Artificial Intelligence

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Artificial Intelligence

• Lecture 5
• Uninformed Search

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Overview

• Searching for Solutions
• Uninformed Search
• BFS
• UCS
• DFS
• DLS
• IDS

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Searching for Solutions
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Tree Search Algorithms
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Tree Search Example
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ImplementationState vs. Nodes
and state
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General Tree Search
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Search Strategies
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Uninformed Search
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Uninformed Search Strategies

• Use only the information available in the problem
  definition
• Breadth-first search
• Uniform-cost search
• Depth-first search
• Depth-limit search
• Iterative deepening search

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Breadth-First Search

• Expand shallowest unexpanded node
• Implementation fringe is a FIFO queue, that is
  new successors go at end

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Properties of BFS

• Complete?
• Yes. (if b is finite)
• Time?
• 1bb2b(bd-1)O(bd1), exp in d
• Space?
• O(bd1) (keeps every node in memory)
• Optimal?
• Yes, if cost 1 per step not optimal in general
  when actions have different cost
• Space is the big problem can easily generate
  nodes at 10MB/sec, so 24hrs 860GB

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Uniform-Cost Search
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Depth-First Search

• Expanded deepest unexpanded node
• Implementation
• Fringe LIFO queue, i.e. put successors at front

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Properties of DFS

• Complete?
• No. Fails in infinite-depth spaces, spaces with
  loops
• Modify to avoid repeated states along path gt
  complete in finite space
• Time?
• O(bm), terrible if m is much larger than d, but
  if solutions are dense, may be much faster than
  BFS
• Space?
• O(bm), linear space
• Optimal?
• No

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Depth-Limit Search

• Depth-first search with depth limit L, that is
  nodes at depth L have no successors

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Depth-Limited search

• Is DF-search with depth limit l.
• i.e. nodes at depth l have no successors.
• Problem knowledge can be used
• Solves the infinite-path problem.
• If l lt d then incompleteness results.
• If l gt d then not optimal.
• Time complexity
• Space complexity

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Depth-Limit Search

• Algorithm

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Iterative Deepening Search

• Iterative deepening search
• A general strategy to find best depth limit l.
• Goals is found at depth d, the depth of the
  shallowest goal-node.
• Often used in combination with DF-search
• Combines benefits of DF- en BF-search

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Iterative Deepening Search
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Properties of IDS
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Bidirectional search

• Two simultaneous searches from start an goal.
• Motivation
• Check whether the node belongs to the other
  fringe before expansion.
• Space complexity is the most significant
  weakness.
• Complete and optimal if both searches are BF.

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How to search backwards?

• The predecessor of each node should be
  efficiently computable.
• When actions are easily reversible.

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Summary of Algorithms
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Repeated States
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Graph Search
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Summary

• Searching for Solutions
• Uninformed Search
• BFS
• UCS
• DFS
• DLS
• IDS