search problemscadia.ru.is/wiki/_media/public:t-622-arti-11-1:arti-c03...search problems russell and...
TRANSCRIPT
![Page 1: Search problemscadia.ru.is/wiki/_media/public:t-622-arti-11-1:arti-c03...Search Problems Russell and Norvig: Chap. 3, Sect. 3.1 – 3.2 Slides by Jean-Claude Latombe, from an introductory](https://reader033.vdocuments.mx/reader033/viewer/2022052020/60343c91eb287b1b2b55352a/html5/thumbnails/1.jpg)
Search Problems
Russell and Norvig:
Chap. 3, Sect. 3.1 – 3.2
Slides by Jean-Claude Latombe, from an introductory AI course given at Stanford University (used with permission).
![Page 2: Search problemscadia.ru.is/wiki/_media/public:t-622-arti-11-1:arti-c03...Search Problems Russell and Norvig: Chap. 3, Sect. 3.1 – 3.2 Slides by Jean-Claude Latombe, from an introductory](https://reader033.vdocuments.mx/reader033/viewer/2022052020/60343c91eb287b1b2b55352a/html5/thumbnails/2.jpg)
Goal-Based Agent
environment agent
?
sensors
actuators
Goal: One way towards maximizing performance measure (to be rational)
![Page 3: Search problemscadia.ru.is/wiki/_media/public:t-622-arti-11-1:arti-c03...Search Problems Russell and Norvig: Chap. 3, Sect. 3.1 – 3.2 Slides by Jean-Claude Latombe, from an introductory](https://reader033.vdocuments.mx/reader033/viewer/2022052020/60343c91eb287b1b2b55352a/html5/thumbnails/3.jpg)
Goal-Based Agent
environment agent
?
sensors
actuators
Goal: One way towards maximizing performance measure (to be rational)
Can it find a sequence of actions achieving its goals, when no single action will do?
![Page 4: Search problemscadia.ru.is/wiki/_media/public:t-622-arti-11-1:arti-c03...Search Problems Russell and Norvig: Chap. 3, Sect. 3.1 – 3.2 Slides by Jean-Claude Latombe, from an introductory](https://reader033.vdocuments.mx/reader033/viewer/2022052020/60343c91eb287b1b2b55352a/html5/thumbnails/4.jpg)
Problem-Solving Agent
environment agent
?
sensors
actuators
• Actions • Initial state • Goal test It can do this through
graph searching!
![Page 5: Search problemscadia.ru.is/wiki/_media/public:t-622-arti-11-1:arti-c03...Search Problems Russell and Norvig: Chap. 3, Sect. 3.1 – 3.2 Slides by Jean-Claude Latombe, from an introductory](https://reader033.vdocuments.mx/reader033/viewer/2022052020/60343c91eb287b1b2b55352a/html5/thumbnails/5.jpg)
Problem as a Search Problem
• Actions • Initial state • Goal test
state space
transition model
![Page 6: Search problemscadia.ru.is/wiki/_media/public:t-622-arti-11-1:arti-c03...Search Problems Russell and Norvig: Chap. 3, Sect. 3.1 – 3.2 Slides by Jean-Claude Latombe, from an introductory](https://reader033.vdocuments.mx/reader033/viewer/2022052020/60343c91eb287b1b2b55352a/html5/thumbnails/6.jpg)
Initial State
• Actions • Initial state • Goal test
state space
transition model
![Page 7: Search problemscadia.ru.is/wiki/_media/public:t-622-arti-11-1:arti-c03...Search Problems Russell and Norvig: Chap. 3, Sect. 3.1 – 3.2 Slides by Jean-Claude Latombe, from an introductory](https://reader033.vdocuments.mx/reader033/viewer/2022052020/60343c91eb287b1b2b55352a/html5/thumbnails/7.jpg)
Goal Test
• Actions • Initial state • Goal test
state space
transition model
