1. Intelligent Systems (2II40) C3 Alexandra I. Cristea September 2005

2. Outline II.Intelligent agents III.Search 1.Uninformed 2.Informed A.Heuristic B.Local C.Online

3. Iterative deepening search Depth first search with growing depth l l = allowed maximal depth in tree

4. Iterative deepening search example Arad l = 0

5. Iterative deepening search example Arad l = 1

6. Iterative deepening search example l = 1 Arad ZerindSibiuTimisoara

7. Iterative deepening search example Arad l = 2

8. Iterative deepening search example l = 2 Arad ZerindSibiuTimisoara

9. Iterative deepening search example l = 2 AradOradea Arad ZerindSibiuTimisoara

10. Iterative deepening search example l = 2 Arad SibiuTimisoara OradeaFagarash Ramnicu Valcea

11. Iterative deepening search example l = 2 Arad Timisoara AradLugoj

12. Proprieties of iterative deepening search Complete?Complete? Yes (b,d finite) Time?Time? (d+1) + db + (d-1)b 2 + …+ b d = O(b d ) Space?Space? O(bd) Optimal?Optimal? Yes (b,d finite & cost/step=1)

13. Outline II.Intelligent agents III.Search 1.Uninformed 2.Informed A.Heuristic B.Local C.Online

14. Uniform cost search Expand least cost node first Implementation: increasing cost order queue   = min(cost/step): the smallest step cost

15. Ex: Romania w. step costs (km)

16. Uniform cost example Arad

17. Uniform cost example Arad ZerindSibiuTimisoara 75 140 118

18. Uniform cost example Arad Sibiu 75 140 118 AradOradea Zerind 75+75= 150 75+71= 146 Timisoara AradLugoj 236 111+118= 229

19. Uniform cost example Arad Sibiu 75 140 118 AradOradea Zerind 150 146 Timisoara AradLugoj 220 229 AradOradea Ramnicu Valcea Fagarash 280 239 291236

20. Uniform cost example Arad Sibiu 75 140 118 AradOradea Zerind 150 146 Timisoara AradLugoj 220 229 AradOradea Ramnicu Valcea Fagarash 280 239 291236 Zerind Sibiu 297217

21. Uniform cost example Arad Sibiu 75 140 118 AradOradea Zerind 150 146 Timisoara AradLugoj 220 229 AradOradea Ramnicu Valcea Fagarash 280 239 291236 Zerind Sibiu 297217 225 290 268

22. Uniform cost example Arad Sibiu 75 140 118 AradOradea Zerind 150 146 Timisoara AradLugoj 220 229 AradOradea Ramnicu Valcea Fagarash 280 239 291236 Zerind Sibiu 297217 225 290 268 SibiuPitestiCraiova 300 317 382

23. Uniform cost example Arad Sibiu 75 140 118 AradOradea Zerind 150 146 Timisoara AradLugoj 220 229 AradOradea Ramnicu Valcea Fagarash 280 239 291236 Zerind Sibiu 297217 225 290 268 SibiuPitestiCraiova 300 317 382

24. Properties of uniform cost search Complete?Complete? Yes (b,d finite & cost/step   ) Optimal?Optimal? Yes (b,d finite & cost/step   ) Time?Time? O(b C*/  ) ( C* : cost optimal solution) Space?Space? O(b C*/  )

25. III.2. Informed search algorithms

26. III.2. Informed Search Strategies A. Heuristic –Best-first search Greedy search A* search B. Local –Hill climbing –Simulated annealing –Genetic algorithms

27. Best first search f(n)f(n) : evaluation function: –desirability of n Implementation: –queue of decreasing desirability

28. Greedy search f(n) = h(n)f(n) = h(n), h(n): heuristic : distance from n to goal expands n closest to goal admissibleImportant: heuristic should be admissible: –h(n)  h*(n), with: –h*(n)= real cost from n to goal

