1. ARTIFICIAL INTELLIGENCE
CS 414
ARTIFICIAL INTELLIGENCE
LECTURE 02

2. Agents
An agent is anything that can be viewed as perceiving its environment through sensors and acting upon that environment through actuators.

3. Agents

4. Solving problems by searching
We will consider the problem of designing goal-based agents in fully observable, deterministic, discrete, known environments.
The agent must find a sequence of actions that reaches the goal.
The performance measure is defined by
reaching the goal and
how “expensive” the path to the goal is

5. Search problem components
Initial state :
Actions :
Transition model :
What state results from performing a given action in a given state?
Goal state :
Path cost :
Assume that it is a sum of nonnegative step costs

6. Search Space Definitions
State
A description of a possible state of the world
Initial state
the state in which the agent starts the search
Goal test
Conditions the agent is trying to meet
Goal state
Any state which meets the goal condition
Action
Function that maps (transitions) from one state to another

7. Example: Romania
On vacation in Romania; currently in Arad and
flight leaves tomorrow from Bucharest.

8. Example: Romania Initial state : Arad Actions :
Go from one city to another
Transition model :
If you go from city A to city B, you end up in city B
Goal state : Bucharest
Path cost :
Total distance traveled

9. State space
The initial state, actions, and transition model define the state space of the problem.
State space :
The set of all states reachable from initial state by any sequence of actions.
Can be represented as a directed graph where the nodes are states and links between nodes are actions.

10. Building Goal-Based Agents
What are the key questions needing to be addressed?
What goal does the agent need to achieve?
What knowledge does the agent need?
What actions does the agent need to do?

11. Search Example: Route Finding
Actions: go straight, turn left, turn right
Goal: shortest? fastest? most scenic?

12. Search Example: 8-Puzzle
Actions: move tiles (e.g., Move2Down)
Goal: reach a certain configuration

13. – Agent location and dirt location – How many possible states? Actions
Example: Vacuum world
Initial State
States :
– Agent location and dirt location
– How many possible states?
Actions
– Left, right, suck
Vacuum world state space graph

14. Example: River Crossing
A farmer wants to get his cabbage, sheep, wolf across a river. He has a boat that only holds two. He and at most one item on boat. Unsupervised, wolf bites sheep, sheep eats cabbage. How should computers solve this?

15. Example: River Crossing
State space S : all valid configurations
Initial states = {(CSDF, _ )}  S
Goal states G = {( _ , CSDF )}  S
Cost(s,s’) = 1 for all transitions.
Initial State
Goal State

16. Example: River Crossing
State space S :

17. Search Example: Water Jugs Problem
Given 4-liter and 3-liter pitchers, how do you get exactly 2 liters into the 4-liter pitcher? 4 3

18. Water Jugs Problem
State: (x, y) for # liters in 4-liter and 3-liter pitchers, respectively Actions: empty, fill, pour water between pitchers Initial state: (0, 0) Goal state: (2, *) 4 3

19. Actions / Successor Functions
1. (x, y | x < 4) (4, y) “Fill 4”
2. (x, y | y < 3) (x, 3) “Fill 3”
3. (x, y | x > 0) (0, y) “Empty 4”
4. (x, y | y > 0) (x, 0) “Empty 3”
5. (x, y | x+y ≥ 4 and y > 0) (4, y - (4 - x))
“Pour from 3 to 4 until 4 is full”
6. (x, y | x+y ≥ 3 and x > 0) (x - (3 - y), 3)
“Pour from 4 to 3 until 3 is full”
7. (x, y | x+y ≤ 4 and y > 0) (x+y, 0)
“Pour all water from 3 to 4”

20. State space

21. Solving problems by searching
Problem solving
We want:
To automatically solve a problem
We need:
A representation of the problem
Algorithms that use some strategy to solve the problem defined in that representation

