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

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

• CSE 573
• Artificial Intelligence I
• Henry 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 search
• Unlike SATPLAN...
• Interleaves instantiation and pruning of plan
  graph
• Employs specialized search engine
• Graphplan - better instantiation
• SATPLAN - 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
Facts
Actions
Facts
Facts
Actions
...
...
...
...
preconditions
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The Plan Graph
Facts
Facts
Actions
Facts
Facts
Actions
...
...
...
...
preconditions
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The Plan Graph
Facts
Facts
Actions
Facts
Facts
Actions
...
...
...
...
preconditions
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Translation of Plan Graph
Act1
Pre1
Fact
Pre2
Act2
Fact ? Act1 ? Act2 Act1 ? Pre1 ? Pre2 Act1 ?
Act2
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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
Graphplan
Blackbox
55 sec
5 sec
rocket.b
31 minutes
5 sec
logistics.a
13 minutes
7 sec
logistics.b
gt 24 hours
9 sec
logistics.c
gt 24 hours
28 sec
logistics.d
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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 (walksatnew
  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)

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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
  encoding
• Issues
• 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

• 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?

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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, France
• Now, dont you wish you were doing research on
  planning?

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BB vs FF
problem BB FF
time 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 FF
time time
log-a(3,2) 1.71 0.12
log-b(3,1) 2.37 1.61
log-c(3,2) 9.96 gt 4 hours
log-d(3,4) 155.1 gt 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