04-chapt4a

04-chapt4a - CSE630 InformedSearch:Greedyand A*Search Prof...

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CSE 630: Informed Search: Greedy and  A* Search Prof. Naeem Shareef

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Heuristic Approaches to Search Heuristic Estimate of the cheapest cost from a particular node to the goal An educated guess or “guesstimate” A description of what a “good” solution looks like Evaluation function f(n), for a node n Sort search queue by smallest f(n) Smaller f(n) means more promising ‘Best first’ rather than depth- or breadth-first search algorithms Node with goal state has f(n) = 0 Improves average-case performance but not worst-case performance
A Heuristic For the Romania Driving Problem Arad … to … Bucharest Heuristic Let f(n) = h(n) = Straight-line distance from city to goal A heuristic may require more information than uninformed search The x,y coordinate of the goal city The longitude, latitude Heuristics are custom-tailored for the problem x,y coord would not work for other search problems

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Greedy search example
Greedy search example

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A Heuristic for the 8-puzzle Heuristic h(n) = number of misplaced tiles = 6 h(n) = sum of the (Manhattan) distances of every tile to its goal position = 2 + 3 + 0 + 1 + 3 + 0 + 3 + 1 = 13 1 4 7 5 2 6 3 8 STATE(N) 6 4 7 1 5 2 8 3 Goal state
A Heuristic for Robot Navigation 11 N x y 2 2 g g 1 N N h (N) = (x -x ) +(y -y ) (Euclidean distance) 2 N g N g (Manhattan distance)

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Admissible Heuristic Let C* be the cost of the optimal path from n to a goal node admissible if: 0 h(n) C* An admissible heuristic function is always optimistic !
8-Puzzle Heuristics h(n) = number of misplaced tiles = 6 is admissible h(n) = sum of the (Manhattan) distances of every tile to its goal position = 2 + 3 + 0 + 1 + 3 + 0 + 3 + 1 = 13 is admissible 1 4 7 5 2 6 3 8 STATE(N) 6 4 7 1 5 2 8 3 Goal state

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14 Cost of one horizontal/vertical step = 1 Cost of one diagonal step = 2 2 2 g g 1 N N h (N) = (x -x ) +(y -y ) h 2 (N) = | x N -x g | + | y N -y g | are both admissible Robot Navigation Heuristics
15 Best-First   Efficiency f(n) = h(n) = straight distance to the goal Local-minimum problem

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151 99 415 671

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151 99 415 671 A* search example
A* search example 151 99 415 671

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A* search example 151 99 415 671
21 0+4 1+5 1+5 1+3 3+3 3+4 3+4 3+2 4+1 5+2 5+0 2+3 2+4 2+3 f(N) = g(N) + h(N) with h(N) = number of misplaced tiles 8-Puzzle Heuristics

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23 Robot Navigation 0 2 1 1 5 8 7 7 3 4 7 6 7 6 3 2 8 6 4 5 2 3 3 3 6 5 2 4 4 3 5 5 4 6 5 6 4 5 f(N) = h(N), with h(N) = Manhattan distance to the goal (not A*)

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24 Robot Navigation 0 2 1 1 5 8 7 7 3 4 7 6 7 6 3 2 8 6 4 5 2 3 3 3 6 5 2 4 4 3 5 5 4 6 5 6 4 5 f(N) = h(N), with h(N) = Manhattan distance to the goal (not A*) 7 0
25 Robot Navigation f(N) = g(N)+h(N), with h(N) = Manhattan distance to goal (A*) 0 2 1 1 5 8 7 7 3 4 7 6 7 6 3 2 8 6 4 5 2 3 3 3 6 5 2 4 4 3 5 5 4 6 5 6 4 5 7+0 6+1 6+1 8+1 7+2 7+2 8+3 6+3

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04-chapt4a - CSE630 InformedSearch:Greedyand A*Search Prof...

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