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**Informed Search CS 171/271 (Chapter 4)**

Some text and images in these slides were drawn from Russel & Norvig’s published material

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**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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**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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**Informed Search Greedy Best-First Search A* Search**

Local Search Algorithms

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**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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**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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**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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**Sum of Manhattan distances: 3+1+2+2+2+3+3+2 = 18**

Sum of misplaced tiles: 8

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**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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**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 cost to reach node heuristic: node to goal

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**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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**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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Hill-Climbing Search

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**Climb Illustration Number of “hostile” queen-pairs: 17**

Several possible moves improve this measure to 12

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**Problem: Local Maximum**

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**Getting Stuck in a Local Maximum**

Not a goal state but improvement is not possible

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**Escaping Local Maxima Simulated Annealing Local Beam Search**

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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Feng Zhiyong Tianjin University Fall 2008. Best-first search Greedy best-first search A * search Heuristics Local search algorithms Hill-climbing.

Feng Zhiyong Tianjin University Fall 2008. Best-first search Greedy best-first search A * search Heuristics Local search algorithms Hill-climbing.

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