Artificial Intelligence Expert Systems State Space Search

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Artificial Intelligence / Expert SystemsState
Space Search

• Justin Gaudry
• May 22, 2007

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Semantic Trees

• Acyclic semantic net with directed edges
• One node designated as root (start)
• Nodes have 0 or more children
• If 0 children, leaf node
• Goal nodes are leaf nodes representing end state

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Semantic Trees

• Path is a route from one node to another
• Branching factor of a tree is the average number
  of children each internal node has
• The longer the paths, the deeper the tree
• The larger the branching factor, the wider the
  breadth of the tree

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Semantic Trees

• Directed edges reduce (but do not eliminate)
  chance of cycles and infinite search in semantic
  net
• Creating semantic tree eliminates possibility of
  infinite search
• Brute-force search of large tree is inefficient
• Heuristics reduce size of search space
• Next-neighbor heuristic is greedy algorithm
  yielding not-necessarily optimal solution

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Applications of Semantic Trees

• Traveling Salesman semantic tree has
  combinatorial explosion (permutations) of breadth
  but not depth
• Towers of Hanoi has combinatorial explosion of
  depth but not breadth
• Map-coloring has combinatorial explosion of
  breadth but not depth
• Chess has both
• Go has both

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Neural Networks

• Modeled after the human brain
• Neurons in brain represented by nodes in network
• Synapses represented by weight matrices
• Visual inspection of weights is meaningless
• Patterns that are produced from input to output
  via matrix multiplications of weight matrices are
  meaningful

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Neural Networks

• Multi-Layer Perceptrons (MLPs)

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...
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Input
Hidden
Output
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Goal Trees

• Break problem into subgoals then recursively into
  smaller subgoals
• Use and/or trees to indicate whether all subgoals
  must be solved (and) or any subgoal (or)
• Towers of Hanoi, map-coloring all goals
• Game playing alternates or/and per level

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Search Strategies

• Breadth-first search
• Depth-first search
• Depth-first search with iterative deepening
• All on same order of magnitude O(BN)
• Best-first search (requires heuristic value at
  each node) greedy

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Search Approaches

• Data-driven search
• Start at initial state
• Move forward until goal reached
• Forward chaining
• Unknown or numerous potential goals
• Goal-driven search
• Start at goal state
• Move backward until start reached
• Backward chaining
• Well-defined, known goal

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Generate and Test

• Generate all possible nodes in search space
• Test to see if at a goal node at each point
• Brute-force, exhaustive search
• Inappropriate for large or deep search spaces

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Depth-first Search

• Put first node on stack and visit (can use
  recursion)
• While stack is not empty and no goal found
• Peek
• If node is not leaf
• Generate new node and visit
• Push new node
• Else
• Pop (chronological backtracking)
• EndIf
• Endwhile
• Works better than breadth-first for high
  branching factor
• Works poorly for tree with long paths
• Uses backtracking tentative method

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Breadth-first search

• Put first node on queue
• While queue is not empty and no goal found
• Remove node and visit
• Generate all 1-ply neighbors and insert
• Endwhile
• Works well for tree with long paths
• Works poorly for high branching factor
• Larger memory requirement

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Properties of Search Methods

• Time complexity how long to find goal state
• Space complexity amount of memory usage
• Good enough goal state
• Complete method is guaranteed to find goal
  breadth not depth
• Optimal method is guaranteed to find the best
  solution that exists breadth not depth (aka
  admissibility)

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Depth-first Iterative Deepening

• Combination of depth-first and breadth-first
• Depth to 1-ply, then 2-ply, then 3-ply
• Memory efficiency of depth-first without
  repercussion of infinite path
• Complete and optimal like breadth-first
• 1 b(d1) nodes in tree depth d branching b
• 1 - b