![Page 8: Search problemscadia.ru.is/wiki/_media/public:t-622-arti-11-1:arti-c03...Search Problems Russell and Norvig: Chap. 3, Sect. 3.1 – 3.2 Slides by Jean-Claude Latombe, from an introductory](https://reader033.vdocuments.mx/reader033/viewer/2022052020/60343c91eb287b1b2b55352a/html5/thumbnails/8.jpg)
Example: 8-puzzle
1
2
3 4
5 6
7
8 1 2 3
4 5 6
7 8
Initial state Goal state
State: Any arrangement of 8 numbered tiles and an empty tile on a 3x3 board
![Page 9: Search problemscadia.ru.is/wiki/_media/public:t-622-arti-11-1:arti-c03...Search Problems Russell and Norvig: Chap. 3, Sect. 3.1 – 3.2 Slides by Jean-Claude Latombe, from an introductory](https://reader033.vdocuments.mx/reader033/viewer/2022052020/60343c91eb287b1b2b55352a/html5/thumbnails/9.jpg)
Example: 8-puzzle
1
2
3 4
5 6
7
8
1
2
3 4
5 6
7
8
1
2
3 4
5 6
7 8
1
2
3 4
5 6
7
8
Action set and transition model is knowledge about the 8-puzzle game, but it does not tell us which transition to take.
Search is about the exploration of alternatives to find a goal state
![Page 10: Search problemscadia.ru.is/wiki/_media/public:t-622-arti-11-1:arti-c03...Search Problems Russell and Norvig: Chap. 3, Sect. 3.1 – 3.2 Slides by Jean-Claude Latombe, from an introductory](https://reader033.vdocuments.mx/reader033/viewer/2022052020/60343c91eb287b1b2b55352a/html5/thumbnails/10.jpg)
Example: 8-puzzle
Size of the state space = 9! = 362,880 (but half reachable)
15-puzzle ~2 x 1013
24-puzzle ~1 x 1025
10 millions states/sec
0.36 sec
24 days
40 billion years
![Page 11: Search problemscadia.ru.is/wiki/_media/public:t-622-arti-11-1:arti-c03...Search Problems Russell and Norvig: Chap. 3, Sect. 3.1 – 3.2 Slides by Jean-Claude Latombe, from an introductory](https://reader033.vdocuments.mx/reader033/viewer/2022052020/60343c91eb287b1b2b55352a/html5/thumbnails/11.jpg)
Search of State Space
state graph
![Page 12: Search problemscadia.ru.is/wiki/_media/public:t-622-arti-11-1:arti-c03...Search Problems Russell and Norvig: Chap. 3, Sect. 3.1 – 3.2 Slides by Jean-Claude Latombe, from an introductory](https://reader033.vdocuments.mx/reader033/viewer/2022052020/60343c91eb287b1b2b55352a/html5/thumbnails/12.jpg)
Search of State Space
state graph
![Page 13: Search problemscadia.ru.is/wiki/_media/public:t-622-arti-11-1:arti-c03...Search Problems Russell and Norvig: Chap. 3, Sect. 3.1 – 3.2 Slides by Jean-Claude Latombe, from an introductory](https://reader033.vdocuments.mx/reader033/viewer/2022052020/60343c91eb287b1b2b55352a/html5/thumbnails/13.jpg)
Search of State Space
state graph
![Page 14: Search problemscadia.ru.is/wiki/_media/public:t-622-arti-11-1:arti-c03...Search Problems Russell and Norvig: Chap. 3, Sect. 3.1 – 3.2 Slides by Jean-Claude Latombe, from an introductory](https://reader033.vdocuments.mx/reader033/viewer/2022052020/60343c91eb287b1b2b55352a/html5/thumbnails/14.jpg)
Search of State Space
state graph
![Page 15: Search problemscadia.ru.is/wiki/_media/public:t-622-arti-11-1:arti-c03...Search Problems Russell and Norvig: Chap. 3, Sect. 3.1 – 3.2 Slides by Jean-Claude Latombe, from an introductory](https://reader033.vdocuments.mx/reader033/viewer/2022052020/60343c91eb287b1b2b55352a/html5/thumbnails/15.jpg)
Search of State Space
state graph
