1. Uninformed Search
Reading: Chapter 3 by today, Chapter by Wednesday, 9/12
Homework #2 will be given out on Wednesday
DID YOU TURN IN YOUR SURVEY? USE COURSEWORKS AND TAKE THE TEST

2. Pending Questions Class web page:
Reminder: Don’t forget assignment 0 (survey). See courseworks

3. When solving problems, dig at the roots instead of just hacking at the leaves.
Anthony J. D'Angelo, The College Blue Book

4. Agenda Introduction of search as a problem-solving paradigm
Uninformed search algorithms
Example using the 8-puzzle
Formulation of another example: sodoku
Transition to greedy search, one method for informed search

5. Goal-based Agents Agents that work towards a goal
Select the action that more likely achieve the goal
Sometimes an action directly achieves a goal; sometimes a series of actions are required

6. Problem solving as search
Goal formulation
Problem formulation
Actions
States

7. Uninformed Search through the space of possible solutions
Use no knowledge about which path is likely to be best

8. Characteristics
Before actually doing something to solve a puzzle, an intelligent agent explores possibilities “in its head”
Search = “mental exploration of possibilities”
Making a good decision requires exploring several possibilities
Execute the solution once it’s found

9. Formulating Problems as Search
Given an initial state and a goal, find the sequence of actions leading through a sequence of states to the final goal state.
Terms:
Successor function: given action and state, returns {action, successors}
State space: the set of all states reachable from the initial state
Path: a sequence of states connected by actions
Goal test: is a given state the goal state?
Path cost: function assigning a numeric cost to each path
Solution: a path from initial state to goal state

10. Example: the 8-puzzle
How would you use AI techniques to solve the 8-puzzle problem?

11. 8-puzzle URLS http://www.permadi.com/java/puzzle8

12. 8 Puzzle States: integer locations of tiles
( B)
(0 1 2)(3 4 5) (6 7 B)
Action: left, right, up, down
Goal test: is current state = ( B)?
Path cost: same for all paths
Successor function: given {up, (5 2 3 B )} -> ?
What would the state space be for this problem?

13. What are we searching? State space vs. search space Nodes Expand
State represents a physical configuration
Search space represents a tree/graph of possible solutions… an abstract configuration
Nodes
Abstract data structure in search space
Parent, children, depth, path cost, associated state
Expand
A function that given a node, creates all children nodes, using successsor function

15. Data structures: Searching data
AI: Searching solutions

16. Uninformed Search Strategies
The strategy gives the order in which the search space is searched
Breadth first
Depth first
Depth limited search
Iterative deepening
Uniform cost

17. Breadth first Algorithm

22. Depth-first Algorithm

31. Complexity Analysis
Completeness: is the algorithm guaranteed to find a solution when there is one?
Optimality: Does the strategy find the optimal solution?
Time: How long does it take to find a solution?
Space: How much memory is needed to perform the search?

32. Cost variables Time: number of nodes generated
Space: maximum number of nodes stored in memory
Branching factor: b
Maximum number of successors of any node
Depth: d
Depth of shallowest goal node
Path length: m
Maximum length of any path in the state space

33. Can we combine benefits of both?
Depth limited
Select some limit in depth to explore the problem using DFS
How do we select the limit?
Iterative deepening
DFS with depth 1
DFS with depth 2 up to depth d

37. Properties of the task environment?
Fully observable
Deterministic
Episodic
Static
Discrete
Single agent
Partially observable
Stochastic
Sequential
Dynamic
Continuous
Multiagent

38. Three types of incompleteness
Sensorless problems
Contingency problems
Adversarial problems
Exploration problems

39. End of Class Questions?

40. Sodoku

41. Informed Search

42. Heuristics Suppose 8-puzzle off by one
Is there a way to choose the best move next?
Good news: Yes!
We can use domain knowledge or heuristic to choose the best move

43. 1 2 3 4 5 6 7

44. Nature of heuristics
Domain knowledge: some knowledge about the game, the problem to choose
Heuristic: a guess about which is best, not exact
Heuristic function, h(n): estimate the distance from current node to goal

45. Heuristic for the 8-puzzle
# tiles out of place (h1)
Manhattan distance (h2)
Sum of the distance of each tile from its goal position
Tiles can only move up or down  city blocks

46. 1 2 3 4 5 6 7
Goal State 2 5 3 1 7 6 4 1 2 3 4 5 6 7
h1=1
h2=1
h1=5
h2= =7

47. Best first searches A class of search functions
Choose the “best” node to expand next
Use an evaluation function for each node
Estimate of desirability
Implementation: sort fringe, open in order of desirability
Today: greedy search, A* search

48. Greedy search Evaluation function = heuristic function
Expand the node that appears to be closest to the goal

49. Greedy Search OPEN = start node; CLOSED = empty
While OPEN is not empty do
Remove leftmost state from OPEN, call it X
If X = goal state, return success
Put X on CLOSED
SUCCESSORS = Successor function (X)
Remove any successors on OPEN or CLOSED
Compute heuristic function for each node
Put remaining successors on either end of OPEN
Sort nodes on OPEN by value of heuristic function
End while

50. End of Class Questions?