Fast Planning through Planning Graph Analysis

1
Fast Planning through Planning Graph Analysis

• By
• Jan Weber
• Jörg Mennicke

2
Outline

• Characteristics
• Graphstructure
• GRAPHPLAN Algorithm
• Expand - Graph
• Extract Solution
• Importance of Graphplan
• Pros
• Cons
• Example
• References

3
Characteristics

• Graphplan
• A non-linear, partial-order planer using forward
  construction and backward path extraction in
  STRIPS-like domains
• Planer vs. Search Algorithm
• Forward vs. backward
• Partial-Order vs. Total-Order
• Linear vs. non-linear
• Strips-like

4
Graphstructure

• Objects
• (not directly represented in Graph)
• Propositions
• Initial Conditions
• Operators
• No-Ops
• Goals

Propositions / Initial Conditions
Propositions
Operator
Goal
No-Op
5
Graphstructure
Proposition level
Proposition level
Action Level

• Layers
• Proposition level
• (represents multiple states)
• Action level
• Time Step
• Connections
• Precondition edges
• Add- Delete-Effects

Precond.
Add/Del
---------- Time Step -----------
6
Graphstructure

• Mutual Exclusions of Actions
• Inconsistent Effects vs. Interference vs.
  Competing needs
• Inconsistent Effects

7
Graphstructure

• Mutual Exclusions of Actions, cont.
• Interference
• Competing needs
• Mutual Exclusions of Propositions
• Recursive Exclusions / Inconsistent Support

8
GRAPHPLAN Algorithm

• If all goals are present in the current level
  with no exclusion links (A solution might exist)
  or the graph has levelled off (Two consecutive
  levels are identical - No solution exists).
• EXTRACT-SOLUTION
• Else
• EXPAND-GRAPH

9
Expand graph

• Algorithm
• For each Proposition level check every Op whether
  its preconditions are true
• Construct next Action level including those Ops
• Construct next Proposition level considering all
  add delete effects
• Check for Mutex links in Action and Proposition
  level (actions-that-I-am-exclusive-of-list)

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Extract Solution

• Backward search
• Level-by-level approach makes best use of mutexes
• For each goal at time t, find an operator that
  has this goal as an add-effect and that is not
  exclusive with an operator already selected
• The preconditions of these actions are a set of
  subgoals at time t-1
• Find operators adding the subgoals of time t-1
• If no set of operators can achieve the subgoals
  at time t-n -gt Backtrack
• Memoisation

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Importance of Graphplan

• Aips 98
• 3 of 5 planners in the competition used graphplan
  completely (IPP, SGP, and STAN)
• 1 exploited the graphplan technology (Blackbox)
• Aips 2002 75 of the planners used graphplan
• ICAPS 2004 More than half of the planners
  competing use heuristic based search (such as
  Fast Diagonally Downward, Macro-FF, Yahsp,
  HSPa)
• Graphplan made researchers think about more
  efficient algorithms -gt started new planning era
• ? BUTGraphplan plays less important role at the
  moment

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Pros

• Non-linear Planner -gt partial goals are
  independent
• and can be achieved by interleaving
• -gt different from STRIPS
• Planning Graphs can be constructed relatively
  efficient
• Effective for solving hard planning problems
• Keeps Graph as small as possible (MUTEX)
• Memoization
• Low level costs construction of graph before
  backwards search
• Termination is guaranteed for finite problem
  domains even if problem unsolvable

13
Cons

• Problems with a large numbers of objects have a
  huge number of possible actions
• Planning only possible in strips-like domains
• Guarantees to find shortest plan
• -gt overcomplicates problem
• Loss of performance if no reduction by mutex
  links possible

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Example

• Full Example (Coming up with an example)
• Objects team idea concept
• Propositions creative(team) found(idea)
  checked(idea) prepared(?concept)
  revised(?concept)
• Operators

• Brainstorm(?team,?idea)
• Preconditions creative(?team)
• ADD found(?idea)
• DELETE creative(?team)
• Check(?idea)
• Preconditions found(?idea)
• ADD checked(?idea), creative(?team)
• DELETE found(?idea)

• Prepare(?team, ?idea, ?concept)
• Preconditions creative(?team), checked(?idea)
• ADD prepared(?concept)
• DELETE checked(?idea)
• Revise(?idea, ?concept)
• Preconditions checked(?idea),
  prepared(?concept)
• ADD revised(?concept)
• DELETE

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Example

• Full Example (Coming up with an example) Cont

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References

• Blum Avrim Furst Merrick, Fast Planning Through
  Planning Graph Analysis, 1997
• Russel Stuart Norvig Peter, Artificial
  Intelligence A Modern Approach, Prentice Hall,
  New Jersey (http//aima.cs.berkeley.edu/)
• http//www-2.cs.cmu.edu/avrim/graphplan.html
• http//www.cs.bham.ac.uk/mmk/Teaching/Planning/
• www.cdf.toronto.edu/csc384h/fall/Lectures/Lecture
  12.pdf
• www.dgp.toronto.edu/ppacheco/course/384/Lectures/
  Lecture13.pdf
• J. Koehler, B. Nebel, J. Hoffmann, Y. Dimopoulos,
  Extending Planning Graphs to an ADL Subset,
  ECP-97, pages 273-285 (http//www.informatik.uni-f
  reiburg.de/koehler/papiere/ecp-97.ps.gz)
• www.cs.washington.edu/homes/kautz/papers/plan.ps
• http//www.fh-wedel.de/mo/lectures/planning.html
• Gerevini, A., Serina, I., "Fast Planning through
  Greedy Action Graphs", TR710, Computer Science
  Dept., U. Rochester, February 1999