s Gobay h-preserving derives perfect heuristics Coarser than bisimuation (s and s are simiar but not bisimiar) 1 s t 2 I u G s 1 t ( 3 2 ) Redundant with subsumed transition pruning (mod abe reduction) Torraba, Kissmann From Dominance to Irreevance Pruning SoCS / 16

30 Experiments Configuration P i : Incrementa computation: recompute simuation after each merge No abe reduction, no shrinking Preprocess successfu in 1463 of 1612 tasks Takes around 100s but up to s in arger tasks Suitabe for optima but not for satisficing panning Torraba, Kissmann From Dominance to Irreevance Pruning SoCS / 16

31 Experiments: M&S Heuristic Expanded nodes Tota time (s) M&S with P i M&S with P i M&S M&S Torraba, Kissmann From Dominance to Irreevance Pruning SoCS / 16

32 Experiments: Removing Irreevant Operators % pruned operators Coverage LM-cut Domain P i h 2 h 2 + P i - P i h 2 h 2 + P i Foortie Logistics NoMystery ParcPrint Rovers Sateite TPP Trucks Woodwk Tota (1612) probems for symboic bidirectiona uniform-cost search (over 964) Torraba, Kissmann From Dominance to Irreevance Pruning SoCS / 16

33 Experiments: Comparison with State of the Art HHJ (Hasum, Hemert, and Jonsson ICAPS 2013) Anayzes path subsumption in DTGs Current impementation ony appicabe to unary domains Operators LM-Cut Domain P i HHJ P i HHJ Bocksword Driverog Logistics Logistics Miconic Tota Torraba, Kissmann From Dominance to Irreevance Pruning SoCS / 16

34 Concusions Take home messages: 1 M&S is suitabe for transformation of panning tasks 2 Simuation reations usefu for: Subsumed transition pruning very good in practice! Simiarity shrinking: perfect shrinking better than bisimuation but... redundant with subsumed transition pruning + bisimuation 3 Irreevance pruning greaty simpifies panning tasks Future work: Extensions of abe-dominance simuation Path subsumption More types of probem transformations Torraba, Kissmann From Dominance to Irreevance Pruning SoCS / 16

35 Thanks for your attention! Questions? Torraba, Kissmann From Dominance to Irreevance Pruning SoCS / 16