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

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)

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

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

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

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

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

Sum of Manhattan distances: 3+1+2+2+2+3+3+2 = 18 Sum of misplaced tiles: 8

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

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

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

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)

Hill-Climbing Search

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

Problem: Local Maximum

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

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)