22. Uninformed Search on Trees
Uninformed means we only know:
The goal test
The successors() function
But not which non-goal states are better
For now, also assume state space is a tree
Search process constructs a "search tree"
root is the start state
leaf nodes are:
unexpanded nodes (in the Frontier list)
"dead ends" (nodes that aren't goals and have no successors because no operators were applicable)
goal node is last leaf node found

23. Uninformed Search Strategies
Uninformed Search: strategies that order nodes without using any domain specific information, i.e., don’t use any information stored in a state
BFS: breadth-first search
Queue (FIFO) used for the Frontier
remove from front, add to back
DFS: depth-first search
Stack (LIFO) used for the Frontier
remove from front, add to front
CLICK EACH SUB

24. Depth First Search ( DFS )
Expand deepest unexpanded node

25. Depth First Search ( DFS )

26. Depth First Search ( DFS )

27. Depth First Search ( DFS )

28. Depth First Search (DFS)
Put start state in the agenda
Loop
Get a state from the agenda
If goal, then return
Expand state (put children to the front of agenda)
Avoiding loops
Don’t add a node to the agenda if it’s already in the agenda
Don’t expand a node (or add it to the agenda) if it has already been expanded.

29. Depth-First Search (DFS)
S start
# of nodes tested: 0, expanded: 0
expnd. node
Frontier
{S} 5 2 4 A B C
CLICK DESC: 1. interior nodes, 2. leaf nodes, 3. arcs 9 4 6 2 D E 6 G
goal 1 F 7 H

30. Depth-First Search (DFS)
# of nodes tested: 1, expanded: 1
expnd. node
Frontier
{S}
S not goal
{A,B,C}
S start 5 2 4 A B C
CLICK ONCE 9 4 6 2 D E 6 G
goal 1 F 7 H

31. Depth-First Search (DFS)
# of nodes tested: 2, expanded: 2
S start
expnd. node
Frontier
{S} S
{A,B,C}
A not goal
{D,E,B,C} 5 2 4 A B C
CLICK ONCE 9 4 6 2 D E 6 G
goal 1 F 7 H

32. Depth-First Search (DFS)
# of nodes tested: 3, expanded: 3
S start
expnd. node
Frontier
{S} S
{A,B,C} A
{D,E,B,C}
D not goal
{H,E,B,C} 5 2 4 A B C
CLICK ONCE 9 4 6 2 D E 6 G
goal 1 F 7 H

33. Depth-First Search (DFS)
# of nodes tested: 4, expanded: 4
expnd. node
Frontier
{S} S
{A,B,C} A
{D,E,B,C} D
{H,E,B,C}
H not goal
{E,B,C}
S start 5 2 4 A B C
CLICK ONCE 9 4 6 2 D E 6 G
goal 1 F 7 H

34. Depth-First Search (DFS)
# of nodes tested: 5, expanded: 5
expnd. node
Frontier
{S} S
{A,B,C} A
{D,E,B,C} D
{H,E,B,C} H
{E,B,C}
E not goal
{G,B,C}
S start 5 2 4 A B C
CLICK ONCE 9 4 6 2 D E 6 G
goal 1 F 7 H

35. Depth-First Search (DFS)
# of nodes tested: 6, expanded: 5
expnd. node
Frontier
{S} S
{A,B,C} A
{D,E,B,C} D
{H,E,B,C} H
{E,B,C} E
{G,B,C}
G goal
{B,C} no expand
S start 5 2 4 A B C
CLICK ONCE 9 4 6 2 D E 6 G
goal 1 F 7 H

36. Depth-First Search (DFS)
# of nodes tested: 6, expanded: 5
expnd. node
Frontier
{S} S
{A,B,C} A
{D,E,B,C} D
{H,E,B,C} H
{E,B,C} E
{G,B,C} G
{B,C}
S start 5 2 4 A B C
CLICK ONCE 9 4 6 2 D E 6 G
goal 1 F 7
path: S,A,E,G cost: 15 H