Introduction Classical planning Neoclassical planning Heuristics Planning in the real world Automated Planning PLG Group Universidad Carlos III de Madrid AI. 2008-09 Automated Planning 1
Introduction Classical planning Neoclassical planning Heuristics Planning in the real world Indice Introduction 1 Classical planning 2 Neoclassical planning 3 Heuristics 4 Heuristic planning Hierarchical Task Networks Control knowledge Machine learning Planning in the real world 5 Automated Planning 2
Introduction Classical planning Neoclassical planning Heuristics Planning in the real world Indice Introduction 1 Classical planning 2 Neoclassical planning 3 Heuristics 4 Heuristic planning Hierarchical Task Networks Control knowledge Machine learning Planning in the real world 5 Automated Planning 3
Introduction Classical planning Neoclassical planning Heuristics Planning in the real world Indice Introduction 1 Classical planning 2 Neoclassical planning 3 Heuristics 4 Heuristic planning Hierarchical Task Networks Control knowledge Machine learning Planning in the real world 5 Automated Planning 4
Introduction Classical planning Neoclassical planning Heuristics Planning in the real world Indice Introduction 1 Classical planning 2 Neoclassical planning 3 Heuristics 4 Heuristic planning Hierarchical Task Networks Control knowledge Machine learning Planning in the real world 5 Automated Planning 5
Introduction Classical planning Neoclassical planning Heuristics Planning in the real world Heuristic planning Types of heuristics Domain-independent : they can be safely used in any domain, tipically for the selection of descendants Domain-dependent : especially devised for a given domain, they are usually employed for all the other steps Real planners do consist of a mixture of both! Domain-independence ensures soundness Domain-dependence improves the performance General idea : to automatically define domain-independent heuristic functions as opposed to ad-hoc domain-dependent functions as in the N -puzzle or the Sokoban domains. Automated Planning 6
Introduction Classical planning Neoclassical planning Heuristics Planning in the real world Heuristic planning Heuristics as relaxed problems Origin of heuristics: optimal solutions to relaxed problems [Pearl, 1983] Relaxations are derived by dropping literals from the delete lists: given P = ( O , I , G ) , its relaxation P ′ is defined as P ′ = ( O ′ , I , G ) where: O ′ = { ( pre ( o ) , add ( o ) , ∅ ) | ( pre ( o ) , add ( o ) , del ( o )) ∈ O} A sequence of actions is a relaxed plan if and only if it is a solution of the relaxed task P ′ of the original problem P : The closer P ′ to P , the more informed the resulting heuristic function, h ( · ) The more simplified P ′ , the easiest to compute h ( · ) Automated Planning 7
Introduction Classical planning Neoclassical planning Heuristics Planning in the real world Heuristic planning Relaxation on reachability Let us define the minimum distance from state s to literal p , g s ( p ) , as the minimum number of required actions to step from s to another state that embraces p : � 0 si p ∈ s g s ( p ) = o ∈ O ( p ) [ 1 + g s ( pre ( o ))] min otherwise g s ( C ) with C being a set of literals can be computed as: Additive: g + s ( C ) = � g s ( r ) r ∈ C Max: g max ( C ) = max r ∈ C g s ( r ) s Automated Planning 8
Introduction Classical planning Neoclassical planning Heuristics Planning in the real world Heuristic planning Example g(en−mesa(B)) = 2 g(encima(C,B)) = 3 g+ = 2+3 = 5 B brazo−libre gmax = max {2,3} = 3 sujeto(C) libre(B) C sujeto(C) encima(B,C) libre(B) Estado inicial B DEJAR(C,B) DEJAR(C) QUITAR(B,C) C Estado inicial libre(C) libre(C) encima(B,C) en−mesa(B) encima(C,x) en−mesa(C) libre(B) libre(B) brazo−libre brazo−libre brazo−libre brazo−libre QUITAR(C,x) LEVANTAR(C) QUITAR(B,C) LEVANTAR(B) sujeto(C) sujeto(B) libre(B) C DEJAR(B) B PONER(C,B) Estado final en−mesa(B) encima(C,B) Automated Planning 9
