1 / 58

Efficient Automated Planning with New Formulations

Efficient Automated Planning with New Formulations. Ruoyun Huang Advisors : Dr. Yixin Chen and Dr. Weixiong Zhang Washington University in St. Louis. Efficient Automated Planning with New Formulations. Ruoyun Huang Advisors : Dr. Yixin Chen and Dr. Weixiong Zhang

lanza
Télécharger la présentation

Efficient Automated Planning with New Formulations

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Efficient Automated Planning with New Formulations Ruoyun Huang Advisors: Dr. Yixin Chen and Dr. Weixiong Zhang Washington University in St. Louis • Efficient Automated Planning with New Formulations Ruoyun Huang Advisors: Dr. Yixin Chen and Dr. Weixiong Zhang Washington University in St. Louis

  2. Committee Members Dr. Yixin Chen (co-advisor) Dr. Christopher D. Gill Dr. Norman I. Katz Dr. Yinjie Tang Dr. KilianWeinburger Dr. Weixiong Zhang(co-advisor)

  3. Classical Planning (STRIPS) loc1 loc1 loc2 loc2 Init State: (AT pkg loc1); (AT truck loc2); ? Applicable actions: MOVE; LOAD; UNLOAD; Goal: (AT pkg loc2) • One solution with time step N=4: • Time Step 1: MOVE truck loc2 loc1 • Time Step 2: LOAD pkg truck loc1 • Time Step 3: MOVE truck loc1 loc2 • Time Step 4: UNLOAD pkg truck loc2 Each action is consisted of a set of preconditions and a set of effects 3

  4. Applications • NASA Mars rover • High speed printer in PARC • Hubble space telescope[Zweben94] • Mobile robots[Talamadupula10] • Anti-air defense system[Benaskeur10] • Biological network[Bryce10] • Natural language processing[Geib07] • … Research in “Automated” planning provides a basis for any domain specific planning applications 4

  5. Key Challenge state action Branching factor: O(2A) Number of states: O(2AN) … … … … … … … … A: Number of actions N: Length of plan … … … … … … • Expressiveness • Complicated real world scenarios • High complexity 5

  6. Summayof Dissertation Motivation: Formulation/Representation is vital to problem solving

  7. Agenda • The SAS+ formulation • SAS+ on planning algorithms • Abstraction search • SAS+ formulation as Satisfiability(SASE) • Why SASE works? • Temporally expressive planning • A planning as SAT approach • Apply SASE to temporal planning • Further handle action costs

  8. SAS+ Representation[Backstrom:96] loc1 loc2 Strips SAS+ Transitions pkg:loc1truck pkg:truckloc1 pkg:truckloc2 pkg:loc2truck AT pkg loc1 V(pkg) in truck AT pkg loc2 at loc1 at loc2 IN pkg truck AT truck loc1 V(truck) DTG(Domain Transition Graph) at loc1 at loc2 AT truck loc2 Transition: Change between values in a multi-valued variable 9

  9. SAS+ is more compact fact… fact… fact… fact… fact… fact… fact… fact… fact… fact… fact… fact… … fact… … 2F … … 10F/10 … F: number of STRIPS facts Assume avg. facts/value per DTG is 10 … … … … … … SAS+ also captures more hidden problem structures 10

  10. Causal Dependency and Causal Graph loc1 loc2 LOAD pkg truck loc2: Pre: (AT truck loc2) pkg’s DTG pkg’s DTG in truck truck’s DTG truck’s DTG at loc1 at loc2 at loc1 at loc2 Causal Graph

  11. Example of Hierarchy To build a house 1.a Drive to the city call 1.b Fill out an application 1. Drive to the city hall 2. Fill out an application 3. Drive to the bank 4. Ask for money 5. Drive somewhere 6. Look for a builder 7. Sign a Contract 8. Build foundation 9. Build frame 10. Build roof 11. Build wall 13. Buy furniture … … 1. Get a permit 2. Get enough money 3. Construction 4. Interior … … 2.a Drive to bank 2.b Fill out an application 3.a Find a builder 3.b Sign a contract 3.c Build foundation 3.d Build frame 3.e Build roof 3.f build wall … …

  12. Abstraction State Space loc1 loc2 Abstraction package’s DTG truck’s DTG full state space in truck 1.a MOVE truck loc2 loc1 1.b LOAD pkg truck loc1 LOAD pkg truck loc1 UNLOAD pkg truck loc2 at loc1 at loc2 2.a MOVE truck loc1 loc2 2.b UNLOAD pkg truck loc2

  13. Abstraction State Space Search (Iteration #1) Abstraction State Space DTG DTG Goal1 Goal2 DTG DTG DTG DTG … … … … … … … … DTG DTG DTG DTG Finds a plan quickly

