CSE 5731 Lecture 21 State-Space Search vs. Constraint- Based Planning CSE 573 Artificial Intelligence I Henry Kautz Fall 2001

CSE 5732 Road Map Today Plan graphs Planning as state space search Comparison of the two approaches

CSE 5733 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 5734 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 5735 The Plan Graph Facts Actions... Facts Actions... preconditions mutually exclusive add effects delete effects

CSE 5736 The Plan Graph Facts Actions... Facts Actions... preconditions

CSE 5737 The Plan Graph Facts Actions... Facts Actions... preconditions add effects delete effects

CSE 5738 Translation of Plan Graph Fact  Act1  Act2 Act1  Pre1  Pre2 ¬Act1  ¬Act2 Act1 Act2 Fact Pre1 Pre2

CSE 5739 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 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 Results: Logistics Planning > 24 hours28 seclogistics.d > 24 hours9 seclogistics.c 13 minutes7 seclogistics.b 31 minutes5 seclogistics.a 55 sec5 secrocket.b GraphplanBlackbox

CSE 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 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 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 Search Heuristics 1.Count number of false goal propositions in current state Admissible? 2.Delete all preconditions from actions, solve easy relaxed problem, use length Admissible? 3.Delete negative effects from actions, solve easier relaxed problem, use length Admissible?

CSE 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 BB vs FF problemBBFF timeflightstimeflights log-a1.20(3,4)0.08(4,0) log-b2.06(4,2)0.09(5,0) log-c3.08(4,5)0.09(6,0) log-d7.75(5,3)0.25(7,0)

CSE 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 Modified STRIPS Logistics (: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)... )

CSE BB vs FF (modified logistics) problemBBFF time log-a (3,2) log-b (3,1) log-c (3,2) 9.96> 4 hours log-d (3,4) 155.1> 4 hours

CSE 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 28 th