![Page 16: Search problemscadia.ru.is/wiki/_media/public:t-622-arti-11-1:arti-c03...Search Problems Russell and Norvig: Chap. 3, Sect. 3.1 – 3.2 Slides by Jean-Claude Latombe, from an introductory](https://reader033.vdocuments.mx/reader033/viewer/2022052020/60343c91eb287b1b2b55352a/html5/thumbnails/16.jpg)
Search of State Space
search tree
state graph
![Page 17: Search problemscadia.ru.is/wiki/_media/public:t-622-arti-11-1:arti-c03...Search Problems Russell and Norvig: Chap. 3, Sect. 3.1 – 3.2 Slides by Jean-Claude Latombe, from an introductory](https://reader033.vdocuments.mx/reader033/viewer/2022052020/60343c91eb287b1b2b55352a/html5/thumbnails/17.jpg)
Search of State Space
solution
state graph
![Page 18: Search problemscadia.ru.is/wiki/_media/public:t-622-arti-11-1:arti-c03...Search Problems Russell and Norvig: Chap. 3, Sect. 3.1 – 3.2 Slides by Jean-Claude Latombe, from an introductory](https://reader033.vdocuments.mx/reader033/viewer/2022052020/60343c91eb287b1b2b55352a/html5/thumbnails/18.jpg)
Search Problem
Initial state
Actions
Transition model
State space
Goal test
Path cost
![Page 19: Search problemscadia.ru.is/wiki/_media/public:t-622-arti-11-1:arti-c03...Search Problems Russell and Norvig: Chap. 3, Sect. 3.1 – 3.2 Slides by Jean-Claude Latombe, from an introductory](https://reader033.vdocuments.mx/reader033/viewer/2022052020/60343c91eb287b1b2b55352a/html5/thumbnails/19.jpg)
Search Problem
Initial state: usually the current state
sometimes one or several hypothetical states (“what if …”)
Actions
Transition model
State space
Goal test
Path cost
![Page 20: Search problemscadia.ru.is/wiki/_media/public:t-622-arti-11-1:arti-c03...Search Problems Russell and Norvig: Chap. 3, Sect. 3.1 – 3.2 Slides by Jean-Claude Latombe, from an introductory](https://reader033.vdocuments.mx/reader033/viewer/2022052020/60343c91eb287b1b2b55352a/html5/thumbnails/20.jpg)
Search Problem
Initial state
Actions: possible actions available to agent
Transition model
State space
Goal test
Path cost
![Page 21: Search problemscadia.ru.is/wiki/_media/public:t-622-arti-11-1:arti-c03...Search Problems Russell and Norvig: Chap. 3, Sect. 3.1 – 3.2 Slides by Jean-Claude Latombe, from an introductory](https://reader033.vdocuments.mx/reader033/viewer/2022052020/60343c91eb287b1b2b55352a/html5/thumbnails/21.jpg)
Search Problem
Initial state
Actions
Transition model: Result of doing action in state
Successor: reachable state by single action from current state
State space
Goal test
Path cost
![Page 22: Search problemscadia.ru.is/wiki/_media/public:t-622-arti-11-1:arti-c03...Search Problems Russell and Norvig: Chap. 3, Sect. 3.1 – 3.2 Slides by Jean-Claude Latombe, from an introductory](https://reader033.vdocuments.mx/reader033/viewer/2022052020/60343c91eb287b1b2b55352a/html5/thumbnails/22.jpg)
Search Problem
Initial state
Actions
Transition model
State space (implicitly defined by the above): each state is an abstract representation of the environment
the state space is discrete
Goal test
Path cost
![Page 23: Search problemscadia.ru.is/wiki/_media/public:t-622-arti-11-1:arti-c03...Search Problems Russell and Norvig: Chap. 3, Sect. 3.1 – 3.2 Slides by Jean-Claude Latombe, from an introductory](https://reader033.vdocuments.mx/reader033/viewer/2022052020/60343c91eb287b1b2b55352a/html5/thumbnails/23.jpg)
Search Problem
Initial state
Actions
Transition model
State space
Goal test:
