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

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)

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

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

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

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

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

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

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

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
cost to reach node
heuristic: node to goal

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

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)

13. Hill-Climbing Search

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

15. Problem: Local Maximum

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

17. 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)