Ch4: Searching Techniques Define the problem: must include precise specifications ~ initial solution & final solution. Analyze the problem: select the most important features that can have an immense impact. Isolate and represent : convert these important features into knowledge representation. Problem solving technique(s): choose the best technique and apply it to particular problem. Search space  possible conditions and solutions. Initial state  state where the searching process started. Goal state  the ultimate aim of searching process. Problem space  “what to solve” Searching strategy strategy for controlling the search. Search tree  tree representation of search space, showing possible solutions from initial state.

1. Chap 4:
Searching Techniques
Artificial Intelligence
Chapter 4

2. Motivation
Attempt the end, and never stand to
doubt, nothing’s so hard, but search
will find it out
“Robert Herrick”

3. What we will cover ?
 Ideas in searching
 Searching tree
representation
 Uninformed and informed
search
 Game playing search

4. Problem as a State Space
Search
 To build as system to solve a particular problem, we
need:
 Define the problem: must include precise
specifications ~ initial solution & final solution.
 Analyze the problem: select the most important
features that can have an immense impact.
 Isolate and represent : convert these important
features into knowledge representation.
 Problem solving technique(s): choose the best
technique and apply it to particular problem.

5. The Quest
 Typical questions that need to be answered:
 Is the problem solver guaranteed to find a solution?
 Will the system always terminate or caught in a infinite
loop?
 If the solution is found, it is optimal?
 What is the complexity of searching process?
 How the system be able to reduce searching complexity?
 How it can effectively utilize the representation
paradigm?

6. Important Terms
 Search space  possible conditions and solutions.
 Initial state  state where the searching process
started.
 Goal state  the ultimate aim of searching process.
 Problem space  “what to solve”
 Searching strategy strategy for controlling the
search.
 Search tree  tree representation of search space,
showing possible solutions from initial state.

7. Example: The Bridges of
Konigsberg Problem
•Classical graph
applications.
•Introduced by Leonhard
Euler.
•Problem: Can a person
walk around the city
crosses each bridge
exactly once?

8. Example: The Bridges of
Konigsberg Problem (cont)
B
D
C
A
b1
b2
b3
b4
b6
b5
b7
Predicates: Connect (B, C, b5)

9. Example: Traveling
Salesperson Problem
•Suppose a salesperson has five cities to visit and them
must return home. Goal  find the shortest path to
travel.
B
C
D
E
75
50
100
100
125
125
125
75
50
A

10. Searching for Solution
•Search through state space (explicitly using searching
tree).
•Node expansion :- generating new node related to previous
nodes.
•Concepts:
•State :- conditions in which the node corresponds.
•Parent node :- the superior node
•Path cost :- the cost, from initial to goal state.
•Depth:- number of steps along the path from initial state

11. Node expansion

12. Node expansion (initial)

13. Node expansion
(expanding Arad)

14. Node expansion
(expanding Sibiu)

15. Measuring Searching
Performance
•The output from problem-solving (searching) algorithm is
either FAILURE or SOLUTION.
•Four ways:
•Completeness : is guaranteed to find a solution?
•Optimality: does it find optimal solution ?
•Time complexity: how long?
•Space complexity: how much memory?
•Complexity : branching factor (b), depth (d), and
max. depth (m)

16. Searching Strategies
•Heuristic search  search
process takes place by
traversing search space with
applied rules (information).
•Techniques: Greedy Best
First Search, A* Algorithm
•There is no guarantee that
solution is found.
•Blind search  traversing
the search space until the
goal nodes is found (might be
doing exhaustive search).
•Techniques : Breadth First
Uniform Cost ,Depth first,
Interactive Deepening
search.
•Guarantees solution.

