Download presentation

Presentation is loading. Please wait.

Published bySeth Postlethwait Modified over 2 years ago

1
Optimality of A*(standard proof) Suppose suboptimal goal G 2 in the queue. Let n be an unexpanded node on a shortest path to optimal goal G. f(G 2 ) = g(G 2 )since h(G 2 )=0 > g(G)since G 2 is suboptimal >= f(n)since h is admissible Since f(G 2 ) > f(n), A* will never select G 2 for expansion

2
A* - Optimality A* is optimally efficient (Dechter and Pearl 1985): –It can be shown that all algorithms that do not expand a node which A* did expand may miss an optimal solution

3
Memory-bounded heuristic search A* keeps all generated nodes in memory –On many problems A* will run out of memory Iterative deepening A* (IDA*) –Like IDS but uses f-cost rather than depth at each iteration SMA* (Simplified Memory-Bounded A*) –Uses all available memory –Proceeds like A* but when it runs out of memory it drops the worst leaf node (one with highest f-value) –If all leaf nodes have the same f-value then it drops oldest and expands the newest –Optimal and complete if depth of shallowest goal node is less than memory size

4
Iterative Deepening A* (IDA*) Use f(n) = g(n) + h(n) like in A* Each iteration is depth-first with cutoff on the value of f of expanded nodes

5
8-Puzzle 4 6 f(N) = g(N) + h(N) with h(N) = number of misplaced tiles Cutoff=4

6
8-Puzzle 4 4 6 f(N) = g(N) + h(N) with h(N) = number of misplaced tiles Cutoff=4 6

7
8-Puzzle 4 4 6 f(N) = g(N) + h(N) with h(N) = number of misplaced tiles Cutoff=4 6 5

8
8-Puzzle 4 4 6 f(N) = g(N) + h(N) with h(N) = number of misplaced tiles Cutoff=4 6 5 5

9
4 8-Puzzle 4 6 f(N) = g(N) + h(N) with h(N) = number of misplaced tiles Cutoff=4 6 5 56

10
8-Puzzle 4 6 f(N) = g(N) + h(N) with h(N) = number of misplaced tiles Cutoff=5 G

11
8-Puzzle 4 4 6 f(N) = g(N) + h(N) with h(N) = number of misplaced tiles Cutoff=5 6

12
8-Puzzle 4 4 6 f(N) = g(N) + h(N) with h(N) = number of misplaced tiles Cutoff=5 6 5

13
8-Puzzle 4 4 6 f(N) = g(N) + h(N) with h(N) = number of misplaced tiles Cutoff=5 6 57

14
8-Puzzle 4 4 6 f(N) = g(N) + h(N) with h(N) = number of misplaced tiles Cutoff=5 6 5 7 5

15
8-Puzzle 4 4 6 f(N) = g(N) + h(N) with h(N) = number of misplaced tiles Cutoff=5 6 5 7 55

16
8-Puzzle 4 4 6 f(N) = g(N) + h(N) with h(N) = number of misplaced tiles Cutoff=5 6 5 7 55

17
Iterative Improvement Algorithms Example: n queens Try to find the highest peaks which are optimal Keep track of only the current state and do not look ahead beyond the immediate neighbours Two classes Hill climbing algoritms make changes to improve the current state Simulated annealing algoritms Allow some bad moves to get out of a local maxima

18
Hill Climbing

20
Simulated Annealing

Similar presentations

Presentation is loading. Please wait....

OK

An Introduction to Artificial Intelligence

An Introduction to Artificial Intelligence

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on classical economics unemployment Mp ppt online form Ppt on effect of western culture on indian youth Ppt on leadership styles in banking sector Ppt on latest technology in electronics and communication free download Ppt on hydro power plant in india Ppt on crash fire tender picture Ppt on natural disasters for kids Ppt on indian politics today Forms of energy for kids ppt on batteries