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Lecture 21 State-Space Search vs. Constraint-Based Planning

Lecture 21 State-Space Search vs. Constraint-Based Planning. CSE 573 Artificial Intelligence I Henry Kautz Fall 2001. Road Map. Today Plan graphs Planning as state space search Comparison of the two approaches. Graphplan. Planning as graph search (Blum & Furst 1995)

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Lecture 21 State-Space Search vs. Constraint-Based Planning

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  1. Lecture 21State-Space Search vs. Constraint-Based Planning CSE 573 Artificial Intelligence I Henry Kautz Fall 2001 CSE 573

  2. Road Map • Today • Plan graphs • Planning as state space search • Comparison of the two approaches CSE 573

  3. Graphplan • Planning as graph search (Blum & Furst 1995) Set new paradigm for planning • Like SATPLAN... • Two phases: instantiation of propositional structure, followed by search • Unlike SATPLAN... • Interleaves instantiation and pruning of plan graph • Employs specialized search engine • Graphplan - better instantiation • SATPLAN - better search CSE 573

  4. Graph Pruning • Graphplan instantiates in a forward direction, pruning unreachable nodes • conflicting actions are mutex • if all actions that add two facts are mutex, the facts are mutex • if the preconditions for an action are mutex, the action is unreachable! • In logical terms: limited application of resolution where one clause is negative binary • given:  P V  Q, P V R V S V ... • infer:  Q V R V S V ... CSE 573

  5. mutually exclusive add effects delete effects The Plan Graph Facts Facts Actions Actions Facts Facts ... ... ... ... preconditions CSE 573

  6. The Plan Graph Facts Facts Actions Actions Facts Facts ... ... ... ... preconditions CSE 573

  7. add effects delete effects The Plan Graph Facts Facts Actions Actions Facts Facts ... ... ... ... preconditions CSE 573

  8. Translation of Plan Graph Pre1 Act1 Fact Pre2 Act2 • Fact  Act1  Act2 • Act1  Pre1  Pre2 • ¬Act1  ¬Act2 CSE 573

  9. Improved Encodings • Translations of Logistics.a: • STRIPS  Axiom Schemas  SAT (Medic system, Weld et. al 1997) • 3,510 variables, 16,168 clauses • 24 hours to solve • STRIPS  Plan Graph  SAT (Blackbox) • 2,709 variables, 27,522 clauses • 5 seconds to solve! CSE 573

  10. Blackbox = Reachability + Satisfiability • Blackbox Planner(Kautz 1997) uses the first part of Graphplan (reachability analysis) to determine which propositions to instantiate • Then formula is generated (up to a bounded length K) and checked for SAT • can specify Walksat, various kinds of DP • current best: CHAFF (version DP) • can also run Graphplan on reachability graph for a few seconds to catch “easy” cases • If a solution found, then model is translated back to a parallel plan • Else max length K is incremented, and repeat CSE 573

  11. Results: Logistics Planning • Blackbox • Graphplan • rocket.b • 5 sec • 55 sec • logistics.a • 5 sec • 31 minutes • logistics.b • 7 sec • 13 minutes • logistics.c • 9 sec • > 24 hours • logistics.d • 28 sec • > 24 hours CSE 573

  12. How Well Does it Work? • 1992 – first incarnation of SATPLAN (Kautz & Selman), competitive with other planners (UCPOP) at the time • 1995 – Graphplan (Blum & Furst) best planning algorithm • Constraint-satisfaction style solver, but no explicit translation to SAT • Blew everything previous out of the water! • 1996 – SATPLAN with new SAT solvers (walksat+new local search heuristics, satz-rand, etc.) • competitive with Graphplan – sometimes much faster – but requires hand-written axioms • 1998 – Debut of Blackbox • Generates axioms automatically from STRIPS operators • Beats Graphplan when size & cost of generating formula small compared to graph search cost • Some domains kill it by blowing up size of formula: Blocks World, “Gripper” • Overall “winners” at AIP-98 competition were all constraint-based approaches (variants of SATPLAN and Graphplan) CSE 573

  13. AIPS-2000 • Another planning competition at the AI and Planning Systems Conference 2000 provided a big surprise: • Fastest planners were all based on A* search! • Heuristics derived automatically from STRIPS encoding • Issues: • How to derive a search heuristic • How does A* really compare with constraint-based planning (Graphplan / SATPLAN / Blackbox)? CSE 573

  14. Planning as A* Search • Simple formulation: • State = node in search tree • Action = arc in search tree • Distance to goal = number of actions in plan • Note: purely sequential plans (no parallelism) • Search heuristic: estimate of distance to goal • How to estimate? Ideas? CSE 573

  15. Search Heuristics • Count number of false goal propositions in current state Admissible? • Delete all preconditions from actions, solve easy relaxed problem, use length Admissible? • Delete negative effects from actions, solve easier relaxed problem, use length Admissible? CSE 573

  16. AIPS-2000 Planning Competition • Fast-Forward (FF) • Joerg Hoffmann & Bernhard Nebel (Albert-Ludwigs-University Freiburg, Germany) • “Delete negative effects” heuristic • Competed in fully automated track of the 2nd International Planning Systems Competition (AIPS 2000 conference in Breckenridge, CO) • Granted ``Group A distinguished performance Planning System'‘ • Schindler Award for the best performing planning system in the Miconic 10 Elevator domain • AIPS 2002 – Toulouse, France • Now, don’t you wish you were doing research on planning? CSE 573

  17. BB vs FF CSE 573

  18. Hardness of Planning • FF (and other state-space planners) find solutions with unbalanced use of airplanes – little opportunities for post-facto parallelization • Logistics domain is actually polytime solvable if parallel plan length not considered! • NP-hard to find a solution with minimum parallel length • Huang, Kautz, Selman 2002 – modify STRIPS operators to force solutions to be ones that can be parallelized! CSE 573

  19. (:action FLY-AIRPLANE :parameters (?airplane ?loc-from ?loc-to ?r) :precondition (and (AIRPLANE ?airplane) (AIRPORT ?loc-from) (AIRPORT ?loc-to) (at ?airplane ?loc-from) (can_use ?airplane ?r) (resource ?r)) :effect (and (not (at ?airplane ?loc-from)) (not (resource ?r)) (at ?airplane ?loc-to))) ) (:init (at package bos-po) ... (resource r1) (resource r2) (resource r3) (resource r4) (can_use airplane1 r1) (can_use airplane1 r2) (can_use airplane2 r3) (can_use airplane2 r4) ...) (:goal (at package la-po) ...) Modified STRIPS Logistics CSE 573

  20. BB vs FF (modified logistics) CSE 573

  21. Coming Up • Wednesday • Prob(Prob) = 100% • Ch 14 – Review of basic probability theory • Ch 15 – start on Bayesian networks • Change in schedule • Only one more homework (not two), distributed Nov 28th CSE 573

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