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chapter4 - Informed search algorithms CHAPTER 4 HASSAN...

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CHAPTER 4 HASSAN KHOSRAVI SPRING2011 Informed search algorithms

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Outline Best-first search Greedy best-first search A * search Heuristics Local search algorithms Hill-climbing search Simulated annealing search Local beam search Genetic algorithms
Review: Tree search A search strategy is defined by picking the order of node expansion

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Best-first search Idea: use an evaluation function f(n) for each node estimate of "desirability" Expand most desirable unexpanded node Implementation : Order the nodes in fringe in decreasing order of desirability Special cases: greedy best-first search A * search
Romania with step costs in km

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Greedy best-first search Evaluation function f(n) = h(n) ( h euristic) = estimate of cost from n to goal e.g., h SLD (n) = straight-line distance from n to Bucharest Greedy best-first search expands the node that appears to be closest to goal
Greedy best-first search example

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Greedy best-first search example
Greedy best-first search example

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Greedy best-first search example
Properties of greedy best-first search Complete? No can get stuck in loops, e.g. as Oradea as goal Iasi Neamt Iasi Neamt Time? O(b m ) , but a good heuristic can give dramatic improvement Space? O(b m ) -- keeps all nodes in memory Optimal? No

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A * search Idea: avoid expanding paths that are already expensive Evaluation function f(n) = g(n) + h(n) g(n) = cost so far to reach n h(n) = estimated cost from n to goal f(n) = estimated total cost of path through n to goal
A * search example

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A * search example
A * search example

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A * search example
A * search example

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A * search example
Admissible heuristics A heuristic h(n) is admissible if for every node n , h(n)

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• Winter '09
• STEVENPEARCE
• Search algorithms, A* search algorithm, Best-first search, Admissible heuristic, Consistent heuristic

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chapter4 - Informed search algorithms CHAPTER 4 HASSAN...

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