sometimes the description of a state
usually a condition
Path cost
![Page 24: Search problemscadia.ru.is/wiki/_media/public:t-622-arti-11-1:arti-c03...Search Problems Russell and Norvig: Chap. 3, Sect. 3.1 – 3.2 Slides by Jean-Claude Latombe, from an introductory](https://reader033.vdocuments.mx/reader033/viewer/2022052020/60343c91eb287b1b2b55352a/html5/thumbnails/24.jpg)
Search Problem
Initial state
Actions
Transition model
State space
Goal test
Path cost: [path positive number]
usually, path cost = sum of step costs
e.g., number of moves of the empty tile
![Page 25: Search problemscadia.ru.is/wiki/_media/public:t-622-arti-11-1:arti-c03...Search Problems Russell and Norvig: Chap. 3, Sect. 3.1 – 3.2 Slides by Jean-Claude Latombe, from an introductory](https://reader033.vdocuments.mx/reader033/viewer/2022052020/60343c91eb287b1b2b55352a/html5/thumbnails/25.jpg)
Simple Agent Algorithm
Problem-Solving-Agent
1. formulate: (abstraction!)
1. initial-state sense/read state
2. goal select/read goal
3. actions select/read action models
4. transition model select/read model
5. problem (initial-state, goal, actions, transition model)
2. solution search(problem)
3. perform(solution)
![Page 26: Search problemscadia.ru.is/wiki/_media/public:t-622-arti-11-1:arti-c03...Search Problems Russell and Norvig: Chap. 3, Sect. 3.1 – 3.2 Slides by Jean-Claude Latombe, from an introductory](https://reader033.vdocuments.mx/reader033/viewer/2022052020/60343c91eb287b1b2b55352a/html5/thumbnails/26.jpg)
Example: 8-queens
Place 8 queens in a chessboard so that no two queens are in the same row, column, or diagonal.
A solution Not a solution
![Page 27: Search problemscadia.ru.is/wiki/_media/public:t-622-arti-11-1:arti-c03...Search Problems Russell and Norvig: Chap. 3, Sect. 3.1 – 3.2 Slides by Jean-Claude Latombe, from an introductory](https://reader033.vdocuments.mx/reader033/viewer/2022052020/60343c91eb287b1b2b55352a/html5/thumbnails/27.jpg)
Example: 8-queens
Formulation #1: • States: any arrangement of 0 to 8 queens on the board • Initial state: 0 queens on the board • Actions: add a queen in any empty square • Transition model: board contains queen • Goal test: 8 queens on the board, none attacked
648 states with 8 queens
![Page 28: Search problemscadia.ru.is/wiki/_media/public:t-622-arti-11-1:arti-c03...Search Problems Russell and Norvig: Chap. 3, Sect. 3.1 – 3.2 Slides by Jean-Claude Latombe, from an introductory](https://reader033.vdocuments.mx/reader033/viewer/2022052020/60343c91eb287b1b2b55352a/html5/thumbnails/28.jpg)
Example: 8-queens Formulation #2: • States: any arrangement of k = 0 to 8 queens in the k leftmost columns with none attacked • Initial state: 0 queens on the board • Actions: add a queen to any square in the leftmost empty column such that it is not attacked by any other queen • Transition model: board contains queen • Goal test: 8 queens on the board
2,057 states
![Page 29: Search problemscadia.ru.is/wiki/_media/public:t-622-arti-11-1:arti-c03...Search Problems Russell and Norvig: Chap. 3, Sect. 3.1 – 3.2 Slides by Jean-Claude Latombe, from an introductory](https://reader033.vdocuments.mx/reader033/viewer/2022052020/60343c91eb287b1b2b55352a/html5/thumbnails/29.jpg)
Example: Robot navigation
What is the state space?
