1. Chap 4: Searching Techniques
Artificial Intelligence
Chapter 4
TIN 5013: Artificial Intelligence

2. TIN 5013: Artificial Intelligence
Motivation
Attempt the end, and never stand to doubt, nothing’s so hard, but search will find it out
“Robert Herrick”
TIN 5013: Artificial Intelligence

3. TIN 5013: Artificial Intelligence
What we will cover ?
Ideas in searching
Searching tree representation
Uninformed and informed search
Game playing search
TIN 5013: Artificial Intelligence

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.
TIN 5013: Artificial Intelligence

5. TIN 5013: Artificial Intelligence
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?
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6. TIN 5013: Artificial Intelligence
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.
TIN 5013: Artificial Intelligence

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?
TIN 5013: Artificial Intelligence

8. Example: The Bridges of Konigsberg Problem (cont)
Predicates: Connect (B, C, b5)
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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. A B 75
125
125 75
100 E 50
125 C 50
100 D
TIN 5013: Artificial Intelligence

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
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11. TIN 5013: Artificial Intelligence
Node expansion
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12. Node expansion (initial)
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13. Node expansion (expanding Arad)
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14. Node expansion (expanding Sibiu)
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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)
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16. TIN 5013: Artificial Intelligence
Searching Strategies
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.
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.
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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)
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18. Blind Search : Breadth First Search2 1 4 3
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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
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20. Blind Search : Depth First Search (DFS)3 1 2 4 5
…….
N+1
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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)
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22. Blind Search : Iterative Deepening DFS (ID-DFS)
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23. TIN 5013: Artificial Intelligence
Summary
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24. TIN 5013: Artificial Intelligence
Heuristic Search :
h(n)=67
h(n)=34 E A*
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) D
h(n)=9
h(n)=12 B C*
h(n)=24
h(n)=0
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25. Heuristic Search : Heuristic Function
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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)
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27. Heuristic Search :Greedy-Best Search1 2
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28. Heuristic Search :Greedy-Best Search3
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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!
TIN 5013: Artificial Intelligence

30. Heuristic Search : A* Algorithm
Path cost for S-D-G S G E D A G’ H
:10 :8 :9 :0 :4 :3 2 3 5 1
f(S) = g(S) + h(S) =  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) =  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. Heuristic Search : A* Algorithm
TIN 5013: Artificial Intelligence

34. Heuristic Search : A* Algorithm

35. Heuristic Search : A* Algorithm
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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.