Search in Artificial Intelligence

1
Search in Artificial Intelligence

• Find the next move in chess, checkers.
• Scheduling finding a good class schedule.
• Theorem proving given a set of axioms and
  inference rules, find a proof of a theorem.
• Planning find a sequence of actions to achieve a
  goal for a robot.
• Natural language understanding find the best
  parse of a sentence.

2
Dimensions of Search Problems

• In its general form find a desired object among
  a set of objects.
• Sometimes, you dont even know if the object
  exists or not.
• In other cases, the goal is to find the best
  object.
• Blind vs. informed search.

3
Specifying a search problem?

• What are states (nodes in graph)?
• What are the operators (arcs between nodes)?
• Initial state?
• Goal test
• Metric (e.g., distance to goal)

1 2 3
7 2 3
4 5 6
4 1 6
E.g., Eight Puzzle
7 8
8 5
4
Search

• Types of Search
• Blind
• Heuristic optimization
• Adversary Search
• Analysis
• Completeness
• Time complexity
• Space Complexity
• Guaranteed to find best solution?
• Guaranteed to find the closest solution?

5
Search Strategies

• Blind Search
• Generate test
• Depth first search
• Breadth first search
• Iterative deepening search
• Iterative broadening search
• Heuristic search
• Optimizing search

6
Depth First Search

• Maintain stack of nodes to visit
• Evaluation
• Complete?
• Time Complexity?
• Space Complexity?

Not for infinite spaces
a
O(bd)
b
e
O(d)
g
h
c
d
f
7
Breadth First Search

• Maintain queue of nodes to visit
• Evaluation
• Complete?
• Time Complexity?
• Space Complexity?

Yes
a
O(bd)
b
c
O(bd)
g
h
d
e
f
8
Iterative Deepening Search

• DFS with limit incrementally grow limit
• Evaluation
• Complete?
• Time Complexity?
• Space Complexity?

Yes
a
b
e
O(bd)
c
d
f
i
O(d)
L
g
h
j
k
9
Search Strategies
?

• Blind Search
• Heuristic Search
• Best-first
• Beam
• Hill climbing
• Simulated annealing
• Optimizing Search

10
Heuristic Search

• A heuristic (metric) is
• Function from a state to a real number
• Low number means state is close to goal
• High number means state is far from the goal

Designing a good heuristic is very
important! (And hard) More on this in a bit...
11
Best First Search

• Idea
• Breadth first but use priority queue instead of a
  queue
• Evaluation
• Complete?
• Time Complexity?
• Space Complexity?

a
b
e
No
c
d
f
i
O(bd)
L
g
h
j
k
O(bd)
12
Beam Search

• Idea
• Best first but only keep N best items on priority
  queue
• Evaluation
• Complete?
• Time Complexity?
• Space Complexity?

a
b
e
No
c
d
f
i
O(bd)
L
g
h
j
k
O(b N)
13
Hill Climbing

• Idea
• Always choose best child no backtracking
• Evaluation
• Complete?
• Time Complexity?
• Space Complexity?

a
b
e
No - suffers from plateau, local maxima, ridges
c
d
f
i
O(bd) but only in pathological cases
L
g
h
j
k
O(b)
14
Simulated Annealing

• Objective avoid local minima
• Technique
• For the most part use hill climbing
• Occasionally take non-optimal step
• Reduce probability(non-optimal) over time
• Comparison to Hill Climbing
• Completeness?
• Speed?
• Space Complexity?

temp
15
Search Strategies
?

• Blind Search
• Heuristic Search
• Optimizing Search
• A
• IDA
• SMA

?
Objective is to find the very best solution.
16
A Search

Underestimates cost of any solution which can
reached from node

• Idea
• Best first search with admissible heuristic
• Plus keep checking until all possibilities look
  worse
• Evaluation
• Finds optimal solution?
• Time Complexity?
• Space Complexity?

Yes
O(bd)
O(bd)
17
Admissible Heuristics

• f(x) g(x) h(x)
• g cost so far
• h underestimate of remaining costs

e
12
8
d
a
f
10
8
For eight puzzle?
14
20
b
15
c
18
Importance of Heuristics

• h1 number of tiles in wrong place
• h2 sum of distances of tiles from correct loc

D IDS A(h1) A(h2) 2 10
6 6 4 112 13 12 6
680 20 18 8 6384 39 25 10
47127 93 39 12 364404 227
73 14 3473941 539 113 18
3056 363 24 39135 1641
19
Iterative Deepening A

• Like iterative deepening depth first, but...
• Depth bound modified to be an f-cost limit
• Contour lines bounding search

e
d
a
f
b
c
20
SMA

• Problem is f-cost bound increases slowly
• Must do iterative search again and again
• Storing little state between each iteration
• Just one number next highest contour level
• SMA
• Uses all available memory to store state
• Duplicates minimal work
• Optimal in a number of nice ways

21
Adversary Search

• Game playing want to make the move for which the
  opponent cannot respond well.

a
b
e
max
c
d
f
i
min
L
g
h
j
k
max
-1
min
c
c
c
c
1
f
f
f
f
-1
1
1
max
g
h
h
g
g
h
1
-1
-1
-1
22
Alpha-beta Pruning

a
max
b
e
min
c
d
f
i
max
L
g
h
j
k
min
c
c
c
c
f
f
f
f
max