![Page 30: Search problemscadia.ru.is/wiki/_media/public:t-622-arti-11-1:arti-c03...Search Problems Russell and Norvig: Chap. 3, Sect. 3.1 – 3.2 Slides by Jean-Claude Latombe, from an introductory](https://reader033.vdocuments.mx/reader033/viewer/2022052020/60343c91eb287b1b2b55352a/html5/thumbnails/30.jpg)
Example: Robot navigation #1
Cost of one horizontal/vertical step = 1 Cost of one diagonal step = 2
![Page 31: Search problemscadia.ru.is/wiki/_media/public:t-622-arti-11-1:arti-c03...Search Problems Russell and Norvig: Chap. 3, Sect. 3.1 – 3.2 Slides by Jean-Claude Latombe, from an introductory](https://reader033.vdocuments.mx/reader033/viewer/2022052020/60343c91eb287b1b2b55352a/html5/thumbnails/31.jpg)
Example: Robot navigation #1
This path is the shortest in the discretized state space, but not in the original continuous space
![Page 32: Search problemscadia.ru.is/wiki/_media/public:t-622-arti-11-1:arti-c03...Search Problems Russell and Norvig: Chap. 3, Sect. 3.1 – 3.2 Slides by Jean-Claude Latombe, from an introductory](https://reader033.vdocuments.mx/reader033/viewer/2022052020/60343c91eb287b1b2b55352a/html5/thumbnails/32.jpg)
sweep-line
Example: Robot navigation #2
![Page 33: Search problemscadia.ru.is/wiki/_media/public:t-622-arti-11-1:arti-c03...Search Problems Russell and Norvig: Chap. 3, Sect. 3.1 – 3.2 Slides by Jean-Claude Latombe, from an introductory](https://reader033.vdocuments.mx/reader033/viewer/2022052020/60343c91eb287b1b2b55352a/html5/thumbnails/33.jpg)
Example: Robot navigation #2
![Page 34: Search problemscadia.ru.is/wiki/_media/public:t-622-arti-11-1:arti-c03...Search Problems Russell and Norvig: Chap. 3, Sect. 3.1 – 3.2 Slides by Jean-Claude Latombe, from an introductory](https://reader033.vdocuments.mx/reader033/viewer/2022052020/60343c91eb287b1b2b55352a/html5/thumbnails/34.jpg)
Example: Robot navigation #2
states
![Page 35: Search problemscadia.ru.is/wiki/_media/public:t-622-arti-11-1:arti-c03...Search Problems Russell and Norvig: Chap. 3, Sect. 3.1 – 3.2 Slides by Jean-Claude Latombe, from an introductory](https://reader033.vdocuments.mx/reader033/viewer/2022052020/60343c91eb287b1b2b55352a/html5/thumbnails/35.jpg)
Example: Robot navigation #2
transition model
![Page 36: Search problemscadia.ru.is/wiki/_media/public:t-622-arti-11-1:arti-c03...Search Problems Russell and Norvig: Chap. 3, Sect. 3.1 – 3.2 Slides by Jean-Claude Latombe, from an introductory](https://reader033.vdocuments.mx/reader033/viewer/2022052020/60343c91eb287b1b2b55352a/html5/thumbnails/36.jpg)
A path-smoothing post-processing step is usually needed to shorten the path further
Example: Robot navigation #2
![Page 37: Search problemscadia.ru.is/wiki/_media/public:t-622-arti-11-1:arti-c03...Search Problems Russell and Norvig: Chap. 3, Sect. 3.1 – 3.2 Slides by Jean-Claude Latombe, from an introductory](https://reader033.vdocuments.mx/reader033/viewer/2022052020/60343c91eb287b1b2b55352a/html5/thumbnails/37.jpg)
Cost of one step: length of segment
Example: Robot navigation #3
![Page 38: Search problemscadia.ru.is/wiki/_media/public:t-622-arti-11-1:arti-c03...Search Problems Russell and Norvig: Chap. 3, Sect. 3.1 – 3.2 Slides by Jean-Claude Latombe, from an introductory](https://reader033.vdocuments.mx/reader033/viewer/2022052020/60343c91eb287b1b2b55352a/html5/thumbnails/38.jpg)
