Informed Search

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Informed Search

• Reading Chapter 4.5

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Agenda

• Introduction of heuristic search
• Greedy search
• Examples 8 puzzle, word puzzle
• A search
• Algorithm, admissable heuristics, optimality
• Heuristics for other problems
• Homework

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8-puzzle URLS

• http//www.permadi.com/java/puzzle8
• http//www.cs.rmit.edu.au/AI-Search/Product

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Breadth first Algorithm
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Depth-first Algorithm
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Heuristics

• Suppose 8-puzzle off by one
• Is there a way to choose the best move next?
• Good news Yes!
• We can use domain knowledge or heuristic to
  choose the best move

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Nature of heuristics

• Domain knowledge some knowledge about the game,
  the problem to choose
• Heuristic a guess about which is best, not
  exact
• Heuristic function, h(n) estimate the distance
  from current node to goal

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Heuristic for the 8-puzzle

• tiles out of place (h1)
• Manhattan distance (h2)
• Sum of the distance of each tile from its goal
  position
• Tiles can only move up or down ? city blocks

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Goal State
h15 h2111227
h11 h21
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Best first searches

• A class of search functions
• Choose the best node to expand next
• Use an evaluation function for each node
• Estimate of desirability
• Implementation sort fringe, open in order of
  desirability
• Today greedy search, A search

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Greedy search

• Evaluation function heuristic function
• Expand the node that appears to be closest to the
  goal

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Greedy Search

• OPEN start node CLOSED empty
• While OPEN is not empty do
• Remove leftmost state from OPEN, call it X
• If X goal state, return success
• Put X on CLOSED
• SUCCESSORS Successor function (X)
• Remove any successors on OPEN or CLOSED
• Compute fheuristic function for each node
• Put remaining successors on either end of OPEN
• Sort nodes on OPEN by value of heuristic function
• End while

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8-puzzle URLS

• http//www.permadi.com/java/puzzle8
• http//www.cs.rmit.edu.au/AI-Search/Product

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Sodoku
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Analysis of Greedy Search

• Like depth-first
• Not Optimal
• Complete if space is finite

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A Search

• Try to expand node that is on least cost path to
  goal
• Evaluation function f(n)
• f(n)g(n)h(n)
• h(n) is heuristic function cost from node to
  goal
• g(n) is cost from initial state to node
• f(n) is the estimated cost of cheapest solution
  that passes through n
• If h(n) is an underestimate of true cost to goal
• A is complete
• A is optimal
• A is optimally efficient no other algorithm
  using h(n) is guaranteed to expand fewer states

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A Search

• OPEN start node CLOSED empty
• While OPEN is not empty do
• Remove leftmost state from OPEN, call it X
• If X goal state, return success
• Put X on CLOSED
• SUCCESSORS Successor function (X)
• Remove any successors on OPEN or CLOSED
• Compute f(n) g(n) h(n)
• Put remaining successors on either end of OPEN
• Sort nodes on OPEN by value of heuristic function
• End while

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8-puzzle URLS

• http//www.permadi.com/java/puzzle8
• http//www.cs.rmit.edu.au/AI-Search/Product

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Admissable heuristics

• A heuristic that never overestimates the cost to
  the goal
• h1 and h2 for the 8 puzzle are admissable
  heuristics
• Consistency the estimated cost of reaching the
  goal from n is no greater than the step cost of
  getting to n plus estimated cost to goal from n
• h(n) ltc(n,a,n)h(n)

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Which heuristic is better?

• Better means that fewer nodes will be expanded in
  searches
• h2 dominates h1 if h2 gt h1 for every node n
• Intuitively, if both are underestimates, then h2
  is more accurate
• Using a more informed heuristic is guaranteed to
  expand fewer nodes of the search space
• Which heuristic is better for the 8-puzzle?

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Relaxed Problems

• Admissable heuristics can be derived from the
  exact solution cost of a relaxed version of the
  problem
• If the rules of the 8-puzzle are relaxed so that
  a tile can move anywhere, then h1 gives the
  shortest solution
• If the rules are relaxed so that a tile can move
  to any adjacent square, then h2 gives the
  shortest solution
• Key the optimal solution cost of a relaxed
  problem is no greater than the optimal solution
  cost of the real problem.

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Heuristics for other problems

• Problems
• Shortest path from one city to another
• Touring problem visit every city exactly once
• Challenge Is there an admissable heuristic for
  sodoku?

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End of Class Questions
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Homework
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Homework
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Fill-In Station
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Language Models

• Knowledge about what letters in words are most
  frequent
• Based on a sample of language
• What is the probability that A is the first
  letter
• Having seen A, what do we predict is the next
  letter?
• Tune our language model to a situation
• 3 letter words only
• Medical vocabulary
• Newspaper text

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Formulation

• Left-right, top-down as path
• Choose a letter at a time
• Heuristic Based on language model
• Cost of choosing letter A first 1 probability
  of A next
• Subtract subsequent probabilities
• Successor function Choose next best letter, if
  3rd in a row, is it a word?
• Goal test?

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How does heuristic help us get there?