  14. Abstraction State Space Search (Iteration #2) Abstraction State Space G2 G1 DTG DTG DTG DTG DTG DTG … … … … … … … … DTG DTG DTG DTG Keep running to improve the plan quality

  15. Agenda • SAS+ on planning algorithms • Abstraction search • STRIPS based planning as SAT • An encoding completely based on SAS+ (SASE) • Recent work • Why SASE works? • Temporally expressive planning • A planning as SAT approach • Recent work: • Apply SASE to temporal planning • Further handle action costs

  16. Agenda of SAT & SAS+ • Long distance mutual exclusion • Limitations • SAS+ Planning as Satisfiability, a new encoding • Motivation • How it works • Experimental Results • Why it works

  17. Mutual Exclusion (Mutex) (in pkgtruck) (in pkgtruck) (at truck loc1) (at truck loc1) (at truck loc2) (at truck loc2) (at pkg loc1) (at pkg loc1) (at pkg loc2) (at pkg loc2) Move-truck-loc1-loc2 Move-truck-loc2-loc1 A key reason for the efficiency of SAT-based planning • Two facts/actions cannot be true at the same time • Fact mutual exclusion • Action mutual exclusion 18

  18. Mutual Exclusion Invalid Time #1 Time #2 Time #3 #4 #5 #6 #7 #8 #9 #10 (at truck loc1) (at truck loc2)

  19. Long Distance Mutual Exclusion(Londex) DTG of truck (at truck loc1) (at truck loc2) (at truck loc3) (at truck loc4) Invalid #4 Time#1 #5 Time #2 #6 Time #3 #9 #10 #8 #7 (at truck loc1) (at truck loc4) Several limitations

  20. SAS+ Based Encoding (SASE) • Limitations of long distance mutual exclusion • SAS+ not fully exploited • Not memory efficient • We want to make better use of SAS+

  21. Actions versus Transitions Representing Actions: Hierarchical relationships between actions and transitions 22

  22. Motivation: Clumsy Actions :action move :parameters (?a - airplane ?t - planetype ?d1 ?d2- direction ?s1 ?s2 - segment) :effects (occupied ?s2) (blocked ?s2 ?a) (not (occupied ?s1)) (when (not (is-blocked ?s1 ?t ?s2 ?d2)) (not (blocked ?s1 ?a))) (when (not (= ?d1 ?d2)) (not (facing ?a ?d1))) (not (at-segment ?a ?s1)) (forall (?s - segment) (when (is-blocked ?s ?t ?s2 ?d2) (blocked ?s ?a))) (at-segment ?a ?s2) (when (not (= ?d1 ?d2)) (facing ?a ?d2)) ) … … More .. …. :precondition (has-type ?a ?t) (is-moving ?a) (not (= ?s1 ?s2)) (facing ?a ?d1) (can-move ?s1 ?s2 ?d1) (move-dir ?s1 ?s2 ?d2) (at-segment ?a ?s1) (not (exists (?a1 - airplane) (and (not (= ?a1 ?a)) (blocked ?s2 ?a1)))) (forall (?s - segment) (imply (and (is-blocked ?s ?t ?s2 ?d2) (not (= ?s ?s1))) (not (occupied ?s)) )) This action can be break into 7 transitions • AIRPORT benchmark domain[Hoffmann:04] • 10 actions (in first order logic)

  23. Agenda

  24. A Typical Strips Encoding Compile from planning graph Time step 3,4,5,… Time step 1 Time step 2 (at pkg loc1) (at pkg loc1) (at pkg loc1) … … … … … load (in pkg truck) (at truck loc2) (at truck loc2) (at truck loc2) move move (at truck loc1) (at truck loc1) move Planning Graph Nodes (facts, actions) Edges SAT Instance: Variables Clauses Results in a whole chunk of encoding 25

  25. New Encoding, An Overview Planning graph SAT Instance: Facts and actions … … … … … … … Actions& Facts t = 1 t =2 t =3, 4, … Strips Based Encoding Transitions SAT Instance (Part 1): transitions SAT Instance (Part 2): matching actions and transitions (multiple independent ones) Actions … … … t = 1 t =2 t =3 Transition Based Encoding 26

  26. Constraints Time step 1 Time step 2 Time step 3,4,5,… truck:loc2 truck:loc2 truck:loc2 … … … … … truck:loc1 truck:loc1 truck:loc1 pkg: loc1 pkg: loc1 pkg: loc1 pkg: truck pkg: truck pkg: truck pkg: loc2 pkg: loc2 pkg: loc2 Find matchings … … set of actions set of actions • Progression of transitions over time steps (blue one implies green ones) • Initial state and goal (Bold ones) • Matching actions and transitions • Action mutual exclusions and transition mutual exclusions