Cost of one step: length of segment
Visibility graph
Example: Robot navigation #3
![Page 39: Search problemscadia.ru.is/wiki/_media/public:t-622-arti-11-1:arti-c03...Search Problems Russell and Norvig: Chap. 3, Sect. 3.1 – 3.2 Slides by Jean-Claude Latombe, from an introductory](https://reader033.vdocuments.mx/reader033/viewer/2022052020/60343c91eb287b1b2b55352a/html5/thumbnails/39.jpg)
The shortest path in this state space is also the shortest in the original continuous space
Example: Robot navigation #3
![Page 40: Search problemscadia.ru.is/wiki/_media/public:t-622-arti-11-1:arti-c03...Search Problems Russell and Norvig: Chap. 3, Sect. 3.1 – 3.2 Slides by Jean-Claude Latombe, from an introductory](https://reader033.vdocuments.mx/reader033/viewer/2022052020/60343c91eb287b1b2b55352a/html5/thumbnails/40.jpg)
Example: Assembly Planning
![Page 41: Search problemscadia.ru.is/wiki/_media/public:t-622-arti-11-1:arti-c03...Search Problems Russell and Norvig: Chap. 3, Sect. 3.1 – 3.2 Slides by Jean-Claude Latombe, from an introductory](https://reader033.vdocuments.mx/reader033/viewer/2022052020/60343c91eb287b1b2b55352a/html5/thumbnails/41.jpg)
Example: Assembly Planning
![Page 42: Search problemscadia.ru.is/wiki/_media/public:t-622-arti-11-1:arti-c03...Search Problems Russell and Norvig: Chap. 3, Sect. 3.1 – 3.2 Slides by Jean-Claude Latombe, from an introductory](https://reader033.vdocuments.mx/reader033/viewer/2022052020/60343c91eb287b1b2b55352a/html5/thumbnails/42.jpg)
Example: Assembly Planning
State: Collection of sub-assemblies Initial state: All sub-assemblies are individual parts Goal state: Complete assembly Actions: Merge two subassemblies (check
for collision) Transition model: Merged assembly Cost function: Longest sequence of assembly operation
![Page 43: Search problemscadia.ru.is/wiki/_media/public:t-622-arti-11-1:arti-c03...Search Problems Russell and Norvig: Chap. 3, Sect. 3.1 – 3.2 Slides by Jean-Claude Latombe, from an introductory](https://reader033.vdocuments.mx/reader033/viewer/2022052020/60343c91eb287b1b2b55352a/html5/thumbnails/43.jpg)
Example: Assembly Planning
![Page 44: Search problemscadia.ru.is/wiki/_media/public:t-622-arti-11-1:arti-c03...Search Problems Russell and Norvig: Chap. 3, Sect. 3.1 – 3.2 Slides by Jean-Claude Latombe, from an introductory](https://reader033.vdocuments.mx/reader033/viewer/2022052020/60343c91eb287b1b2b55352a/html5/thumbnails/44.jpg)
Assumptions in Basic Search
The environment is static
The environment is discretizable
The environment is observable
The actions are deterministic
![Page 45: Search problemscadia.ru.is/wiki/_media/public:t-622-arti-11-1:arti-c03...Search Problems Russell and Norvig: Chap. 3, Sect. 3.1 – 3.2 Slides by Jean-Claude Latombe, from an introductory](https://reader033.vdocuments.mx/reader033/viewer/2022052020/60343c91eb287b1b2b55352a/html5/thumbnails/45.jpg)
Search Problem Formulation
Real-world environment -> Abstraction
![Page 46: Search problemscadia.ru.is/wiki/_media/public:t-622-arti-11-1:arti-c03...Search Problems Russell and Norvig: Chap. 3, Sect. 3.1 – 3.2 Slides by Jean-Claude Latombe, from an introductory](https://reader033.vdocuments.mx/reader033/viewer/2022052020/60343c91eb287b1b2b55352a/html5/thumbnails/46.jpg)
Search Problem Formulation
Real-world environment -> Abstraction
Validity:
Can the solution be executed?
