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1 Informed Search CS 171/271 (Chapter 4) Some text and images in these slides were drawn from Russel & Norvigs published material

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2 Search Strategies Revisited Strategy defines order of node expansion We can view BFS, Uniform-Cost, DFS, and others as strategies that select nodes according to an evaluation function f(n): some measure on node n Select the node with minimum f(n)

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3 Search Strategies Revisited Uninformed search Evaluation function dependent on states and successor function only Improvements achieved if repeated states are detected Informed (heuristic) search Problem-specific information may be incorporated in the evaluation function

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4 Informed Search Greedy Best-First Search A* Search Local Search Algorithms

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5 Greedy Best-First Search Strategy: expand node that is closest to goal Based on a heuristic function on each node that represents closeness to goal Closeness measure not necessarily accurate (of course!), but has some basis

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6 Example 1: Route Finding Straight-line distance heuristic Direct distance from node to goal Actual cost is not always this distance since not all nodes are connected by a straight line path Practical significance You have a map where straight-line distances are more obvious than the sums of connections

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7 Example 2: 8-puzzle Sum of Manhattan distances Select the move that yields the minimum sum of distances of tiles from their goal positions (horizontal/vertical steps only) Number of misplaced tiles Select the move that renders a configuration with the fewest number of misplaced tiles

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8 Sum of Manhattan distances: = 18 Sum of misplaced tiles: 8

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9 About Greedy Best-First Search Not always optimal/complete Completeness depends on heuristic Example? (see page 97) Implementation requires a priority queue Uninformed (and Informed) Search Algorithms are in fact special cases of Greedy Best-First search

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10 A* Search Greedy Best-First Search where the evaluation function is g(n) + h(n) Guaranteed to be optimal as long as h is admissible heuristic: node to goal cost to reach node

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11 Admissible Heuristics A heuristic is admissible if it never overestimates the cost to reach the goal Examples Straight-line distance Manhattan distance Number of misplaced tiles Note: a relaxed version of a problem yields an admissible heuristic

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12 Local Search Most appropriate when the path-cost is not relevant Strategy: start with an initial complete state, and then improve incrementally Example: n-queens use complete-state formulation instead of incremental formulation Repeatedly move to a successor (move a queen within a column) that has the fewest queen-pairs that attack each other (hill-climbing)

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13 Hill-Climbing Search

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14 Climb Illustration Number of hostile queen-pairs: 17 Several possible moves improve this measure to 12

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15 Problem: Local Maximum

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16 Getting Stuck in a Local Maximum Not a goal state but improvement is not possible

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17 Escaping Local Maxima Simulated Annealing Select successors randomly Allow downhill moves in early iterations Local Beam Search Keep k states instead of just one Choose top states from all successors Mimics natural selection (survival of the fittest)

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