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חיפוש

חיפוש. בינה מלאכותית אבי רוזנפלד. סוכנים פותרי בעיות. Reflex agents לא יכולים לתכנן קדימה כדי לחפש, יש צורך לייצר מודל לחפש בו!. להגדרת אלגוריתם חיפוש. סוכן צריך לדחות פעולות שלא מקדמות למטרה Goal formulation - נוסחת מטרה המבוססת על מדד הביצועים הנוכחיים של הסוכן ועל המצב הנוכחי

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חיפוש

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  1. חיפוש בינה מלאכותית אבי רוזנפלד

  2. סוכנים פותרי בעיות • Reflex agents לא יכולים לתכנן קדימה • כדי לחפש, יש צורך לייצר מודל לחפש בו!

  3. להגדרת אלגוריתם חיפוש • סוכן צריך לדחות פעולות שלא מקדמות למטרה • Goal formulation - נוסחת מטרה המבוססת על מדד הביצועים הנוכחיים של הסוכן ועל המצב הנוכחי • מטרה – אוסף של מצבים בעולם שצריכים להתקיים אם המטרה הושגה. • מטרת הסוכן היא למצוא את רצף הפעולות שיביא אותו לאוסף הזה של מצבים • קודם לכן, עליו להחליט אילו פעולות ואילו מצבים הם רלוונטיים.

  4. State Space 1. initial state 2. successor function

  5. Goal Test 3. goal test

  6. מפת רומניה

  7. Example: 8-Puzzle

  8. (Partial) Search Space for 8-Puzzle Problem 1. initial state 2. successor function 3. goal test

  9. Example: Route Planning in a Map Graph: nodes are cities and links are roads. • Map gives world dynamics • Current state is known • World is fully predictable • World (set of cities) is finite and enumerable. Cost: total distance or total time for path.

  10. על מה לומדים היום? • BFS • DFS • Best-first search • A* search • Heuristics • Local search algorithms • Hill-climbing search • Backtracking • Simulated annealing

  11. איך מבצעים את החיפוש?

  12. Breadth-First Search • Breadth-first search tree after 0,1,2 and 3 node expansions • CLASSIC FIFO! (Queue!) • אופטימאלי

  13. Depth-First Search Alternatively can use a recursive implementation. • לא אופטימאלי!

  14. O S F Z A R B P D M T L C Breadth-First Search

  15. O S F Z A R B P D M T L C Breadth-First Search A

  16. O S F Z A R B P D M T L C Breadth-First Search A ZA SA TA

  17. O S F Z A R B P D M T L C Breadth-First Search A ZA SA TA SA TA OAZ

  18. O S F Z A R B P D M T L C Breadth-First Search A ZA SA TA SA TA OAZ TA OAZ OAS FAS RAS

  19. O S F Z A R B P D M T L C Breadth-First Search A ZA SA TA SA TA OAZ TA OAZ OAS FAS RAS OAZ OAS FAS RAS LAT

  20. O S F Z A R B P D M T L C Breadth-First Search A ZA SA TA SA TA OAZ TA OAZ OAS FAS RAS OAZ OAS FAS RAS LAT OAS FAS RAS LAT

  21. O S F Z A R B P D M T L C Breadth-First Search A ZA SA TA SA TA OAZ TA OAZ OAS FAS RAS OAZ OAS FAS RAS LAT OAS FAS RAS LAT

  22. O S F Z A R B P D M T L C Breadth-First Search A ZA SA TA SA TA OAZ TA OAZ OAS FAS RAS OAZ OAS FAS RAS LAT OAS FAS RAS LAT RAS LAT BASF Result = BASF

  23. O S F Z A R P D M T L C Breadth-First Search B

  24. Evaluation of Search Strategies • Completeness • Time Complexity • Space Complexity • Optimality To evaluate, we use the following terms • b = branching factor • m = maximum depth • d = goal depth

  25. Evaluation of BFS • Complete • Complexity: • O(bd) time • O(bd) space • Optimal (counting by number of arcs).

  26. O S F Z A R B P D M T L C Depth-First Search

  27. O S F Z A R B P D M T L C Depth-First Search A

  28. O S F Z A R B P D M T L C Depth-First Search A ZA SA TA

  29. O S F Z A R B P D M T L C Depth-First Search A ZA SA TA

  30. O S F Z A R B P D M T L C Depth-First Search A ZA SA TA OAZ SA TA

  31. O S F Z A R B P D M T L C Depth-First Search A ZA SA TA OAZ SA TA SAZO SA TA

  32. O S F Z A R B P D M T L C Depth-First Search A ZA SA TA OAZ SA TA SAZO SA TA FAZOS RAZOS SA TA

  33. O S F Z A R B P D M T L C Depth-First Search A ZA SA TA OAZ SA TA SAZO SA TA FAZOS RAZOS SA TA BAZOSF RAZOS SA TA

  34. O S F Z A R B P D M T L C Depth-First Search A ZA SA TA OAZ SA TA SAZO SA TA FAZOS RAZOS SA TA BAZOSF RAZOS SA TA Result = BAZOSF

  35. S F Z A R B P D M T L C Depth-first Search O

  36. Evaluation of DFS • Not complete • Complexity: • O(bm) time • O(mb) space • Non-optimal

  37. Bi-Directional Search

  38. Romania with step costs in km

  39. Greedy best-first search example

  40. Greedy best-first search example

  41. Greedy best-first search example

  42. Greedy best-first search example

  43. Romania with step costs in km המחיר הכולל: 450. האם זה אופטימאלי? לא!

  44. Properties of greedy best-first search • Complete?No – can get stuck in loops, e.g., Iasi  Neamt  Iasi  Neamt Complete in finite space with checking for repeated states • Time?O(bm), but a good heuristic can give dramatic improvement • Space?O(bm) – keeps all nodes in memory • Optimal?No b is branching factor, m is maximum depth of the search space

  45. A*חיפוש • הרעיון המרכזי: קח בחשבון את המחיר הכללי (עד עכשיו) • Evaluation function f(n) = g(n) + h(n) • g(n) = cost so far to reach n • h(n) = estimated cost from n to goal • f(n) = estimated total cost of path through n to goal A* search uses an admissableheuristic: • h(n) <= h*(n), where h*(n) is the true cost from n • Also require h(n) >= 0, so h(G) = 0 for any goal G

  46. A* search example

  47. A* search example

  48. A* search example

  49. A* search example

  50. A* search example

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