Introduction Classical planning Neoclassical planning Heuristics Planning in the real world Heuristic planning Heuristic Search Planning (HSP) [Bonet and Geffner, 2001] HSP: it employs the heuristic function h add = g + s for guiding a hill-climbing search algorithm from s —i.e., progression HSP2: it makes use of the heuristic function h add along with a BFS search algorithm from s Drawbacks: HSP takes up to 80% of the time for computing h ( · ) h add does not account for the interactions among operators. Thus, it looks for suboptimal sequential plans instead of optimal parallel plans Alternatives: HSPr (plus regression ), GRT (bidirectional search) or, more recently HSP ∗ To use GRAPHPLAN as a mean for capturing the interaction among operators Automated Planning 10
Introduction Classical planning Neoclassical planning Heuristics Planning in the real world Heuristic planning G RAPHPLAN as a heuristic Let P ′ = ( O ′ , I , G ) be a relaxed problem.GRAPHPLAN is guaranteed to do not find any mutex, since there are no deletes ! GRAPHPLAN is known to find a solution to P ′ in polynomial time in l (the largest add list), |I| and |O ′ | : � O 0 , O 1 , . . . , O m − 1 � where O i is the set of selected operators in layer i and m is the goal layer FF employs the following heuristic function: � h ( S ) = | O i | i = 0 ,..., m − 1 Tipically h ( S ) ≤ h add Automated Planning 11
Introduction Classical planning Neoclassical planning Heuristics Planning in the real world Heuristic planning Example Nivel 3 Nivel 1 Nivel 2 Nivel 0 encima(B,C) en−mesa(C) encima(B,C) sujeto(B) en−mesa(C) brazo−libre libre(C) B sujeto(B) sujeto(C) libre(B) libre(C) en−mesa(B) encima(B,C) C en−mesa(C) LEVANTAR (C) sujeto(C) encima(C,B) en−mesa(B) PONER (C,B) libre(C) brazo−libre sujeto(B) DEJAR (B) libre(B) brazo−libre libre(B) QUITAR (B,C) libre(C) brazo−libre encima(B,C) en−mesa(C) C B Solucion = {QUITAR(B,C), <LEVANTAR(C),DEJAR(B)>, PONER(C,B)} h(S) = 1 + 2 + 1 = 4 Automated Planning 12
Introduction Classical planning Neoclassical planning Heuristics Planning in the real world Heuristic planning Fast-Forward Plan Generation (FF) [Hoffmann and Nebel, 2001] FF: it makes use of the heuristic function h ( S ) with a variant of breadth-first search known as enforced hill-climbing which is substituted by a BFS when the former does not find any solution The computation of the relaxed GRAPHPLAN is “ improved ” trying to compute the shortest paths: NOOP S -First Dificulty measures: � dif ( o ) = min { i | p appears in layer i } p ∈ pre ( o ) Linearized sets of actions Automated Planning 13
Introduction Classical planning Neoclassical planning Heuristics Planning in the real world Heuristic planning FF [Hoffmann and Nebel, 2001] FF: it makes use of the heuristic function h(S) with a variant of breadth-first search known as enforced hill-climbing which is substituted by a BFS when the former does not find any solution The computation of the relaxed GRAPHPLAN is “improved” trying to compute the shortest paths: NOOPs-First Difficulty measures: � dif ( o ) = min { i | p appears in layer i } p ∈ pre ( o ) Linearized sets of actions M ETRIC -FF: cost-based FF [Hoffmann, 2003] Automated Planning 14
Introduction Classical planning Neoclassical planning Heuristics Planning in the real world Indice Introduction 1 Classical planning 2 Neoclassical planning 3 Heuristics 4 Heuristic planning Hierarchical Task Networks Control knowledge Machine learning Planning in the real world 5 Automated Planning 15
Introduction Classical planning Neoclassical planning Heuristics Planning in the real world References Blai Bonet and Hector Geffner. Planning as heuristic search. Artificial Intelligence , 129(1-2):5–33, 2001. J¨ org Hoffmann and Bernhard Nebel. The FF planning system: Fast plan generation through heuristic search. Journal of Artificial Intelligence Research , 14:253–302, 2001. J¨ org Hoffmann. The Metric-FF planning system: Translating “ignoring delete lists” to numeric state variables. Journal of Artificial Intelligence Research , 20:291–341, 2003. Judea Pearl. Heuristics: Intelligent Search Strategies for Computer Problem Solving . Automated Planning 16
Introduction Classical planning Neoclassical planning Heuristics Planning in the real world Addison-Wesley, 1983. Automated Planning 17
Recommend
More recommend
