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Problem Solving and Search

Artificial Intelligence. Problem Solving and Search. Dae-Won Kim. School of Computer Science & Engineering Chung-Ang University. Outline Problem-solving agents Problem types Problem formulation Example problems Basic search algorithms. Problem-Solving Agents. On holiday In Romania;

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Problem Solving and Search

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  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

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

  5. Goal: be in Bucharest

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

  7. Solution: sequence of cities

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

  9. Problem Formulation: How To vs. Problem Modeling

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

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

  12. Problem Formulation: Romania

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

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

  15. Problem Formulation: Vacuum Cleaner

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

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

  18. Problem Formulation: Robot Assembly

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

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

  21. Problem Formulation: The 8-Puzzle

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

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

  24. Answer: ?

  25. Answer: Tree Search Algorithms

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

  27. Implementation: States vs. Nodes

  28. 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.

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

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

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

  32. Uninformed Search Strategies

  33. 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

  34. Breath-First Search

  35. Expand shallowest unexpanded node. Implementation: FIFO queue

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

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

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

  39. Depth-First Search

  40. Expand deepest unexpanded node. Implementation: LIFO queue

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

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

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

  44. Iterative Deepening Search

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