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What were your answers?

What were your answers?. Breadth-First Depth-First Uniform Cost Iterative-Deepening. What were your answers?. Breadth-First a , b, c, d, e, e, f, f, z Depth-first a, b, e, z Uniform Cost a, c, d, b, f, e, e, f, z Iterative Deepening

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What were your answers?

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  1. What were your answers? • Breadth-First • Depth-First • Uniform Cost • Iterative-Deepening

  2. What were your answers? • Breadth-First a, b, c, d, e, e, f, f, z • Depth-first a, b, e, z • Uniform Cost a, c, d, b, f, e, e, f, z • Iterative Deepening a, a,b,c,d, a,b,e,c,e,f,d,f, a,b,e,z

  3. Questions about HW1

  4. A Note about Wednesday

  5. Chapter 3Heuristic Search

  6. Learning Objectives • Heuristic search strategies • Best-first search • A* algorithm • Heuristic functions

  7. Review • Review: tree searcha strategy is defined by picking the order of node expansion

  8. Summary of algorithms

  9. Review • Review: tree searcha strategy is defined by picking the order of node expansion • Even when we try to use knowledge about the problem (uniform cost search) we are limited to what we have “learned” This makes it a “backward looking” search.

  10. But, when I ask you to get from Arad to Bucharest, what do you do?

  11. Heuristic Search • Heuristic searches use knowledge about the problem to include “forward looking” information. • That is, which move do I THINK would get me closest to the goal.

  12. Heuristic Search • Best-first search: use an evaluation function for each node • Estimate of “desirability” • Expand most desirable unexpanded node • Implementation: frontier is a queue sorted in decreasing order of desirability • Special cases: • Greedy search • A* search

  13. Heuristic Search • Romania with step costs in km

  14. Heuristic Search • Greedy search • Evaluation function h(n) (heuristic) = estimate of cost from n to closest goal • Example: hSLD(n) = straight-line distance from n to Bucharest • Greedy search expands the node that appears to be closest to goal

  15. Heuristic search • Greedy search example

  16. Heuristic Search • Greedy search example

  17. Heuristic Search • Greedy search example

  18. Heuristic Search • Properties of greedy search • Complete??

  19. Heuristic Search • Complete?? No – can get stuck in loops, e.g., start in Iasi with Oradea as goal…. • Iasi  Neamt  Iasi  Neamt  • Complete in finite space with repeated-state checking

  20. Heuristic Search • Properties of greedy search • Complete?? No – can get stuck in loops, e.g., Complete in finite space with repeated-state checking • Time??

  21. Heuristic Search • Properties of greedy search • Complete?? No – can get stuck in loops, e.g., Complete in finite space with repeated-state checking • Time?? O(bm), but a good heuristic can give dramatic improvement

  22. Heuristic Search • Properties of greedy search • Complete?? No – can get stuck in loops, e.g., Complete in finite space with repeated-state checking • Time?? O(bm), but a good heuristic can give dramatic improvement • Space??

  23. Heuristic Search • Properties of greedy search • Complete?? No – can get stuck in loops, e.g., Complete in finite space with repeated-state checking • Time?? O(bm), but a good heuristic can give dramatic improvement • Space?? O(bm) – keeps all nodes in memory

  24. Heuristic Search • Properties of greedy search • Complete?? No – can get stuck in loops, e.g., Complete in finite space with repeated-state checking • Time?? O(bm), but a good heuristic can give dramatic improvement • Space?? O(bm) – keeps all nodes in memory • Optimal??

  25. Heuristic Search • Properties of greedy search • Complete?? No – can get stuck in loops, e.g., Complete in finite space with repeated-state checking • Time?? O(bm), but a good heuristic can give dramatic improvement • Space?? O(bm) – keeps all nodes in memory • Optimal?? No

  26. Heuristic Search • A* search • Premise - Avoid expanding paths that are already expansive • Evaluation function f(n) = g(n) + h(n)g(n) = cost so far to reach nh(n) = estimated cost to goal from nf(n) = estimated total cost of path through n to goal

  27. Heuristic Search • A* search • A* search uses an admissible heuristici.e., 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.)example, hSLD(n) never overestimates the actual road distance.

  28. Heuristic Search • A* search example

  29. Heuristic Search • A* search example

  30. Heuristic Search • A* search example

  31. Heuristic Search • A* search example

  32. Heuristic Search • A* search example

  33. Heuristic Search • Properties of A* • Complete?? Yes, unless there are infinitely many nodes with f  f(G) • Time?? Exponential in [relative error in h x length of solution.] • Space?? Keeps all nodes in memory • Optimal?? Yes – cannot expand f i+1 until fi is finished A* expands all nodes with f(n) < C* A* expands some nodes with f(n) = C* A* expands no nodes with f(n) > C*

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