29. Example Greedy search Map of Romania possible heuristic : h sld (n) = straight_line_distance (n, Bucharest)

30. Greedy search example Arad 366

31. Greedy search example 366 Arad ZerindTimisoara 374 253 329 Sibiu

32. Greedy search example 366 Arad ZerindTimisoara 366 253 329 Arad Sibiu Oradea Ramnicu Valcea 380178193 Fagarash 374

33. Greedy search example 366 Arad ZerindTimisoara 366 253 329 Arad Sibiu Oradea Ramnicu Valcea 380178193 Fagarash SibiuBucharest 2530 374

34. Properties of Greedy search Complete?Complete? No (could get stuck in loops) Optimal?Optimal? No Time?Time? O(b m ) Space?Space? O(b m )

35. Homework 3 – part 1 1.Check Dijkstra’s Greedy algorithm and shortly compare! 2.Give 3 recent applications of a (modified) Greedy algorithm. Explain in what consists the application, evtl. the modification, and give your source.

36. A* search f(n) = g(n) + h(n)f(n) = g(n) + h(n): –g(n) –g(n): real (!!) cost from start to n –h(n) –h(n): heuristic: distance from n to goal NOTE: –considers the whole cost incurred from start to goal at all times !!

37. A* search example Arad 366

38. A* search example 366 Arad ZerindTimisoara 374+75 =449 393 447 Sibiu 75 140 118

39. A* search example 366 Arad ZerindTimisoara 646 393 447 Arad Sibiu Oradea Ramnicu Valcea 671417413 Fagarash 75 140 118 140 151 99 80 449

40. A* search example 366 Arad ZerindTimisoara 646 393 447 Arad Sibiu Oradea Ramnicu Valcea 671417413 Fagarash 75 140 118 140 80 449 SibiuCraiovaPitesti 80 146 97 553526 415 151 99

41. A* search example 366 Arad ZerindTimisoara 646 393 447 Arad Sibiu Oradea Ramnicu Valcea 671417413 Fagarash 75 140 118 140 80 449 SibiuCraiovaPitesti 80 146 97 553526 415 Rm.VilceaCraiova Bucharest 607 615 418 97 138 101 151 99

42. A* search example 366 Arad ZerindTimisoara 646 393 447 Arad Sibiu Oradea Ramnicu Valcea 671417413 Fagarash 75 140 118 140 80 449 Sibiu Bucharest 591450 211 99 SibiuCraiovaPitesti 80 146 97 553526 415 Rm.VilceaCraiova Bucharest 138 101 97 607 615 418 151 99

43. Properties of A* search Complete?Complete? Yes (if # nodes w. f  C* finite) Optimal?Optimal? Yes; optimally efficient!! Time?Time? O (b (rel. err. in h) x (length of solution) ) Space?Space? All nodes in memory

44. Optimality A* Be G optimal goal state (path cost f*) Be G2 suboptimal goal state (local minimum) f(G2) = g(G2) (heuristic zero in goal state) f(G2) > f* (G2 suboptimal) n fringe node on optimal path to G h is admissible : f(n) = g(n) + h(n)  g(n) + h*(n) = f*. f(n)  f*< f(G2) n will be chosen instead of G2, q.e.d.

45. Improved A* alg. IDA* = A* + iterative deepening depending on f RBFS = recursive depth first search + remembering value of best ancestor; space=O(bd) MA* = memory bound A* (use of available memo only) SMA* = simple MA* (A*; if memo full, discard worst node, but store f value of children w. parents)

46. Summary (un-)informed search Uninformed – ‘blind’ –computationally cheaper (heuristic?) Research continues on finding better search –i.e., problem solving algorithms Informed + uninformed: –global search algorithms –exponential time+space (10 120 molecules in universe)

47. Homework 3 - part 2 3. Read the LAO* paper find the different notations used by the author for the properties of the search algorithm and make a table of equivalences; Describe LAO* in terms of these properties; comment upon dimensions of AI (as in C1) that you find in the LAO* algorithm.LAO* paper

48. II.2.B. Local Search Greedy local search (hill-climbing) Simulated annealing Genetic algorithms

49. Homework 3 – part 2 7.Perform steps FAQ 5-6 of the project.