Flaw Selection Strategies For PartialOrder Planning

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Flaw Selection Strategies For Partial-Order
Planning Pollack, Joslin, Paolucci
Presented By William Halliburton
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Partial Order Planning

• Searching through a space of partial plans, where
  the successors of plan P are refinements of P
• POP requires effective search control strategies
• POP search control has two components
  node selection and flaw selection
• This paper evaluates many flaw and node selection
  strategies

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POP Algorithm
POCL(init,goal) dummy-plan lt- make-skeletal-plan(
init,goal). nodes lt- dummy-plan . While
nodes is not empty do CHOOSE (and remove) a
partial plan P from nodes. If P has no
flaws then return P else do SELECT a
flaw from P. Add all refinements of P to
nodes. Return failure.
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Node selection

• CHOOSE (backtrackable)
• Most POP use a best-first ranking
• S steps
• OC open conditions
• UC unsafe conditions
• F ?
• Example SOC SOCUC SOC.1UCF

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Flaw selection

• SELECT (not backtrackable)
• Select between open conditions or threats
• Open conditions are repaired by establishment
• Adding new step
• Adding causal link
• Threats are repared by
• Promotion
• Demotion
• Separation

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Nonseperable Threats

• Step S1 with effect E and a causal link ltS2, F,
  S3gt
• E not F
• E p(x,y) and F not p(x,y)
• E p(x,y) and F not p(x,z) with binding
  constraint yz
• Repaired by promoting or demoting
• At most two possible repairs
• Over time the repair cost can only decrease

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Seperable Threats

• step S1 with effect E and a causal link
  ltS2, F, S3gt
• Ep(x) and Fp(y) with no binding constraint xy
• May disappear with future binding. Can only
  decrease over time.
• Repaired with promotion, demotion, or separation
• Repair cost may be higher than for nonseperable
  threats because may have numerour separations.
• P(x,y,z) threatens ltS2, not P(t, u, v), S3gt fixed
  by x ! y or y ! u or z !
  v

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Notation

• flaw types repair cost range tie-breaking
  strategy
• flaw types
• o open condition
• n nonseperable threat
• s seperable threat
• Tie breaking
• LC least cost
• LIFO
• R Random
• Example n0-1R / oLIFO / n,sR

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Strategies

• See paper page 234

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Experiment

• Ran each strategy on
• Basic problems from UCPOP system
• Trains problems
• Tileworld problems

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Value of Least-Cost Selection

• Ran LCFR, Dunf, Dunf-LC, UCPOP, UCPOP-LC and
  Dunf-Gen
• Show figure 2 page 236
• LCFR does tend to produce smaller search spaces
• But is this just a side effect of prefering
  forced flaws?

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LCFR vs ZLIFO

• Now compare these two and we find
• ZLIFO does tend to generate smaller search
  spaces. Why?
• Is it because ZLIFO has seperable-threat-delay?
• So try LCFR-DSep n,oLC / sLC in a new
  deathmatch.
• Bingo! LCFR-DSep is better than LCFR and almost
  as good as ZLIFO.
• Figure 12 p. 244

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Domain Infomation

• Trains and Tileworld challenge overly simple
  comclusion from basic problems
• Someproblems benefit from selecting seperable
  threats early

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Computation Time

• LCFR-DSep does pay for its overhead
• LCFR-DSep is almost as good as ZLIFO
• DSep-LC has the best time performance of all the
  basic problem sets. (Closely resembles
  LCFR-DSep). More nodes but less work per node.

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Conclusion

• Compared many strategies - focused on LCFR and
  ZLIFO
• Neither consistantly generate smaller search
  spaces but combining strategies in LCFR-DSep was
  nearly always as good as the better of LCFR and
  ZLIFO
• ZLIFO advantage over LCFR is due to delay of
  separable threats rathar than LIFO
• LFCR-DSep pays for its overhead
• Domain-dependent characteritics must still be
  taken into account