Problem Solving and Search

1. Artificial Intelligence Problem Solving and Search Dae-Won Kim School of Computer Science & Engineering Chung-Ang University

2. Outline • Problem-solving agents • Problem types • Problem formulation • Example problems • Basic search algorithms

3. Problem-Solving Agents

5. On holiday In Romania; currently in Arad. Flight leaves tomorrow for Bucharest.

6. Goal: be in Bucharest

7. Input, Output, Solution: ??? Performance measure: ???

8. Solution: sequence of cities

9. Problem formulation: states – various cities actions – drive between cities

11. Problem Formulation: How To vs. Problem Modeling

12. A problem is defined by four items: • Initial state • Successor function: • set of action-state pairs • Goal test • Path cost (performance measure)

13. A solution is a sequence of actions leading from the initial state to a goal state. Consider a solution in algorithm

14. Problem Formulation: Romania

15. Initial state: • Successor function: sequence • Goal test: • Path cost: performance measure

16. Initial state: x = “at Arad” • Successor function: • S = {<AradZerind,Zerind>, …} • Goal test: x = “at Bucharest” • Path cost: sum of distances

17. Problem Formulation: Vacuum Cleaner

18. States: • Actions: • Goal test: • Path cost:

19. States: integer dirt and robot locations • Actions: left, right, suck, stay • Goal test: no dirt • Path cost: 1 per action (performance measure)

20. Problem Formulation: Robot Assembly

21. States: • Actions: • Goal test: • Path cost:

22. States: real-valued coordinates of joint angles • Actions: continuous motions of robot joints • Goal test: complete assembly • Path cost: time to execute

23. Problem Formulation: The 8-Puzzle

24. States ? • Actions ? • Goal test ? • Path cost ?

25. How to achieve the goal state through the complex state space from the initial state? How to solve problems?

26. Answer: ?

27. Answer: Tree Search Algorithms

28. Idea: exploration of state space by generating successors of already-explored states (expanding states)

30. Implementation: States vs. Nodes

31. A state is a conceptual representation of a physical configuration A node is data structure constituting part of a search tree includes parents, children, depth, path cost.

33. A search strategy is defined by picking the order of what?

34. A search strategy is defined by picking the order of node expansion.

35. Strategies are evaluated along the following dimensions: • Completeness • Time complexity • Space complexity • Optimality

36. Uninformed Search Strategies

37. Uninformed search strategies use only the information available in the problem definition. • Breadth-first search • Uniform-cost search • Depth-first search • Depth-limited search • Iterative deepening search

38. Breath-First Search

39. Expand shallowest unexpanded node. Implementation: FIFO queue

40. Complete? • Time complexity? • Space complexity? • Optimal?

41. Complete? Yes (if b is finite) • Time complexity? O(bd+1) • Space complexity? O(bd+1) • Optimal? Yes (if cost = 1 per step)

42. Uniform-Cost Search Expand least-cost unexpanded node using queue ordered by path cost Equivalent to BFS if step costs equal.

43. Depth-First Search

44. Expand deepest unexpanded node. Implementation: LIFO queue

45. Complete? • Time complexity? • Space complexity? • Optimal?

46. Complete? No (infinite-depth, loops) • Time complexity? O(bm) • Space complexity? O(bm) • Optimal? No

47. Depth-Limited Search = DFS with depth limit (L). i.e., nodes at depth (L) have no successors

48. Iterative Deepening Search