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Projection Global Consistency: Application in AI Planning Pavel Surynek Charles University, Prague Czech Republic

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Outline of the presentation Problem: select a set of non-mutex actions supporting a goal Problem: select a set of non-mutex actions supporting a goal Obstacle: NP-complete Obstacle: NP-complete (Partial) solution: global consistency - projection consistency (Partial) solution: global consistency - projection consistency Application: AI Planning using planning graphs Application: AI Planning using planning graphs Experiments: several planning domains Experiments: several planning domains CSCLP 2006 Pavel Surynek

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Problem - support problem Goal = finite set of atoms Goal = finite set of atoms Action = triple (preconditions, positive effects, negative effects) Action = triple (preconditions, positive effects, negative effects) CSCLP 2006 Pavel Surynek Goal: A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 x atom 1 atom 2 atom 3atom 4 supports for atom 1 supports for atom 2 supports for atom 3 supports for atom 4 x x x x x x x A1 A2 A3 A4 A6 A9 A8 A10 A11 A12 A5 A7 solution - mutex free

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Mutex actions CSCLP 2006 Pavel Surynek (two) actions load(small_truck,box1) load(big_truck,box2) are independent ( two) actions load(small_truck,box1) load(big_truck,box1) are dependent example of action example of action –load(small_truck, box1) = ({empty(truck), on(bottom, box1)}; {loaded(box1, truck)}; {¬empty(truck), ¬on(bottom, box1)}) generalized dependency = mutex generalized dependency = mutex

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Obstacle - NP completeness Instance: Instance: –goal augmented with finite sets of supporting actions –finite set of mutexes between actions Answer: Answer: –set of non-mutex actions supporting the goal NP-complete NP-complete –SAT instance in CNF ►►► support problem CSCLP 2006 Pavel Surynek

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Projection consistency Interpret support problem as a graph Interpret support problem as a graph Greedily find (vertex disjoint) cliques ►►► Greedily find (vertex disjoint) cliques ►►► ►►► clique decomposition ►►► clique decomposition At most one action from each clique can be selected At most one action from each clique can be selected CSCLP 2006 Pavel Surynek a real support problem Trucks, Cranes, Locations

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Counting argument Clique decomposition C 1, C 2,..., C k Clique decomposition C 1, C 2,..., C k Contribution of an action a Contribution of an action a c(a) = number of supported atoms Contribution of a clique C Contribution of a clique C c(C) = max a C c(a) Counting argument (simplest form) Counting argument (simplest form) if ∑ i=1...k c(C i ) < size of the goal ►►► ►►► the goal is unsatisfiable Generalized form = projection consistency Generalized form = projection consistency – w.r.t. sub-goals and singleton approach CSCLP 2006 Pavel Surynek

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Application: AI Planning Planning problem Planning problem – Initial state: set of atoms – Set of allowed actions – Goal: set of atoms (literals) Task Task – determine a sequence of actions transforming initial state to the goal Solution: planning graphs and GraphPlan algorithm (Blum & Furst, 1997) - support problem arise as a frequent sub-problem Solution: planning graphs and GraphPlan algorithm (Blum & Furst, 1997) - support problem arise as a frequent sub-problem CSCLP 2006 Pavel Surynek location B location C location A 5 6 location D location E location F location B location C location A 5 location D location E location F

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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 distance X distance Y distance Z 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 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 CSCLP 2006 Pavel Surynek

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