General Purpose Case-Based Planning

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General Purpose Case-Based Planning
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General Purpose vs Domain Specific (Case-Based)
Planning

• (Case-Based) Planning finding a sequence of
  actions to achieve a goal

• General purpose symbolic descriptions of the
  problems and the domain. The (adaptation)
  generation rules are the same
• Domain Specific The (adaptation) generation
  rules depend on the particular domain

Advantage - opportunity to have clear
semantics Disadvantage - symbolic description
requirement
Advantage - can be very efficient Disadvantag
e - lack of clear semantics
- knowledge-engineering for adaptation
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Derivational vs Transformational Adaptation

• Transformational adaptation structural
  transformations are made to the plans
• Derivational transformation

Case Replay re-applying those decisions relative
to the new problem
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Domain Specific Chef
(Hammond, 1986)

• Cases contain cooking recipes (plans) and there
  are rules indicating how to transform pieces of
  the recipes
• Typical transformation rules will indicate
  alternative ingredients and what steps need to be
  added/changed to adapt the recipe

Example if using broccoli instead of beans the
cooking time need to be adjusted.

• The cases contain domain-knowledge and
  transformational adaptation is performed

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Generative Solution Adaptation
If we have operators/rules with general knowledge
about the domain why do we need adaptation?

• To find the solution faster
• To find solutions that are similar to the
  original case, why?

• Solutions may be more acceptable to the user
• Attempt to preserve quality

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General-Purpose Planning State Goals
A

• Initial state (on A Table) (on C A) (on B Table)
  (clear B) (clear C)
• Goals (on C Table) (on B C) (on A B) (clear A)

Initial state
Goals
C
B
A
B
C
(Ke Xu)
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General-Purpose Planning Operators
?x
?y
?y
?x

• Operator (Unstack ?x)
• Preconditions (on ?x ?y) (clear ?x)
• Effects
• Add (on ?x table) (clear ?y)
• Delete (on ?x ?y)

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Planning Search Space
C
A
B
C
A
B
C
B
A
B
A
C
A
B
C
B
A
B
C
B
C
A
B
A
C
C
A
A
A
B
C
B
C
C
B
A
A
B
C
(Michael Moll)
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Planning Formal Definition

• Planning problem a tuple ? ?P,O,I,G?
• P a finite set of ground atoms
• Let L all possible literals, i.e., L P ?
  ?p p ? P
• O a finite set of operators of the form Pre ?
  Post
• Pre ? L and Post ? L are the preconditions and
  effects
• I ? P is the initial state
• G ? L is the goal

move-C-from-A-to-Table Precondition (and (on C
A) (clear C)) Effect (and (on C Table) (? (on C
A)) (clear A))
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Complexity of Plan Generation

• Plan Solution Given a planning problem, ?
  ?P,O,I,G? we will like to find the plan ? that
  solves ?
• For complexity analysis, need to encode plan
  solution as a decision problem
• a problem that has a yes/no answer
• PLAN-EXISTENCE (?)

Given a planning problem ? ?P,O,I,G?,does
there exist a plan ? that solves ? ?
Theorem. PLAN-EXISTENCE (?) is NP-Complete
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Complexity of Plan Adaptation

• Conservative plan-modification
• Given a planning problem ? ?P,O,I,G?, a plan ?
  that solves ?, and another planning problem ?'
  ?P,O,I',G' ? Find a plan ?' that solves ?' and
  reuses as much of ? as possible
• consMODSAT (?, ?, ?', k)

Given ?, ?, and ?' as above and given a k, is
there a plan ?' that solves ?' and contains at
least k steps of ??
Theorem. consMODSAT (?, ?, ?', k) is P-SPACE
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Complexity Issues NP-Complete Problems are Not
the Hardest

• PSPACE is the set of decision problems that can
  be solved by a Turing machine using a polynomial
  amount of memory, and unlimited time
• A problem P is in PSPACE-complete if

• P is in PSPACE,
• every problem P in PSPACE can be reduced to P
• in polynomial time.

• PSPACE-complete problems are believed to be
  harder than NP-Complete ones

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Complexity of Derivational Analogy
Theorem. Derivational Analogy does not perform a
conservative adaptation strategy
Thus, worst-case analysis for P-SPACE result does
not apply to it
How do we proof that some property does not hold?
Construct a counter-example
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Counter-Example
Case
?
?
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Homework

• explain why planning is so hard. Use the search
  space. Propose a heuristic to guide search.
  Explain why your proposed heuristic will not work
  for every case.
• In slide 20, we define the decision problem
  consMODSAT for conservative plan-modification
  defined in the same slide. Define the following
• Plan-modification
• The decision problem for plan modification
  MODSAT
• (Hint see the definition of plan solution and
  its decision problem PLAN-EXISTENCE in Slide 19)

Due Wednesday April 13