Informed Search

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# Informed Search - PowerPoint PPT Presentation

Informed Search. Reading: Chapter 4.5. Agenda. Introduction of heuristic search Greedy search Examples: 8 puzzle, word puzzle A* search Algorithm, admissable heuristics, optimality Heuristics for other problems Homework. 8-puzzle URLS. http://www.permadi.com/java/puzzle8

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## PowerPoint Slideshow about 'Informed Search' - lesa

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### Informed Search

Agenda
• Introduction of heuristic search
• Greedy search
• Examples: 8 puzzle, word puzzle
• A* search
• Heuristics for other problems
• Homework
8-puzzle URLS
• http://www.cs.rmit.edu.au/AI-Search/Product
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
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
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

Goal State

h1=5

h2=1+1+1+2+2=7

h1=1

h2=1

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
Greedy search
• Evaluation function = heuristic function
• Expand the node that appears to be closest to the goal
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 f=heuristic function for each node
• Put remaining successors on either end of OPEN
• Sort nodes on OPEN by value of heuristic function
• End while
8-puzzle URLS
• http://www.cs.rmit.edu.au/AI-Search/Product
Analysis of Greedy Search
• Like depth-first
• Not Optimal
• Complete if space is finite
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
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
8-puzzle URLS
• http://www.cs.rmit.edu.au/AI-Search/Product
• 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) <=c(n,a,n’)+h(n’)
Which heuristic is better?
• Better means that fewer nodes will be expanded in searches
• h2 dominates h1 if h2 >= 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?
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.
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?
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
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?