03-lecture3 - CS 470 Lecture 3: Informed Search Sept 9,...

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Unformatted text preview: CS 470 Lecture 3: Informed Search Sept 9, 2010 Alice Oh 1 Friday, September 10, 2010 Administrivia • Exam is September 14th! Next Tuesday • Moodle has the most accurate information • http://moodle.kaist.ac.kr / • I will put up sample exam questions on Moodle today • For this exam, I will make sure the textbook 2nd edition is okay 2 Friday, September 10, 2010 Today’s Contents (and Readings) • Informed Search • Last Week: Greedy Best First Search (pp. 94~97) • Today • A* Search (pp. 97~101) • Heuristic Functions (pp. 105~110) • Local Search (pp. 110~115) • Hill-climbing • Simulated Annealing • Local Beam Search; stochastic beam search • Genetic algorithms 3 Friday, September 10, 2010 Acknowledgements • Some of the Fgures are from the lecture slides at • http://www.cs.cmu.edu/afs/cs/academic/class//15381-s07/www/ • http://inst.eecs.berkeley.edu/~cs188/sp09/lectures.html 4 Friday, September 10, 2010 Strategy: Choose cheapest node frst Implementation: Priority queue Like BFS, but with Cost, rather than Depth, as priority value Last Time: Uniform Cost Search 5 Friday, September 10, 2010 Last Time: Best First Search Like DFS, but choosing node with lowest h (estimated cost to the Goal) rather than highest depth 6 Friday, September 10, 2010 A* Search Combining UCS and BFS What does UCS do? BFS? 7 Friday, September 10, 2010 A* Search Combining UCS and BFS What does UCS do? BFS? UCS fnds S->a->d->G BFS fnds S->a->e->d->G 7 Friday, September 10, 2010 A* Search A* Search chooses by f(n) = g(n) + h(n) g(n): path cost so far h(n): estimated cost to the goal 8 Friday, September 10, 2010 A* Search <s, 6> <a, 6> <d, 6>, <b, 7>, <e, 7> <G, 6>, <b, 7>, <e, 7> Pop <G, 6>, path found is S->a->d->G 9 Friday, September 10, 2010 What happens here? 10 Friday, September 10, 2010 What happens here? <S, 8> <B, 4>, <A, 8> <C, 4>, <A, 8> <D, 4>, <A, 8> <A, 8>, <G, 10> <G, 2> Pop G Path found: S->A->G • A* Terminates when G is popped • When a state is re- visited, f(n) gets updated 11 Friday, September 10, 2010 Q: When is A* Optimal? A: When you have an “admissible” heuristic function, h(n) 12 Friday, September 10, 2010 Admissible Heuristics • Defne h*(s) = true minimal cost From state s to goal • h is admissible iF h(s ) <= h*(s) For all s An admissible heuristic never overestimates the cost to the goal. It is an “optimistic” estimate oF cost to goal. A* is guaranteed to fnd the optimal path iF h is admissible. 13 Friday, September 10, 2010 A* Optimality Proof Given Admissible h • Suppose G* is a lower-cost Goal state than G. • There must be a state n which is on the path to G*. • By following the equalities and inequalities below, n must be popped, its children added to the queue before G is popped....
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03-lecture3 - CS 470 Lecture 3: Informed Search Sept 9,...

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