  27. Results of SASE

  28. Results of SASE

  29. Worst Case State Space Size State Space: O((2A)N) Planning graph Actions … … … … A Number of actions N Number of Time Step … … … Strips Based Encoding t = 1 t =2 t =3, 4, … Transitions State Space (Part 1): O((2T)N) T Number of transitions State Space (Part 2): O(NK) K K K Actions Total: O((2T)NNK) … … … t = 1 t =2 t =3 Transition Based Encoding Note: T < A 30

  30. Why SASE works? 32 • Worst case analysis has limitations • Real SAT solvers do not enumerate • Real SAT solvers may not favor transition variables • We want better understanding • Reason: significance of transition variables • Why more significant? • How much? • Correlates to the speedup?

  31. SAT Algorithms at certain point V10 V1 - V2 V5 V7 Solution Found … … … … No Solution … … No solution Which variable to pick matters 33 • The DPLL procedure • Depth First Search and Inference • Used by almost all SAT solvers

  32. VSIDS Heuristic we probably want to augment the deviation of the h values of all variables 34 • VSIDS Heuristic • Widely used, very effective • h(), number of times a variable appears in all clauses • EMA of all variables’ h(), clause database changes over time Example: (a∨b∨c) ; (a∨d); (a∨b∨d) h(a) = 3; h(b) = 2; h(c)=1 • What kind of instances make VSIDS effective and what kind of instances not? • Consider an extreme case: random SAT

  33. h() on SASE Instances … … … … Transitions K K K … … … t = 1 t =2 t =3 Actions 36

  34. h() on IPC Domains Action variables even do not exist in top percentage of variables 37

  35. Significance of Transition Variables 38 • If we ranking all variables by h • Transition variables dominates the head of the list • More likely to be picked as decision variables earlier (statistically) • But VSIDS heuristic dynamically updates … • We need evidence that reflects the dynamic updating

  36. Branching Frequency V10 V1 - V2 V7 V5 For every 1000 consecutive decision variables … … … … … … 39 A measurement of how often transition variables (or action variables) are chosen as decision variable

  37. Branching Frequency Zenotravel#15 Speedup = 4.21 Openstack #5 Speedup = 7.88 40 Transition variables have higher branching frequency in most instances

  38. Branching Frequency Storage #12 Speedup = 0.83 Sokoban#8 Speedup = 0.62 41 SASE could be less efficient in a few domains

  39. Transition Index The ratio of transition variables in the top ranked p percent variables Normalized by the ratio of transition variables among all variables 42 Transitions variables are more likely to be decision variables The more branching on transition variables, the higher speedup Transition Index : An indicator of the significance

  40. Transition Index versus Speedup Transition index of 1% Transition index of 10% 43

  41. Transition Index versus Speedup Transition index of 50% Transition index of 90% 44

  42. Conclusions 45 Transition variables occurs more frequently Transition index correlates with the speedup that SASE can achieve

  43. Outline Automated Planning Classical Planning Temporally Expressive Planning STRIPS SAS+ STRIPS SAS+ Search SAT Search SAT Search SAT SAT 4

  44. Temporal Planning e.g. got a blackout: Light a Match Repair a fuse find a manual Time 47 Actions have durations

  45. Temporally Expressive[W. Cushing et al. 2007] Read Manual condition condition requires condition (has light) Light a match • A planning algorithm is temporally expressive if it can handle required concurrency, otherwise it is temporally simple adds fact (has light) deletes fact (has light) Time • Temporally Expressive (Required Concurrency) • Two actions need to be executed in parallel, in any valid plan. 48

  46. Facts about State-of-the-art • Required Concurrency is important in the real world • PDDL2.1 supports temporally expressiveness • e.g. Firework, Missile launch • Most state of the art temporal planners are not able to handle temporally expressive • Action cost is in addition an important feature • No planner can handle both temporal expressiveness and action costs 49

  47. Overview of Our Work Temporally Expressive planning PDDL2.1 Spec STRIPS A STRIPS based encoding [Huang09] SAS+ Extend to support action costs Cost Sensitive Temporally Expressive Planning SASE for temporal planning A MinCost SAT Formulation MaxSAT solvers A Branch & Bound Algorithm 50

  48. Durative Actions as SAS+ Light a match Light a match adds fact (has light) deletes fact (has light) Time Time 51

  49. SASE with Durative Actions

  50. Experimental Results PET and SET are our SAT-based approach, with different encoding schemes; Crikey2, Crikey3, TFD, LPG-c are several heuristic search based planners 53

More Related