Introduction Classical planning Neoclassical planning Heuristics Planning in the real world. Automated Planning. PLG Group

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1 Automated Planning PLG Group Universidad Carlos III de Madrid AI Automated Planning 1

2 Indice 1 Introduction 2 Classical planning 3 Neoclassical planning 4 Heuristics Hierarchical Task Networks Control knowledge Machine learning 5 Planning in the real world Automated Planning 2

3 Indice 1 Introduction 2 Classical planning 3 Neoclassical planning 4 Heuristics Hierarchical Task Networks Control knowledge Machine learning 5 Planning in the real world Automated Planning 3

4 Indice 1 Introduction 2 Classical planning 3 Neoclassical planning 4 Heuristics Hierarchical Task Networks Control knowledge Machine learning 5 Planning in the real world Automated Planning 4

5 Indice 1 Introduction 2 Classical planning 3 Neoclassical planning 4 Heuristics Hierarchical Task Networks Control knowledge Machine learning 5 Planning in the real world Automated Planning 5

6 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

7 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

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:

8 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) = min [1 + g s(pre(o))] o O(p) otherwise g s (C) with C being a set of literals can be computed as: Additive: g s + (C) = g s (r) Max: g max s r C (C) = max r C g s(r) Automated Planning 8

p s g s (p) = min [1 + g s(pre(o))] o O(p) otherwise g s (C) with C being a set of literals can be

9 Example g(en mesa(b)) = 2 g(encima(c,b)) = 3 g+ = 2+3 = 5 gmax = max {2,3} = 3 Estado inicial encima(b,c) libre(b) C B Estado final QUITAR(B,C) B C sujeto(b) DEJAR(B) en mesa(b) en mesa(b) libre(b) LEVANTAR(B) libre(c) encima(c,x) QUITAR(C,x) sujeto(c) libre(b) DEJAR(C,B) sujeto(c) libre(b) PONER(C,B) encima(c,b) sujeto(c) DEJAR(C) libre(c) en mesa(c) LEVANTAR(C) libre(b) encima(b,c) QUITAR(B,C) B C Estado inicial Automated Planning 9

libre(c) encima(c,x) QUITAR(C,x) sujeto(c) libre(b) DEJAR(C,B) sujeto(c) libre(b) PONER(C,B) encima(c,b)

10 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

h( ) h add does not account for the interactions among operators.

11 GRAPHPLAN 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: Tipically h(s) h add h(s) = i=0,...,m 1 O i Automated Planning 11

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,.

12 Example Nivel 0 libre(b) encima(b,c) en mesa(c) B C QUITAR (B,C) Nivel 1 libre(b) encima(b,c) en mesa(c) sujeto(b) libre(c) LEVANTAR (C) DEJAR (B) Nivel 2 encima(b,c) en mesa(c) sujeto(b) libre(c) sujeto(c) en mesa(b) libre(b) PONER (C,B) Nivel 3 encima(b,c) en mesa(c) sujeto(b) libre(c) sujeto(c) en mesa(b) encima(c,b) libre(c) C B Solucion = {QUITAR(B,C), <LEVANTAR(C),DEJAR(B)>, PONER(C,B)} h(s) = = 4 Automated Planning 12

mesa(b) libre(b) PONER (C,B) Nivel 3 encima(b,c) en mesa(c) sujeto(b) libre(c) sujeto(c) en mesa(b)

13 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: NOOPS-First Dificulty measures: dif (o) = p pre(o) Linearized sets of actions min{i p appears in layer i} Automated Planning 13

not find any solution The computation of the relaxed GRAPHPLAN is improved trying to compute the shortest paths:

14 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 METRIC-FF: cost-based FF [Hoffmann, 2003] Automated Planning 14

of the relaxed GRAPHPLAN is improved trying to compute the shortest paths: NOOPs-First Difficulty measures: dif (o) =

15 Indice 1 Introduction 2 Classical planning 3 Neoclassical planning 4 Heuristics Hierarchical Task Networks Control knowledge Machine learning 5 Planning in the real world Automated Planning 15

16 References Blai Bonet and Hector Geffner. Planning as heuristic search. Artificial Intelligence, 129(1-2):5 33, Jörg Hoffmann and Bernhard Nebel. The FF planning system: Fast plan generation through heuristic search. Journal of Artificial Intelligence Research, 14: , Jörg Hoffmann. The Metric-FF planning system: Translating ignoring delete lists to numeric state variables. Journal of Artificial Intelligence Research, 20: , Judea Pearl. Heuristics: Intelligent Search Strategies for Computer Problem Solving. Automated Planning 16

Journal of Artificial Intelligence Research, 14:253 302, 2001. Jörg Hoffmann.

17 Addison-Wesley, Automated Planning 17

Optimal Planning with ACO

Optimal Planning with ACO M.Baioletti, A.Milani, V.Poggioni, F.Rossi Dipartimento Matematica e Informatica Universit di Perugia, ITALY email: {baioletti, milani, poggioni, rossi}@dipmat.unipg.it Abstract.