Basic Search Problem
4
A
4
B
C
3
S
5
5
G
4
3
D
2
E
4
F
1
S
Search Tree from Net
Denotes the path S-D
A
D
B
C
E
D
D
A
E
B
F
D
B
F
G
C
G
C
E
B
E
A
F
C
G
F
Denotes the path S-D-A-B-E-F-G
G
2
Depth-First Search
S
A
B
C
D
E
D
F
G
3
Breadth-First Search
S
A
D
B
C
E
D
F
D
B
D
A
E
B
F
C
E
B
E
A
F
C
G
4
Heuristically Informed
Methods
A
B
C
10.4
6.7
4.0
11.0
S
G
8.9
3.0
6.9
D
E
F
5
Hill Climbing
S
10.4
8.9
A
D
10.4
A
E
6.9
3.0
6.7
B
F
G
6
Problems with
Hill Climbing
Z
N
E
Z
N
E
N
Steps in all
compass directions
from a ridge point
cross contour lines
going down.
High altitude
contour line
Low altitude
contour line
E
7
Beam Search (1)
S
10.4
A
8.9
D
8
Beam Search (2)
S
A
D
6.7
B
8.9
D
10.4
A
6.9
E
9
Beam Search (3)
S
A
B
D
4.0
C
D
6.9
E
A
E
6.7
B
3.0
F
Dead
end
10
Beam Search (4)
A
B
C
D
D
A
E
E
B
F
Dead
end
A
C
G
11
Optimal Search
S
D
A
B
E
F
13
G
13
12
Branch and Bound (1)
S
A
D
3
4
S
A
D
4
13
S
Branch and Bound (2)
A
D
3
4
S
A
D
4
B
D
7
8
S
14
A
Branch and Bound (3)
B
D
7
8
D
C
4
1
S
A
D
B
D
A
E
7
8
9
6
S
C
1
A
D
15
B
D
A
Branch and Bound (4)
7
E
B
8
9
6
S
A
C
E
11
12
D
B
D
A
7
8
9
E
S
B
F
11
10
B
A
D
16
B
D
A
7
8
9
Branch and Bound (5)
E
S
B
F
11
10
B
A
B
D
D
8
A
C
E
11
12
E
9
C
E
B
F
11
12
11
10
17
Branch and Bound (6)
S
A
B
D
D
A
E
B
9
C
E
E
B
F
C
E
11
12
10
11
10
11
12
18
S
11
12
10
11
10
11
12
Branch and Bound (7)
S
A
D
A
E
B
D
A
E
B
6
C
E
E
B
B
F
C
E
11
12
10
13
11
10
11
12
E
S
19
C
E
E
B
B
F
C
E
11
12
10
13
11
10
11
12
Branch and Bound (8)
E
S
F
A
D
10
B
C
E
11
12
D
A
E
B
B
F
C
13
11
10
11
E
B
E
E
D
B
F
D
15
14
14
F
10
20
Branch and Bound (9)
S
A
E
D
B
F
C
E
10
11
12
Dead
end
D
A
E
E
B
B
13
11
F
D
B
F
G
15
14
13
Goal
S
21
D
B
F
G
15
Branch and Bound
(10)14
13
S
A
E
D
B
F
C
E
10
11
12
D
A
E
B
E
B
F
13
D
B
F
A
C
G
15
14
15
15
13
S
22
D
B
F
Branch and Bound15(11)14
A
C
G
15
15
13
S
A
E
D
B
F
C
10
11
E
D
A
E
B
E
B
F
13
D
F
D
B
F
A
C
G
14
16
15
14
15
15
13
23
B&B with
Underestimates (1)
S
A
D
13.4
12.9
S
A
D
13.4
A
19.4
E
12.9
24
B&B with
A
Underestimates
(2)
D
13.4
12.9
S
A
D
13.4
A
E
19.4
12.9
S
A
13.4
D
25
13.4
B&B with
Underestimates (3)
A
E
19.4
12.9
S
A
D
13.4
A
E
19.4
B
17.7
F
13
S
26
19.4
B&B with
Underestimates (4)
B
F
17.7
13
S
A
D
13.4
A
E
19.4
B
F
17.7
G
13
27
Dynamic Programming
S
A
Expanded next
D
4
B
D
7
8
Never expanded
28
B&B with Dynamic
Programming (1)
S
A
D
3
4
S
A
D
29
B&B with Dynamic
Programming (2)
S
A
D
4
B
D
7
8
S
3
A
D
4
30
7
8
B&B with Dynamic
Programming (3)
S
3
A
D
4
B
D
A
E
7
8
9
6
31
B&B with Dynamic
Programming (4)
S
3
A
D
B
D
A
7
8
9
4
E
6
B
F
11
10
S
32
B&B with Dynamic
Programming (5)
B
F
11
10
S
3
7
B
A
D
D
A
8
9
4
E
6
C
E
B
F
11
12
11
10
S
33
C
E
B&B with
Dynamic
11
12
Programming (6)
B
F
11
10
S
3
7
B
A
D
D
A
8
9
4
E
C
E
B
11
12
11
10
6
F
G
34
A* Algorithm



Form a one-element queue consisting of a zero-length path that
contains only the root node.
Until the first path in the queue terminates at the goal node or the
queue is empty,
 Remove the first path from the queue; create new paths by
extending the first path to al the neighbors of the terminal node.
 Reject all paths with loops.
 If two or more paths reach a common node, delete all those paths
except the one that reaches the common node with the minimum
cost.
 Sort the entire queue by the sum of the path length and a lowerbound estimate of the cost remaining, with least-cost paths in front.
If the goal node is found, announce success; otherwise, announce
35
failure.
Obstacle-Avoidance
Problem
Initial position
Desired position
36
Configuration-Space
Transformation
6
5
7
4
8
3
1
2
37
New Configuration
Space
Initial position
Desired position
38
Visibility Graph
Initial position
39
Desired position
Solution by Shortest
Paths
Initial position
40
Desired position