CSE 573 1

Lecture 21State-Space Search vs. Constraint-

Based Planning

CSE 573Artificial

Intelligence IHenry Kautz

Fall 2001

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Road Map

• Today• Plan graphs• Planning as state space search• Comparison of the two approaches

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Graphplan

Planning as graph search (Blum & Furst 1995)Set new paradigm for planning

Like SATPLAN...• Two phases: instantiation of propositional

structure, followed by searchUnlike SATPLAN...

• Interleaves instantiation and pruning of plan graph

• Employs specialized search engineGraphplan - better instantiationSATPLAN - better search

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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 ...

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The Plan Graph

Facts FactsActions

... ...

Facts FactsActions

... ...preconditions

mutually exclusive

add effectsdelete effects

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The Plan Graph

Facts FactsActions

... ...

Facts FactsActions

... ...preconditions

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The Plan Graph

Facts FactsActions

... ...

Facts FactsActions

... ...preconditions add effects

delete effects

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Translation of Plan Graph

Fact Act1 Act2Act1 Pre1 Pre2

¬Act1 ¬Act2

Act1

Act2

Fact

Pre1

Pre2

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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!

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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

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Results: Logistics Planning

> 24 hours28 seclogistics.d

> 24 hours9 seclogistics.c

13 minutes7 seclogistics.b

31 minutes5 seclogistics.a

55 sec5 secrocket.b

GraphplanBlackbox

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How Well Does it Work?1992 – first incarnation of SATPLAN (Kautz & Selman),

competitive with other planners (UCPOP) at the time1995 – 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 axioms1998 – 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)

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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

encodingIssues:

• How to derive a search heuristic• How does A* really compare with constraint-

based planning (Graphplan / SATPLAN / Blackbox)?

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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?

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Search Heuristics

1. Count number of false goal propositions in current state

Admissible?2. Delete all preconditions from actions, solve

easy relaxed problem, use lengthAdmissible?

3. Delete negative effects from actions, solve easier relaxed problem, use length

Admissible?

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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, FranceNow, don’t you wish you were doing research on planning?

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BB vs FF

problem BB FFtime flights time flights

log-a 1.20 (3,4) 0.08 (4,0)

log-b 2.06 (4,2) 0.09 (5,0)

log-c 3.08 (4,5) 0.09 (6,0)

log-d 7.75 (5,3) 0.25 (7,0)

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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!

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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) ...)

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BB vs FF (modified logistics)

problem BB FFtime time

log-a(3,2)

1.71 0.12

log-b(3,1)

2.37 1.61

log-c(3,2)

9.96 > 4 hours

log-d(3,4)

155.1 > 4 hours

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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