Combining Front-to-End Perimeter Search and Pattern Databases

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Combining Front-to-End Perimeter Search and
Pattern Databases

• CMPUT 652
• Eddie Rafols

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Motivation
From Russell, 1992
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Allocating Memory

• More memory for Open/Closed Lists
• Caching
• Perimeter Search
• Pattern Databases

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Allocating Memory

• More memory for Open/Closed Lists
• Caching
• Perimeter Search
• Pattern Databases

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Perimeter Search

• Generate a perimeter around the Goal
• Any path to Goal must pass through a perimeter
  node Bi
• We know the optimal path from Bi to Goal
• Stopping condition for IDA is now
• If A is a perimeter node and g(Start,A)g(A,Goal)
  ? Bound

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Perimeter Search

• Traditional Search O(bd)
• Perimeter Search O(brbd-r)
• Large potential savings!

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Perimeter Search

• Can be used to improve our heuristic
• Kaindl Kainz, 1997
• Add Method
• Max Method

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Pattern Databases

• Provide us with a consistent estimate of the
  distance from any given state to the goal
• This point will become relevant in a few slides

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Approach

• Generate a pattern database to provide a
  heuristic
• Use Kaindl Kainzs techniques to improve on
  heuristic values (Add,Max)
• Determine how perimeter search and PDBs can most
  effectively be combined via empirical testing

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A Digression

• Among other things, the Max method requires
• h(Start, A), where A is a search node
• h(Start, Bi), where Bi is a perimeter node

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A Digression

• Among other things, the Max method requires
• h(Start, A), where A is a search node
• h(Start, Bi), where Bi is a perimeter node

• We are not explicitly given this information in a
  PDB.

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A Digression...

• Recall Alternate PDB lookups
• If we are dealing with a state space where
  distances are symmetric and tile-independant,
  we can use this technique

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A Digression...

• ex. Pancake Problem

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A Digression...

• However, this technique may provide inconsistent
  heuristics

?1
?2
?1 ? ?2
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A Digression...

• Kaindls proof of the max method relies on a
  consistent heuristic
• ...but we can still use our pattern database
• We just have to use it correctly

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A Digression...

• Distances are symmetric, therefore
• h(Start, A) h(A, Start)
• h(Start, Bi) h(Bi, Start)
• We can map the Start state to the Goal state
• In this case, when we do alternate lookups on A
  and Bi, we are using the same mapping!
• Our heuristic is now consistent!

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A Digression...
?
?
?
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A Third Heuristic?

• Since we have the mechanisms in place, why not
  use alternate lookup to get h(Goal, A)?
• Turns out that this is the exact same lookup as
  h(A,Goal)

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Combining the Heuristics

• The Add method lets us adjust our normal PDB
  estimate
• h1(A,goal) h(A,goal) ?
• The Max method gives us another heuristic
• h2(A,goal)mini(h(Bi,start) g(Bi,goal))-h(A,
  start)
• Our final heuristic
• H(A,goal)max(h1(A,goal),h2(A,goal))

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Hypotheses

• All memory used on perimeter, expect poor
  performance
• All memory used on PDB, expect good performance,
  but not the best possible
• Small perimeters combined with large PDBs should
  outperform large perimeters with small PDBs

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Method

• Do a binary search in the memory space.
• Test pure perimeter search and pure PDB
  search
• Give half the memory to the winner, compare
  whether a PDB or a perimeter would be a more
  effective use of the remaining memory
• Repeat until perimeter search becomes a more
  effective use of memory

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Results
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Results
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Results
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Results
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Results
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Discussion

• Discouraging results
• Using extra space for a PDB seems to provide
  better results across the board

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Discussion

• Adding a perimeter does not appear to have a
  significant effect

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Discussion

• Empirically, the Add method is always returning ?
  0
• A directed strategy for perimeter creation is
  likely needed for this method to have any effect

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Discussion

• Further experiments show that given a fixed PDB,
  as perimeters increase in size, there is a
  negligible performance increase

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An Idea

• Is the heuristic effectively causing paths to
  perimeter nodes to be pruned?
• This means that performance is only being
  improved along a narrow search path
• Can we generate the perimeter intelligently to
  make it more useful?

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Questions?