Ch. 4 – Informed Search

Supplemental slides for CSE 327Prof. Jeff Heflin

A* Example• Use A* to solve the 8-puzzle:

1 2 34 6 87 5

1 2 34 5 67 8

initial state: goal state:

• Choose a heuristic– H1: The number of tiles out of place

– H2: Sum of distances of tiles from goal positions

• Ignore moves that return you to the previous state

path cost is the total number of moves made

A* on 8-puzzle1 2 34 6 87 5

1 2 34 67 5 8

1 2 34 6 87 5

1 24 6 37 5 8

1 2 34 67 5 8

1 2 34 87 6 5

1 2 34 6 8

7 5

1 34 2 67 5 8

1 2 34 6

7 5 8

1 2 34 5 67 8

1 2 34 5 6 7 8

1 2 34 5 67 8

f=0+3=3

f=1+3=4 f=1+3=4

f=2+4=6 f=2+2=4 f=2+3=5 f=2+4=6

f=3+3=6 f=3+3=6 f=3+1=4

f=4+2=6 f=4+0=4

1

2 3

4

5

6

Heuristic = H1

Whether or not this node is expanded depends on how you break ties. It could be expanded at any time or not at all.

A* on 8-puzzle1 2 34 6 87 5

1 2 34 67 5 8

1 2 34 6 87 5

1 24 6 37 5 8

1 2 34 67 5 8

1 34 2 67 5 8

1 2 34 6

7 5 8

1 2 34 5 67 8

1 2 34 5 6 7 8

1 2 34 5 67 8

f=0+4=4

f=1+3=4 f=1+5=6

f=2+4=6 f=2+2=4

f=3+3=6 f=3+3=6 f=3+1=4

f=4+2=6 f=4+0=4

1

2

3

4

5

Heuristic = H2

Summary of Search Algorithms

type ordering optimal? complete? efficient?

depth-first uninformed LIFO no no if lucky

breadth-first uninformed FIFO yesa yes no

uniform cost uninformed g(n) yesb yesb no

greedy informed h(n) no no usually

A* informed g(n)+h(n) yesc yes yes

a – optimal if step costs are identicalb – optimal and complete if step costs > 0c – optimal if heuristic is admissible