COMP9414: Artificial Intelligence Informed Search - Sorry

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COMP9414, Wednesday 23 March, 2005 Informed Search 4 Heuristics — Example COMP9414, Wednesday 23 March, 2005 Informed Search 6 Heuristics — Example 8-Puzzle — number of tiles out of place 2 8 3 1 2 3 Another common heuristic is the straight-line distance (“as the crow flies”) from node to goal 1 6 4 8 4 n 7 5 Therefore, h(n) = 5 7 6 5 Therefore, h(n) = distance from n to g g COMP9414 c○UNSW, 2005 Generated: 24 March 2005 COMP9414 c○UNSW, 2005 Generated: 24 March 2005 COMP9414, Wednesday 23 March, 2005 Informed Search 5 Heuristics — Example COMP9414, Wednesday 23 March, 2005 Informed Search 7 Best-First Search 8-Puzzle — Manhattan distance (distance tile is out of place) 2 8 3 1 2 3 1 6 4 8 4 7 5 7 6 5 function BestFirstSearch(problem, EvalFn) returns solution sequence inputs: problem — a problem EvalFn — evaluation function QueueingFn ← function that orders nodes by EvalFn return GeneralSearch(problem, QueueingFn) Therefore, h(n) = 1 + 1 + 0 + 0 + 0 + 1 + 1 + 2 = 6 COMP9414 c○UNSW, 2005 Generated: 24 March 2005 COMP9414 c○UNSW, 2005 Generated: 24 March 2005
COMP9414, Wednesday 23 March, 2005 Informed Search 8 Greedy Search COMP9414, Wednesday 23 March, 2005 Informed Search 10 A ∗ Search Idea: expand node with the smallest estimated cost to reach the goal Use heuristic function h(n) to select node from frontier for expansion (i.e. use h(n) as EvalFn in Best-First Search) Greedy Search — Analysis Similar to depth-first search — tends to follow a single path to goal Not optimal, incomplete Time O(b m ); Space O(b m ) However, good heuristic can reduce time and space complexity significantly Idea: Use both cost of path generated thus far and estimate to goal to select node from frontier to expand g(n) = cost of path from start node to n Accomplished by using an evaluation function f (n) = g(n) + h(n) f (n) represents the estimated cost of the cheapest solution passing through n Expand node from frontier with smallest f -value Essentially combines uniform-cost search and greedy search COMP9414 c○UNSW, 2005 Generated: 24 March 2005 COMP9414 c○UNSW, 2005 Generated: 24 March 2005 COMP9414, Wednesday 23 March, 2005 Informed Search 9 Greedy Search COMP9414, Wednesday 23 March, 2005 Informed Search 11 A ∗ Algorithm 8 3 2 1 4 7 6 5 (4) 2 7 8 3 1 4 6 5 8 3 2 1 4 7 6 5 2 8 3 1 6 4 7 5 (3) (3) 8 1 3 (4) 8 1 3 2 4 2 4 7 6 5 7 6 5 (5) 8 1 3 2 4 7 6 5 2 8 3 (3) 2 1 4 1 7 6 5 7 2 7 (3) 8 3 1 4 6 5 (4) (4) 8 1 3 (4) 2 6 4 7 5 2 3 1 8 4 7 6 5 1 2 3 8 4 7 6 5 1 2 3 8 4 7 6 5 2 1 7 2 1 7 8 6 8 6 (2) (1) (0) 3 4 5 3 4 5 (4) (3) 3 (3) 2 8 3 8 4 1 4 6 5 7 6 5 1 7 2 8 6 2 1 7 3 4 5 3 8 6 4 5 (2) (4) (4) 2 8 3 (5) 1 6 4 7 5 OPEN — nodes on frontier; CLOSED – expanded nodes OPEN = {〈s, nil〉} while OPEN is not empty remove from OPEN the pair 〈n, p〉 with minimal f (n) place 〈n, p〉 on CLOSED if n is a goal node return success (path p) for each edge e connecting n and n ′ with cost c if 〈n ′ , p ′ 〉 is on CLOSED and p ⊕ e is cheaper than p ′ then remove n ′ from CLOSED and put 〈n ′ , p ⊕ e〉 on OPEN else if 〈n ′ , p ′ 〉 is on OPEN and p ⊕ e is cheaper than p ′ then replace p ′ with p ⊕ e else if n ′ is not on OPEN then put 〈n ′ , p ⊕ e〉 on OPEN return failure COMP9414 c○UNSW, 2005 Generated: 24 March 2005 COMP9414 c○UNSW, 2005 Generated: 24 March 2005
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COMP9414: Artificial Intelligence Informed Search - Sorry

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