Chap.12 Practical Planning

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Chap.12 Practical Planning

• CS570 Artificial Intelligence
• Kwang-hyung Lee

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12.1 Practical Planners
12.1 Practical Planners

• Spacecraft assembly, integration, and
  verification
• 1. Hierarchical plans
• 2. Complex conditions
• 3. Time
• 4. Resources
• Job Shop Scheduling
• Scheduling for space missions
• Buildings, aircraft carriers and beer factories

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12.2 Hierarchical Decomposition
12.2 Hierarchical Decomposition

• Solution at a high level abstraction
• Go(Supermarket),Buy(Milk),Buy(Bananas),Go(Home)
• It is a long way from instruction fed to the
  agents effectors
• A low level plan
• Forward(1 cm),Turn(1 deg),Forward(1 cm),
• Hierarchical decomposition an abstract operator
  can be decomposed into a group of steps
• ex) Abstract operator Build(House)
• decomposed operators obtain Permit,Hire
  Builder,Construction, Pay Builder
• Primitive operatorexecuted by the agent

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12.2 Hierarchical Decomposition

• Hierarchical planning work
• (1) provide an extension to the STRIPS for
  nonprimitive operator
• (2) modify the planning algorithm to allow the
  replacement of a nonprimitive operator with its
  decomposition

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Extending STRIPS
12.2 Hierarchical Decomposition

• (1) partition operators into primitive and
  nonprimitive operators
• nonprimitive Install(FloorBoards)
• primitive Hammer(Nail)
• (2) decomposition method
• Decompose(o,p) An operator o is decomposed into
  a plan p

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12.2 Hierarchical Decomposition

• Decomposition of o into p
• The decomposed plan p correctly implements an
  operator if it is complete and consistent
• 1. p must be consistent (no contradiction)
• 2. Every effect of o must be asserted by at least
  one step of p
• 3. Every precondition of the steps in p must be
  achieved by a step in p or be one of the
  preconditions of o

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Modifying the planner
12.2 Hierarchical Decomposition

• Modification of planner POP into HD-POP
• (1) a way to decompose nonprimitive operators
• (2) the algorithm takes a plan as input, rather
  than just a goal

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12.2 Hierarchical Decomposition

• SELECT-NONPRIMITIVEselects a nonprimitive
• CHOOSE-DECOMPOSITIONpicks a decomposition method
• The fields of the plan are altered
• STEPS Add steps, remove Snonprimitive
• BINDINGS Add variable binding constants
• OrderingCall RESOLVE-THREATS
• Links Si c Snonprim Si c Sm a
  step of method

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12.3 Analysis of Hierarchical Decomposition
12.3 Analysis of Hierarchical Decomposition

• Abstract solution a plan containing abstract
  operators, but consistent and complete
• downward solutionif p is an abstract solution
  and there is a primitive solution
• upward solutionif an abstract plan is
  inconsistent then no primitive sol.

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12.3 Analysis of Hierarchical Decomposition

• if a planner(nonhierarchical) has to generate
  n-step plan(where b is branching factor), it
  takes time O(bn)
• Hierarchical planning,
• sb steps at d1
• bs2 at d2
• ?ibs2 O(bsd) (from i1 to d)

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12.3 Analysis of Hierarchical Decomposition

• The Gift of the Magic
• A poor couplehe has a gold watch, she has long
  hair.
• Plan b is inconsistent , but it can be into a
  consistent plan
• The upward solution property does not hold

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Decomposition and Sharing
12.3 Analysis of Hierarchical Decomposition

• Merge each step of the decomposition into
  existing plan
• Divide-and-conquer approachsolve each subproblem
  and then combine it into the rest
• Sharing steps while merging
• Ex) enjoy a honeymoon and raise a baby
• (1) decomposition
• get married and go on honeymoon
• get married and have a baby
• (2) merge
• share the step get married

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Decomposition and approximation
12.3 Analysis of Hierarchical Decomposition

• Hierarchical decomposition
• nonprimitive operator gt primitives
• Hierarchical planning(approximation hierarchy,
  abstraction hierarchy)
• It takes an operator and partitions its
  precondition according to their criticality
  levelOp(ACTIONBuy(x), EFFECT Have(x) ?
  ?Have(Money), PRECOND1Sells(store,x) ?
  2At(store) ?
  3Have(Money))

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12.4 More Expressive Operator Description
12.4 More Expressive Operator Description

• Conditional effects
• ex) block world in section 11.8
• Two operators were needed
• Op(ACTIONMove(b,x,y), PRECOND On(b,x) ?
  Clear(b) ? Clear(y), EFFECTOn(b,y) ? Clear(x) ?
  ?On(b,x) ? ?Clear(y))
• Op(ACTIONMoveToTable(b,x), PRECOND On(b,x) ?
  Clear(b), EFFECTOn(b,Table) ? Clear(x) ?
  ?On(b,x))
• initial situationOn(A,B)goal clear(B)

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12.4 More Expressive Operator Description

• Move A to the table or to somewhere else?
  premature commitment in Move(b,x,y)
• To eliminate it, we include conditional
  effecteffect when condition Q when
  POp(ACTIONMove(b,x,y), PRECOND On(b,x) ?
  Clear(b) ? ?Clear(y), EFFECTOn(b,y) ?
  Clear(x) ? ?On(b,x) ? ?Clear(y) when y?Table)

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Universal quantification
12.4 More Expressive Operator Description

• ex) block world
• clear(b)?x Block(x) ? ?On(x,b)
• ex) shopping problem
• Carry(bag, x, y) (effect) all objects that are
  in the bag are at y and are no longer at
  x.Op(ACTIONCarry(bag,x,y),
  PRECONDBag(bag) ? At(bag,x),
  EFFECTAt(bag,y) ? ?At(bag,x) ? ?I Item(i) ?
  (At(i,y) ? ?At(y) when In(I,bag))