Projection Global Consistency: Application in AI Planning

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Projection Global ConsistencyApplication in AI
Planning

• Pavel Surynek
• Charles University, PragueCzech Republic

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Outline of the presentation
CSCLP 2006
Pavel Surynek

• Problem select a set of non-mutex actions
  supporting a goal
• Obstacle NP-complete
• (Partial) solution global consistency -
  projection consistency
• Application AI Planning using planning graphs
• Experiments several planning domains

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Problem - support problem
CSCLP 2006
Pavel Surynek

• solution - mutex free

• Goal finite set of atoms
• Action triple (preconditions, positive effects,
  negative effects)

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Mutex actions
CSCLP 2006
Pavel Surynek

• (two) actionsload(small_truck,box1)load(big_truc
  k,box2)are independent

• (two) actionsload(small_truck,box1)load(big_truc
  k,box1)are dependent

• example of action
• load(small_truck, box1) (empty(truck),
  on(bottom, box1) loaded(box1, truck)
  empty(truck), on(bottom, box1))
• generalized dependency mutex

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Obstacle - NP completeness
CSCLP 2006
Pavel Surynek

• Instance
• goal augmented with finite sets of supporting
  actions
• finite set of mutexes between actions
• Answer
• set of non-mutex actions supporting the goal
• NP-complete
• SAT instance in CNF ??? support problem

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Projection consistency
CSCLP 2006
Pavel Surynek

• Interpret support problem as a graph
• Greedily find (vertex disjoint) cliques ???
• ??? clique decomposition
• At most one action from each clique can be
  selected

• a real support problem
• Trucks, Cranes, Locations

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Counting argument
CSCLP 2006
Pavel Surynek

• Clique decomposition C1, C2,..., Ck
• Contribution of an action a
• c(a) number of supported atoms
• Contribution of a clique C
• c(C) maxa?C c(a)
• Counting argument (simplest form)
• if ?i1...k c(Ci) lt size of the goal ?????? the
  goal is unsatisfiable
• Generalized form projection consistency
• w.r.t. sub-goals and singleton approach

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Application AI Planning
CSCLP 2006
Pavel Surynek

• Planning problem
• Initial state set of atoms
• Set of allowed actions
• Goal set of atoms (literals)
• Task
• determine a sequenceof actions
  transforminginitial state to the goal
• Solution planning graphs and GraphPlan algorithm
  (Blum Furst, 1997) - support problem arise as a
  frequent sub-problem

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Experiments towers of Hanoi
CSCLP 2006
Pavel Surynek

• Original puzzle (3 pegs, 4 discs, and 1 hand)

• Our generalization (more pegs, discs, and hands)

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Experiments DWR
CSCLP 2006
Pavel Surynek

• Locations with several places for stacks of boxes
  and with several cranes

• Each crane can reach some stacks within location
  (not all)

• Trucks of various capacities (small - 1 box, big
  - 2 boxes)

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Experiments Refueling planes
CSCLP 2006
Pavel Surynek

• Several planes dislocated at several airports

• Transport a fleet of planes at destination airport

• Airport - unlimited source of fuel, planes can
  refuel in-flight

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Experiments Results
CSCLP 2006
Pavel Surynek

• Significant improvements on problems with high
  action parallelism (Dock Worker Robots, Refueling
  Planes, Hanoi Towers with more hands)

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Conclusions
CSCLP 2006
Pavel Surynek

• Improvement of the GraphPlan algorithm
• Better method for finding mutex free set of
  actions supporting a goal
• We use projection consistency
• Experimental evaluation
• Projection consistency especially successful on
  problems with high action parallelism