Part2 AI as Representation and Search

1. Part2 AI as Representation and Search Dr. Bernard Chen Ph.D. University of Central Arkansas Spring 2011

2. Outline • Intro to Representation and Search • Ch3 Structures and strategies for state space search

3. Introduction to Representation • The representation function is to capture the critical features of a problem and make that information accessible to a problem solving procedure • Expressiveness (the result of the feature abstracted) and efficiency (the computational complexity) are major dimensions for evaluating knowledge representation

4. Introduction to Representation • The computer representation of floating-point numbers illustrate these trade-off • To be precise, real number require an infinite string of digits to be fully described. • This cannot be accomplished on a finite device such as computer

5. Introduction to Representation

6. Introduction to Representation • The array is another representation common in computer science • For many problems, it is more natural and efficient than the memory architecture implemented in computer hardware

7. Introduction to Representation

8. Introduction to Search • Given a representation, the second component of intelligent problem solving is search • Human generally consider a number of alternatives strategies on their way to solve a problem • Such as chess • Player reviews alternative moves, select the “best” move • A player can also consider a short term gain

9. Introduction to Search • Consider “tic-tac-toe” • Starting with an empty board, • The first player can place a X on any one of nine places • Each move yields a different board that will allow the opponent 8 possible responses • and so on…

10. Introduction to Search • We can represent this collection of possible moves by regarding each board as a state in a graph • The link of the graph represent legal move • The resulting structure is a state space graph

11. “tic-tac-toe”state space graph

12. Introduction to Search • Consider a task of diagnosing a mechanical fault in an automobile:

13. Introduction to Search

14. Introduction to Search • Human use intelligent search • Human do not do exhaustive search • The rules are known as heuristics, and they constitute one of the central topics of AI search

15. Outline • Intro to Representation and Search • Ch3 Structures and strategies for state space search

16. State Space Representation • In the state space representation of a problem, the nodes of a graph correspond to partial problem solution states and the arcs correspond to steps in a problem solving process • One or more initial states form the root of the graph • The graph also defines one or more goal conditions, which are solutions to a problem

17. State Space Representation • State space search characterizes problem solving as the process of finding a solution path form the start state to a goal • A goal may describe a state, such as winning board in tic-tac-toe

18. “tic-tac-toe”state space graph

19. State Space Representation • In the 8-puzzle, 8 different numbered tiles are fitted into 9 spaces on a grid • One space is left blank so that tiles can be moved around to form different patterns • The goal is to find a series of moves of tiles into the blank space that places the board in a goal configuration:

20. State Space Representation • A goal in configuration in the 8-puzzle

21. State Space Representation • The Traveling salesperson problem • Suppose a salesperson has five cities to visit and then must return home • The goal of the problem is to find the shortest path for the salesperson to travel

22. State Space Representation • An instance of the traveling salesperson problem with some greedy concept

23. State Space Representation

24. State Space Representation • As previous slide suggests, the complexity of exhaustive search in the traveling salesperson problem is (N-1)! • It is a NP problem

25. Outline • Strategies for state space search • Depth-First and Breadth-First Search

26. Strategies for state space search • A state may be searched in two directions: • From the given data of a problem instance toward a foal or • From a goal to the data

27. Strategies for state space search • In data driven search, also called forward chaining, the problem solver begins with the given facts of the problem and set of legal moves for changing state • This process continues until (we hope!!) it generates a path that satisfies the goal condition

28. Strategies for state space search • An alternative approach (Goal Driven) is start with the goal that we want to solve • See what rules can generate this goal and determine what conditions must be true to use them • These conditions become the new goals • Working backward through successive subgoals until (we hope again!) it work back to

29. Strategies for state space search • For example: Consider the problem of confirming or denying the statement “I am a descendant of Thomas Jefferson” • Some facts: • He was born about 250 years ago • Assume 25 years per generation

30. Strategies for state space search • As each person has 2 parents, if we search back(goal driven) starting from “I”, the search space would be 2^10 • If we assume an average of only 3 children per family, the search space for search forward (data driven) would be 3^10 • Therefore, the decision to choose between data- and goal- driven search is based on the structure of the problem

31. Outline • Strategies for state space search • Depth-First and Breadth-First Search

32. BFS and DFS • In addition to specifying a search direction (data-driven or goal-driven), a search algorithm must determine the order in which states are examined in the graph • Two possibilities: • Depth-first search • Breadth-first search

33. BFS and DFS • In DFS, when a state is examined, all of its children and their descendants are examined before any of its siblings • Breadth-first search explores the space in a level-by-level fashion

34. BFS and DFS

35. BFS and DFS • DFS results: ABEKSLTFMCGNHOPUDIQJR • BFS results: ABCDEFGHIJKLMNOPQRSTU

36. 8-puzzle BFS

37. 8-puzzle DFS

38. BFS and DFS • Properties of BFS • Because it always examines all nodes at level n before proceeding to level n+1, BFS always finds the shortest path to a goal • In a problem have a simple solution, the solution will be found • Unfortunately, if the states have a high average number of children, it may use all the memory before it find a solution

39. BFS and DFS • Properties of DFS • If it is known that the solution path will be long, DFS will not spend time searching a large number of “shallow” states in the graph • However, DFS may “lost” deep in a graph, missing short paths to a goal, or even stuck in an infinite loop

40. BFS and DFS • A nice compromise on these trade-offs is to use a depth bound on DFS • New slide shows a DFS with a depth bound of 5

41. BFS and DFS

42. BFS and DFS • DFS with iterative deepening performs a DFS search of the space with a depth bound of 1, • If it fails to find a goal, it performs another DFS with depth bound of 2

43. BFS and DFS • Unfortunately, all the search strategies discussed in this chapter may be shown to have worst-case exponential time complexity • This is true for all uniformed search algorithms • Any other search algorithms???