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Search Problems

Search Problems. Russell and Norvig: Chapter 3, Sections 3.1 – 3.3. sensors. environment. ?. agent. actuators. Problem-Solving Agent. sensors. environment. ?. agent. actuators. Actions Initial state Goal test. Problem-Solving Agent. 문제를 어떻게 탐색 문제로. 단순한 탐색 길 찾기 추적하기

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Search Problems

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  1. Search Problems Russell and Norvig: Chapter 3, Sections 3.1 – 3.3

  2. sensors environment ? agent actuators Problem-Solving Agent Search Problems

  3. sensors environment ? agent actuators • Actions • Initial state • Goal test Problem-Solving Agent Search Problems

  4. 문제를 어떻게 탐색 문제로 • 단순한 탐색 • 길 찾기 • 추적하기 • 규칙 문제를 탐색으로 • If 비교조건 then 행동 또는 결론 • 우선순위 없는 수많은 규칙에서 적합한 것 찾기 • 고차원적 문제 • Meta-knowledge에서 찾기 Search Problems

  5. state space successor function State Space and Successor Function • Actions • Initial state • Goal test Search Problems

  6. state space successor function Initial State • Actions • Initial state • Goal test Search Problems

  7. successor function Goal Test state space • Actions • Initial state • Goal test Search Problems

  8. 8 2 1 2 3 3 4 7 4 5 6 5 1 6 7 8 Initial state Goal state Example: 8-puzzle Search Problems

  9. 8 2 8 2 7 3 4 7 3 4 5 1 6 5 1 6 8 2 8 2 3 4 7 3 4 7 5 1 6 5 1 6 Example: 8-puzzle Search Problems

  10. 0.18 sec 6 days 12 billion years 10 millions states/sec Example: 8-puzzle Size of the state space = 9!/2 = 181,440 15-puzzle  .65 x1012 24-puzzle  .5 x 1025 Search Problems

  11. Search Problem • State space • Initial state • Successor function • Goal test • Path cost Search Problems

  12. Search Problem • State space • each state is an abstract representation of the environment • the state space is discrete • Initial state • Successor function • Goal test • Path cost Search Problems

  13. Search Problem • State space • Initial state: • usually the current state • sometimes one or several hypothetical states (“what if …”) • Successor function • Goal test • Path cost Search Problems

  14. Search Problem • State space • Initial state • Successor function: • [state  subset of states] • an abstract representation of the possible actions • Goal test • Path cost Search Problems

  15. Search Problem • State space • Initial state • Successor function • Goal test: • usually a condition • sometimes the description of a state • Path cost Search Problems

  16. Search Problem • State space • Initial state • Successor function • Goal test • Path cost: • [path  positive number] • usually, path cost = sum of step costs • e.g., number of moves of the empty tile Search Problems

  17. Search of State Space Search Problems

  18. Search of State Space Search Problems

  19. Search State Space Search Problems

  20. Search of State Space Search Problems

  21. Search of State Space Search Problems

  22. Search of State Space  search tree Search Problems

  23. Simple Agent Algorithm Problem-Solving-Agent • initial-state  sense/read state • goal  select/read goal • successor  select/read action models • problem  (initial-state, goal, successor) • solution  search(problem) • perform(solution) Search Problems

  24. 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 Search Problems

  25. Example: 8-queens • Formulation #1: • States: any arrangement of • 0 to 8 queens on the board • Initial state: 0 queens on the • board • Successor function: add a • queen in any square • Goal test: 8 queens on the • board, none attacked  648 states with 8 queens Search Problems

  26. 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 • Successor function: add a • queen to any square in the leftmost empty column such that it is not attacked • by any other queen • Goal test: 8 queens on the • board  2,067 states Search Problems

  27. 실제 n-queen 문제 • Neural, Genetic 또는 Heuristic 방법으로 잘 해결 • 최악의 경우에는 처리 불가능 • 실제 n이 커지면 답이 매우 많으므로 간단한 Heuristics로도 답을 쉽게 찾음 • 따라서 n이 커도 답을 잘 찾는다고 해서 인공지능 접근방법이 문제를 해결한다는 증거는 아님 • 그러나 많은 실제 문제는 알고리즘에서 이야기하는 최악의 경우로는 잘 가지 않음 • 더구나 대부분 우리가 원하는 답은 최적이 아니라 실제 활용해서 도움이 되는, feasible solution을 원하므로 인공지능 기법이 효과적으로 이용될 수 있음 Search Problems

  28. Example: Robot navigation What is the state space? Search Problems

  29. Cost of one horizontal/vertical step = 1 Cost of one diagonal step = 2 Example: Robot navigation Search Problems

  30. Example: Robot navigation Search Problems

  31. Example: Robot navigation Search Problems

  32. Example: Robot navigation Cost of one step = ??? Search Problems

  33. Example: Robot navigation Search Problems

  34. Example: Robot navigation Search Problems

  35. Cost of one step: length of segment Example: Robot navigation Search Problems

  36. Example: Robot navigation Search Problems

  37. Complex function: it must find if a collision-free merging motion exists • Successor function: • Merge two subassemblies Example: Assembly Planning Initial state Goal state Search Problems

  38. Example: Assembly Planning Search Problems

  39. Example: Assembly Planning Search Problems

  40. Assumptions in Basic Search • The environment is static • The environment is discretizable • The environment is observable • The actions are deterministic  open-loop solution Search Problems

  41. Search Problem Formulation • Real-world environment  Abstraction Search Problems

  42. Search Problem Formulation • Real-world environment  Abstraction • Validity: • Can the solution be executed? Search Problems

  43. Search Problem Formulation • Real-world environment  Abstraction • Validity: • Can the solution be executed? • Does the state space contain the solution? Search Problems

  44. Search Problems

  45. Search Problems

  46. Search Problems

  47. Search Problems

  48. 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? Search Problems

  49. 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 real world Search Problems

  50. 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 Search Problems

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