Iterative Deepening

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Iterative Deepening

• G51IAI Introduction to AI
• Andrew Parkes
• http//www.cs.nott.ac.uk/ajp/

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Motivations

• BFS A
• good for optimality
• bad on memory, O(bd)
• DFS
• solutions not guaranteed optimal dives and
  misses good nodes
• good for memory O(bd)
• Iterative Deepening refers to a method that
  tries to combine the best of the above

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Depth-Limited Search

• Simply put an upper limit on the depth (cost) of
  paths allowed
• Motivation
• e.g. inherent limit on range of a vehicle
• tell me all the places I can reach on 10 litres
  of petrol
• prevents search diving into deep solutions
• might already have a solution of known depth
  (cost), but are looking for a shallower (cheaper)
  one

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Depth-Limited Search

• Impose an upper limit on the depth (cost) of
  paths allowed
• Only add nodes to the queue if their depth does
  not exceed the bound
• DepthLimitedDFS ( k ) DFS but only consider
  nodes with depth d k

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Trees Depth-Limited

• Depth limit of 2 would mean that children of E
  are ignored

d0
d1
d2
d3
d4
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Iterative Deepening Search

• Follow the BFS pattern of search all nodes
  of depth d before depth d1
• But do the search at depth d using
  Depth-Limited-DFS
• Schematically
• IDSk0while ( not success k lt depth of
  tree ) Depth-Limited-DFS ( k ) k

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Properties of IDS

• Memory Usage
• Same as DFS O(bd)
• Time Usage
• Worse than BFS because nodes at each level will
  be expanded again at each later level
• BUT often is not much worse because almost all
  the effort is at the last level anyway, because
  trees are leaf heavy
• Typically might be at most a factor two worse

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Memory Usage of A

• We store the tree in order to
• to return the route
• avoid repeated states
• Takes a lot of memory
• But scanning a tree is better with DFS

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IDA

• Combine A and iterative deepening
• f is the estimate of total path cost for start
  to goal
• IDA
• Impose a limit on f
• Use DFS to search within the f limit
• Iteratively relax the limit
• Greatly reduces memory usage
• Can repeat far too much work, and so be slow

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Summary

• Algorithm IDS
• IDS BFS plus DFS for tree search
• Algorithm IDA
• the basis of state of the art complete
  optimal algorithms

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Summary

• BFS A good for optimality, but not memory
• DFS good for memory O(bd), but not optimality
• Iterative Deepening refers to
• IDS Iterative Deeepening Search
• mix of DFS and BFS on trees
• a broad approach used for general search, with
  general aim to combine optimality with low memory
  usage of DFS
• Self-Study carefully work through ids.ppt
• Expectations
• know about the motivations and ideas and the
  search pattern
• do not need details of how to code IDA

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Questions?