1. CSE 4705 Artificial Intelligence
Jinbo Bi
Department of Computer Science & Engineering

2. Search fundamentals
Chapter 3.3

3. Useful concepts

4. Useful concepts
After we formulate a problem, how do we find the solutions for it?
Enumerate in some order all possible paths from the initial state
Here: search through explicit tree generation
ROOT = initial state
Nodes and leafs generated through transition model
In general, search generates a graph (same state through multiple paths), but we will just look at trees in lecture
Treats different paths to the same node as distinct

5. Simple tree search example

6. Simple tree search example
Determines search process

7. 8-Puzzle: states and nodes

8. 8-Puzzle: search tree

9. Uninformed search strategies

10. Uninformed search strategies

11. Uninformed search strategies

12. Breadth-first search

13. Breadth-first search

14. Breadth-first search (simplified)

15. Properties of breadth-first search

16. Exponential space/time complexity

17. Depth-first search

18. Depth-first search

19. Properties of depth-first search

20. Breadth-first vs depth-first search

21. Breadth-first vs depth-first search
How can we get the best of both?

22. Depth-limited search: a building block

23. Iterative deepening search

24. Iterative deepening search

25. Iterative deepening search, example

26. Iterative deepening search, example

27. Iterative deepening search, example

28. Iterative deepening search, example

29. Properties of iterative deepening search

30. Iterative deepening search: time complexity

31. Summary of the algorithms

32. Bidirectional search: very brief review
Two simultaneous searches from start and goal
Motivation:
Check whether the node belongs to the other frontier before expansion
Space complexity is the most significant weakness
Complete and optimal if both searches are breadth-first

33. Bidirectional search: very brief review
The predecessor of each node can be efficiently computable
Works well when actions are easily reversible

34. “Uniform cost” search Motivation: an example Romanian Holiday Problem
All our search methods so far assume
Step-cost = 1
This is not always true

35. “Uniform cost” search g(N): the path cost function
If all moves equal in cost
Cost = # of nodes in path – 1
g(n) = depth(n)
Equivalent to what we have been assuming so far
Assigning a (potentially) unique cost to each step
N0, N1, N2, N3 are nodes visited on path p
C(i,j): Cost of going from Ni to Nj
g(N1) = C(0,1) + C(1,2) + C(2,3)

36. “Uniform cost” search

37. “Uniform cost” search
Start
Goal

38. “Uniform cost” search Example: Romania Holiday Problem Start S
g(R) =80 2 F
g(F) =99 R 1
is updated to 278
g(P) =177 P
g(B) =310 3 4 B
Goal
g(B) =278 B 4
Goal

39. Summary of uninformed search
C* is the cost of the optimal solution, and e is step cost

40. Informed search strategies

41. Informed search Part I (classical search)
Informed = use problem-specific knowledge
Best-first search and its variants
A* - Optimal search using knowledge
Proof of optimality of A*
A* for maneuvering AI agents in games
Heuristic functions
Part II (beyond classical search, Chap 4)
Local search and optimization
Local search in continuous space
Hill climbing, local bean search, …

42. Informed search
Is Uniform cost search the best we can do?

43. A better idea

44. The straight-line distance from each city to Bucharest:
Start
Goal

45. A heuristic function

46. Breadth first for games, robots

47. An optimal informed search (A*)

48. Breadth first for a world with obstacles
Pink: start node;
Dark blue: goal
Breadth-first search expands many nodes

49. Informed search (A*) in that world

50. Questions?