Automated Planning PLG Group Universidad Carlos III de Madrid AI. - - PowerPoint PPT Presentation

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

1

Introduction

2

Classical planning

3

Neoclassical planning

4

Heuristics Heuristic planning Hierarchical Task Networks Control knowledge Machine learning

5

Planning in the real world

Automated Planning 2

Introduction Classical planning Neoclassical planning Heuristics Planning in the real world

Indice

1

Introduction

2

Classical planning

3

Neoclassical planning

4

Heuristics Heuristic planning Hierarchical Task Networks Control knowledge Machine learning

5

Planning in the real world

Automated Planning 3

Introduction Classical planning Neoclassical planning Heuristics Planning in the real world

Indice

1

Introduction

2

Classical planning

3

Neoclassical planning

4

Heuristics Heuristic planning Hierarchical Task Networks Control knowledge Machine learning

5

Planning in the real world

Automated Planning 4

Introduction Classical planning Neoclassical planning Heuristics Planning in the real world

Indice

1

Introduction

2

Classical planning

3

Neoclassical planning

4

Heuristics Heuristic planning Hierarchical Task Networks Control knowledge Machine learning

5

Planning in the real world

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.

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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(· )

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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, gs(p), as the minimum number of required actions to step from s to another state that embraces p: gs(p) = si p ∈ s min

• ∈O(p)[1 + gs(pre(o))]
• therwise

gs(C) with C being a set of literals can be computed as:

Additive: g+

s (C) = r∈C

gs(r) Max: gmax

s

(C) = max

r∈C gs(r)

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Introduction Classical planning Neoclassical planning Heuristics Planning in the real world Heuristic planning

Example

encima(B,C) libre(B) brazo−libre libre(B) brazo−libre en−mesa(B) libre(B) sujeto(C) libre(C) en−mesa(C) brazo−libre brazo−libre libre(B) encima(B,C) sujeto(C) libre(B) C B B C g(en−mesa(B)) = 2 g(encima(C,B)) = 3 g+ = 2+3 = 5 gmax = max {2,3} = 3 B C DEJAR(B) LEVANTAR(B) QUITAR(B,C) en−mesa(B) encima(C,B) PONER(C,B) sujeto(B) QUITAR(C,x) LEVANTAR(C) libre(C) brazo−libre encima(C,x) DEJAR(C) QUITAR(B,C) DEJAR(C,B) sujeto(C)

Estado inicial Estado final Estado inicial

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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 hadd = g+

s for guiding a

hill-climbing search algorithm from s —i.e., progression HSP2: it makes use of the heuristic function hadd along with a BFS search algorithm from s Drawbacks: HSP takes up to 80% of the time for computing h(· ) hadd 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

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Introduction Classical planning Neoclassical planning Heuristics Planning in the real world Heuristic planning

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′|: O0, O1, . . . , Om−1 where Oi is the set of selected

• perators in layer i and m is the goal layer

FF employs the following heuristic function: h(S) =

• i=0,...,m−1

|Oi| Tipically h(S) ≤ hadd

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Introduction Classical planning Neoclassical planning Heuristics Planning in the real world Heuristic planning

Example

encima(B,C) en−mesa(C) libre(B) brazo−libre Nivel 0 QUITAR (B,C) sujeto(B) libre(C) encima(B,C) en−mesa(C) libre(B) brazo−libre Nivel 1 LEVANTAR (C) DEJAR (B) en−mesa(B) libre(B) brazo−libre encima(B,C) en−mesa(C) sujeto(B) libre(C) sujeto(C) Nivel 2 B C encima(B,C) en−mesa(C) C B PONER (C,B) Nivel 3 encima(C,B) brazo−libre libre(C) sujeto(C) sujeto(B) libre(C) en−mesa(B) Solucion = {QUITAR(B,C), <LEVANTAR(C),DEJAR(B)>, PONER(C,B)} h(S) = 1 + 2 + 1 = 4

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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:

NOOPS-First Dificulty measures: dif(o) =

• p∈pre(o)

min{i|p appears in layer i} Linearized sets of actions

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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) =

• p∈pre(o)

min{i | p appears in layer i} Linearized sets of actions

METRIC-FF: cost-based FF [Hoffmann, 2003]

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Introduction Classical planning Neoclassical planning Heuristics Planning in the real world

Indice

1

Introduction

2

Classical planning

3

Neoclassical planning

4

Heuristics Heuristic planning Hierarchical Task Networks Control knowledge Machine learning

5

Planning in the real world

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¨

• rg Hoffmann and Bernhard Nebel.

The FF planning system: Fast plan generation through heuristic search. Journal of Artificial Intelligence Research, 14:253–302, 2001. J¨

• rg 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.

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Introduction Classical planning Neoclassical planning Heuristics Planning in the real world

Addison-Wesley, 1983.

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