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# lecture5 - Articial Intelligence Informed Search Nilsson...

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Informed Search; page 1 of 26 Artiﬁcial Intelligence Informed Search Nilsson - Chapter 9 Russell and Norvig - Chapter 4

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Informed Search; page 2 of 26 state space search tree A BD EF start with a tree that contains only the start state pick a fringe node n (somehow using estimates of the goal distances) if fringe node n represents a goal state: stop expand fringe node n go to start:A B goal: G D E F C 0 inﬁnity 1 2 1 2 3 h(n): heuristic estimate of the goal distance of n (really: of s(n)) for example: h(A) = 3 h: heuristic function best-ﬁrst search:
Informed Search; page 3 of 26 Greedy Search start with a tree that contains only the start state pick a fringe node n with the smallest h(n) if fringe node n represents a goal state: stop expand fringe node n go to search tree? start:A B goal: G D E F C 0 inﬁnity 1 2 1 1 2

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Informed Search; page 4 of 26 start: A B C D E G H works often well in practice but has problems Greedy Search goal: F I J 2 1 3 1 1 1 1 1 1
Informed Search; page 5 of 26 A* start with a tree that contains only the start state pick a fringe node n with the smallest f(n) = g(n) + h(n) if fringe node n represents a goal state: stop expand fringe node n go to search tree? start:A B goal: G D E F C 0 inﬁnity 1 2 1 1 2 depth of n (or weighted distance from root node to n) heuristic estimate of the goal distance of n heuristic estimate of the length of a shortest path from the root to a goal node that goes through n g(n) = h(n) = f(n) = (really: from the start state to a goal state that goes through s(n))

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Informed Search; page 6 of 26 uniform cost search start A* = A* with h(s) = 0! start goal goal uninformed search informed search iso-f value contours Uninformed Search vs. Informed Search
Informed Search; page 7 of 26 1.5 2.0 2.5 3.0 4.5 6.0 3.0 4.5 6.0 6.0 6.0 6.0 4.5 4.5 4.5 6.5 7.0 7.5 3.0 3.5 4.0 6.0 5.0 5.5 6.0 7.5 7.5 9.0 9.0 10.5 7.5 7.5 9.0 7.5 9.0 10.5 6.0 4.5 4.5 3.0 3.5 4.0 6.0 7.5 7.5 6.0 4.5 5.0 5.5 6.0 7.5 9.0 7.5 9.0 6.0 6.5 7.0 7.5 9.0 10.5 7.5 9.0 10.5 start goal h value = goal distance / 2 gridworld - the robot can move north, east, south, or west I don’t guarantee that I have not made mistakes - if you ﬁnd one, please let me know f-value

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Informed Search; page 8 of 26 Properties of Heuristic Functions Let gd(s) be the goal distance of state s. h is admissible iff, for all states s, h is consistent (or, synonymously, monotonic ) iff, for all states s, h(s) = 0 0 <= h(s) <= h(s’) + c(s,s’) for all succ states s’ of s if s is a goal state otherwise “the estimates never overestimate the true goaldistances” 0 <= h(s) <= gd(s) “the triangle inequality holds” Let c(s,s’) be the action cost of the action going from s to s’.
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lecture5 - Articial Intelligence Informed Search Nilsson...

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