17. Blind Search : Breadth First
Search (BFS)
•Strategy ~ search all the nodes expanded at given depth
before any node at next level.
•Concept : First In First Out (FIFO) queue.
•Complete ?: Yes with finite b (branch).
•Complexity:
•Space : similar to complexity – keep nodes in every memory
•Optimal ? = Yes (if cost =1)

18. Blind Search : Breadth First
Search
1 2
4
3

19. Blind Search : Depth First
Search (DFS)
•Strategy ~ search all the nodes expanded in deepest path.
•Last In First Out concept.
•Complete ?: No
•Complexity:
•Space : O(bm) – b ; branching factor, m ; max. depth
•Optimality ? : No

20. Blind Search : Depth First
Search (DFS)
1 2 3
4 5
…….
N+1

21. Blind Search : Iterative
Deepening DFS (ID-DFS)
•Strategy ~ combines DFS with best depth limits.
•Gradually increase the limit; L=0, L=1… and so on.
•Complete ?: Yes (if b is finite)
•Complexity:
•Space :
•Optimality ? : yes (if path costs are all identical)

22. Blind Search : Iterative
Deepening DFS (ID-DFS)

23. Summary

24. Heuristic Search :
•Important aspect: formation of
heuristic function (h(n)).
•Heuristic function  additional
knowledge to guide searching
strategy (short cut).
•Distance: heuristic function
can be straight line distance
(SLD)
A*
B C*
D
E
h(n)=0
h(n)=34
h(n)=24
h(n)=67
h(n)=12
h(n)=9

25. Heuristic Search : Heuristic
Function

26. Heuristic Search :Greedy-
Best Search
•Tries to expand the node that is closest to the
goal.
•Evaluates using only heuristic function : f(n) = h(n)
•Possibly lead to the solution very fast.
•Problem ? ~ can end up in sub-optimal solutions
(doesn’t take notice of the distance it travels).
•Complexity and time:
•Complete & optimal ? : No (stuck in infinite loop)

27. Heuristic Search :Greedy-
Best Search
1
2

28. Heuristic Search :Greedy-
Best Search
3

29. Heuristic Search : A*
Algorithm
•Widely known algorithm – (pronounced as “A star”
search).
•Evaluates nodes by combining g(n) “cost to reach the
node” and h(n) “cost to get to the goal”
•f(n) = g(n) + h(n), f(n)  estimated cost of the
cheapest solution.
•Complete and optimal ~ since evaluates all paths.
•Time ? ~ a bit time consuming
•Space ? ~ lot of it!

30. Heuristic Search : A*
Algorithm
S
G
E
D
A
G’ H
:10
:8 :9
:0
:4 :0 :3
2 3
2
5 1
3
Path cost for S-D-G
f(S) = g(S) + h(S)
= 0 + 10  10
f(D) = (0+3) + 9  12
f(G) = (0+3+3) + 0  6
Total path cost = f(S)+f(D)+f(G)
28
Path cost for S-A-G’
f(S) = 0 + 10  10
f(A) = (0+2) + 8  10
f(G’) = (0+2+2) + 0  4
Total path cost = f(S)+f(A)+f(G’) 24
* Path S-A-G is chosen
= Lowest cost

31. Heuristic Search : A*
Algorithm

32. Heuristic Search : A*
Algorithm

33. TIN 5013: Artificial Intelligence
Heuristic Search : A*
Algorithm

34. Heuristic Search : A*
Algorithm

35. TIN 5013: Artificial Intelligence
Heuristic Search : A*
Algorithm

36. Issues in Heuristic Search
•Searching using heuristic function does not solely on
directed solution  but the best algorithm to find
shortest path towards goal.
•Admissible  attempt to find possible shortest path to
a goal whenever it exists.
•Informedness  question in what sense the heuristic
function is better than another.
•Monotonicity  question if the best state is
discovered by heuristic search, is there any guarantee
that the same state won’t be found later at lowest
searching cost?

37. References
 Cawsey, A. (1998). The Essence of Artificial
Intelligence, Prentice Hall.
 Russell, S. and Norvig, P. (2003). Artificial
Intelligence: A Modern Approach, Prentice-
Hall 2nd
Edition.