![Page 47: Search problemscadia.ru.is/wiki/_media/public:t-622-arti-11-1:arti-c03...Search Problems Russell and Norvig: Chap. 3, Sect. 3.1 – 3.2 Slides by Jean-Claude Latombe, from an introductory](https://reader033.vdocuments.mx/reader033/viewer/2022052020/60343c91eb287b1b2b55352a/html5/thumbnails/47.jpg)
Search Problem Formulation
Real-world environment -> Abstraction
Validity:
Can the solution be executed?
Does the state space contain the solution?
![Page 48: Search problemscadia.ru.is/wiki/_media/public:t-622-arti-11-1:arti-c03...Search Problems Russell and Norvig: Chap. 3, Sect. 3.1 – 3.2 Slides by Jean-Claude Latombe, from an introductory](https://reader033.vdocuments.mx/reader033/viewer/2022052020/60343c91eb287b1b2b55352a/html5/thumbnails/48.jpg)
![Page 49: Search problemscadia.ru.is/wiki/_media/public:t-622-arti-11-1:arti-c03...Search Problems Russell and Norvig: Chap. 3, Sect. 3.1 – 3.2 Slides by Jean-Claude Latombe, from an introductory](https://reader033.vdocuments.mx/reader033/viewer/2022052020/60343c91eb287b1b2b55352a/html5/thumbnails/49.jpg)
![Page 50: Search problemscadia.ru.is/wiki/_media/public:t-622-arti-11-1:arti-c03...Search Problems Russell and Norvig: Chap. 3, Sect. 3.1 – 3.2 Slides by Jean-Claude Latombe, from an introductory](https://reader033.vdocuments.mx/reader033/viewer/2022052020/60343c91eb287b1b2b55352a/html5/thumbnails/50.jpg)
![Page 51: Search problemscadia.ru.is/wiki/_media/public:t-622-arti-11-1:arti-c03...Search Problems Russell and Norvig: Chap. 3, Sect. 3.1 – 3.2 Slides by Jean-Claude Latombe, from an introductory](https://reader033.vdocuments.mx/reader033/viewer/2022052020/60343c91eb287b1b2b55352a/html5/thumbnails/51.jpg)
![Page 52: Search problemscadia.ru.is/wiki/_media/public:t-622-arti-11-1:arti-c03...Search Problems Russell and Norvig: Chap. 3, Sect. 3.1 – 3.2 Slides by Jean-Claude Latombe, from an introductory](https://reader033.vdocuments.mx/reader033/viewer/2022052020/60343c91eb287b1b2b55352a/html5/thumbnails/52.jpg)
Search Problem Formulation
Real-world environment -> Abstraction
Validity:
Can the solution be executed?
Does the state space contain the solution?
Usefulness
Is the abstract problem easier than the real-world problem?
![Page 53: Search problemscadia.ru.is/wiki/_media/public:t-622-arti-11-1:arti-c03...Search Problems Russell and Norvig: Chap. 3, Sect. 3.1 – 3.2 Slides by Jean-Claude Latombe, from an introductory](https://reader033.vdocuments.mx/reader033/viewer/2022052020/60343c91eb287b1b2b55352a/html5/thumbnails/53.jpg)
Search Problem Formulation
Real-world environment Abstraction
Validity: Can the solution be executed?
Does the state space contain the solution?
Usefulness Is the abstract problem easier than the real-world problem?
Without abstraction an agent would be swamped by the complexity of the real world
![Page 54: Search problemscadia.ru.is/wiki/_media/public:t-622-arti-11-1:arti-c03...Search Problems Russell and Norvig: Chap. 3, Sect. 3.1 – 3.2 Slides by Jean-Claude Latombe, from an introductory](https://reader033.vdocuments.mx/reader033/viewer/2022052020/60343c91eb287b1b2b55352a/html5/thumbnails/54.jpg)
Search Problem Variants
One or several initial states
One or several goal states
The solution is the path or a goal node
In the 8-puzzle problem, it is the path to a goal node
In the 8-queen problem, it is a goal node
![Page 55: Search problemscadia.ru.is/wiki/_media/public:t-622-arti-11-1:arti-c03...Search Problems Russell and Norvig: Chap. 3, Sect. 3.1 – 3.2 Slides by Jean-Claude Latombe, from an introductory](https://reader033.vdocuments.mx/reader033/viewer/2022052020/60343c91eb287b1b2b55352a/html5/thumbnails/55.jpg)
Search Problem Variants
One or several initial states
One or several goal states
The solution is the path or a goal node
Any, or the best, or all solutions
![Page 56: Search problemscadia.ru.is/wiki/_media/public:t-622-arti-11-1:arti-c03...Search Problems Russell and Norvig: Chap. 3, Sect. 3.1 – 3.2 Slides by Jean-Claude Latombe, from an introductory](https://reader033.vdocuments.mx/reader033/viewer/2022052020/60343c91eb287b1b2b55352a/html5/thumbnails/56.jpg)
Important Parameters
Number of states in state space
8-puzzle 362,880 15-puzzle 2 x 1013 24-puzzle 1 x 1025
8-queens 2,057 100-queens 1052
There exist techniques to solve N-queens problems efficiently!
Stating a problem as a search problem is not always a good idea!
![Page 57: Search problemscadia.ru.is/wiki/_media/public:t-622-arti-11-1:arti-c03...Search Problems Russell and Norvig: Chap. 3, Sect. 3.1 – 3.2 Slides by Jean-Claude Latombe, from an introductory](https://reader033.vdocuments.mx/reader033/viewer/2022052020/60343c91eb287b1b2b55352a/html5/thumbnails/57.jpg)
Important Parameters
Number of states in state space
Distribution of goal states
Size of memory needed to store a state
![Page 58: Search problemscadia.ru.is/wiki/_media/public:t-622-arti-11-1:arti-c03...Search Problems Russell and Norvig: Chap. 3, Sect. 3.1 – 3.2 Slides by Jean-Claude Latombe, from an introductory](https://reader033.vdocuments.mx/reader033/viewer/2022052020/60343c91eb287b1b2b55352a/html5/thumbnails/58.jpg)
Important Parameters
Number of states in state space
Distribution of goal states
Size of memory needed to store a state
Running time of the successor function
![Page 59: Search problemscadia.ru.is/wiki/_media/public:t-622-arti-11-1:arti-c03...Search Problems Russell and Norvig: Chap. 3, Sect. 3.1 – 3.2 Slides by Jean-Claude Latombe, from an introductory](https://reader033.vdocuments.mx/reader033/viewer/2022052020/60343c91eb287b1b2b55352a/html5/thumbnails/59.jpg)
Applications
Route finding: airline travel, networks
Pipe routing, VLSI routing
Pharmaceutical drug design
Robot motion planning
Video games
![Page 60: Search problemscadia.ru.is/wiki/_media/public:t-622-arti-11-1:arti-c03...Search Problems Russell and Norvig: Chap. 3, Sect. 3.1 – 3.2 Slides by Jean-Claude Latombe, from an introductory](https://reader033.vdocuments.mx/reader033/viewer/2022052020/60343c91eb287b1b2b55352a/html5/thumbnails/60.jpg)
Summary
Problem-solving agent
State space, actions, transition model
Search!
Examples:
8-puzzle, 8-queens, route finding, robot navigation, assembly planning
Assumptions of basic search
Important parameters