Artificial intelligence topic for the btech studentCT II.pptx

AI

1. DR K Nagaiah IUR state-space representation. 1 B hilai State space representation Before a solution can be found, the prime condition is that the problem must be very precisely defined. By defining it properly, one converts the abstract problem into real workable states that are really understood. A set of all possible states for a given problem is known as the state space of the problem.State space representations are highly beneficial in AI because they provide all possible states, operations and goals. If the entire state space representations for a problem is given, it is possible to trace the path from the initial state to the goal state and identify the sequence of operators necessary for doing it. The major deficiency of this method is that it is not possible to visualize all states for a given problem. Moreover, the resources of the computer system are limited to handle huge

2. State space representation of coffee making DR K Nagaiah IUR Bhilai 2

3. DR K Nagaiah IUR Bhilai 3 8- puzzle problem In the 8-puzzle problem we have a 3×3 square board and 8 numbered tiles. The board has one blank position. Tiles can be slid to adjacent blank positions. We can alternatively and equivalently look upon this as the movement of the blank position up, down, left or right. The objective of this puzzle is to move the tiles starting from an initial position and arrive at a given goal configuration.

4. Initial and goal state Th e st a r t st a t e DR K Nagaiah IUR Bhilai 4 (almo s t) i s s o me r a n dom configuration of the tiles The goal state is as shown Operators are Move empty space up Move empty space down Move empty space right Move empty space left

5. State space of the 8 puzzle problem DR K Nagaiah IUR Bhilai 5

6. 8- puzzle problem DR K Nagaiah IUR Bhilai 6

7. Solution 78 DR K Nagaiah IUR Bhilai

8. DR K Nagaiah IUR Bhilai 8 Brute Force or Uninformed Search Strategies T h ese a r e c o m mon l y use d sea r ch p r oced u r e which explore all the alternatives during the search process. They do not have any domain specific knowledge. They need the initial state, the goal state and a set of legal operators. The strategy gives the order in which the search space is searched The followings are example of uninformed search Depth First Search ( DFS ) Breadth First Search ( BFS )

9. Search Strategies: Blind Search Breadth-first search Expand all the nodes of one level first. Depth-first search Expand one of the nodes at the deepest level. DR K Nagaiah IUR Bhilai 9

10. DR K Nagaiah IUR Bhilai 10 Informed Search Informed search tries to reduce the amount of sea r ch th a t m u s t done b y m aki n g be i n t elli g e n t choices f o r the node s th a t a r e selected for expansion. I n g ene r al this i s do n e using a heuristic function.

11. DR K Nagaiah IUR Bhilai 11 Heuristic Function A heuristic function is a function that ranks alternatives in various search algorithms at each branching step based on the available information (heuristically) in order to make a decision about which branch to follow during a search. Well designed heuristic functions can play an important part in efficiently guiding a search process toward a solution. Sometimes very simple heuristic functions can provide a fairly good estimate of whether a path is any good or not. In other situations, more complex heuristic functions should be employed.

12. Heuristic Example : 8-puzzle The first picture shows the current state and the second picture the goal state. Heuristics  is the number of tiles out of place. h(n) = 5 because the tiles 2, 8, 1, 6 and 7 are out of place. DR K Nagaiah IUR Bhilai 12

13. DR K Nagaiah IUR Bhilai 13 Heuristic Search Algorithm Algorithms that use a heuristic function are as follows Hill Climbing Best First Search A* AO* Constraint satisfaction

14. DR K Nagaiah IUR Bhilai 14 Best First Search It is a way of combining the advantages of both depth-first search and breadth first search into a single method. One way of combining the DFS and BFS is to follow a single path at a time, but switch paths whenever some competing path looks more promising than the current one does. At each step of the best-first search process, we select the most promising of the nodes we have generated so far. This is done by applying an appropriate heuristic function to each of them. We then expand the chosen node by using the rules to generate its successors. If one of them is a solution, we can quit. If not, all those new nodes are added to the set of nodes generated so far. Again the most promising node is selected and the process continues.

15. Best First Search Example DR K Nagaiah IUR Bhilai 15

16. DR K Nagaiah IUR Bhilai 16 List to maintain in Best-First Search OPE N : n odes that have b e en gene r a ted, but have not examined. This is organized as a priority queue. CLOSED: nodes that have already been examined. Whenever a new node is generated, check whether it has been generated before.

17. DR K Nagaiah IUR Bhilai 17 Algorithm of Best First Search OPEN = {initial state}. Loop until a goal is found or there are no nodes left in OPEN do: Pick the best node in OPEN Generate its successors. For each successor do: If it has not been generated before, evaluate it, add it to OPEN, and record its parent. If it has been generated before, change the parent if this new path is better than the previous one. In that case, update the cost of getting to this node and to any successors that this node may already, have.

18. A Sample tree for best first search Start Node M I L K J B A C E D F G H 3 6 5 9 8 12 14 7 5 6 1 2 Goal Node DR K Nagaiah IUR Bhilai 18

19. DR K Nagaiah IUR Bhilai 19 Search process of best first search Step Node being e x p a n d ed Children OPEN List CLOSE List 1 S (A:3)(B:6)(C:5) (A:3)(B:6)(C:5) (A;3) 2 A (D:9)(E:8) (B:6)(C:5) (D:9)(E:8) (C:5) 3 C (H:7) (B:6) (D:9) (E:8) (H:7) (B:6) 4 B (F:12) (G:14) (D:9) (E:8) (H:7) (F:12) (G:14) (H:7) 5 H (I:5) (J:6) (D:9) (E:8) (F:12) (G:14) (I;5) (J:6) (I:5) 6 I (K:1) (L:0) (M:2) (D:9) (E:8) (F:12) (G:14) (J:6) (K:1)(L:0)(M:2) Search stops as goal is reached

20. A* A* algorithm was given by Hart, Nilsson and Rafael in 1968. DR K Nagaiah IUR Bhilai 20

21. 157 DR K Nagaiah IUR Bhilai

22. DR K Nagaiah IUR Bhilai 158 Example Obtain the fitness number for node K F(n)=g(n)+h(n) =(cost function involved from start node S to node K)+(evaluation function for K) =6+5+7+1+1 =20

23. DR K Nagaiah IUR Bhilai 6. Loop: go to step 2 23 A* Algorithm Initialize: set OPEN= {s}, CLOSED={ } g(s)=0, f(s)=h(s) Fail: if OPEN ={ }, Terminate & fail. Select: select the minimum cost state, n, from OPEN. Save n in CLOSED. Terminate: if n  G, terminate with success, and return f(n). Expand: for each successor , m, of n If m ∉ [open U closed] Set g(m) =g(n) + C(n,m) Set f(m) =g(m) + h(m) Insert m in OPEN. If m  [open U closed] Set g(m) =min{g(m) ,g(n)+ C(n,m)} Set f(m) =g(m) + h(m) If f(m) has decreased and m  CLOSED, move m to OPEN

24. E x ample OPEN 1 ( 5 ) 2 ( 7 ) 3 ( 2 5 ) 3 ( 2 5 ) 4 ( 9 ) 3 ( 2 5 ) 5 ( 1 1 ) 3 ( 2 5 ) 6 ( 2 8 ) 4 ( 7 ) 6 ( 2 8 ) 6 ( 28 ) 5 ( 9 ) 6 ( 2 8 ) 6 ( 2 6 ) DR K Nagaiah IUR Bhilai 24 CLOSED 1 ( 5) 2 ( 7) 4 ( 9) 5 ( 11) 3 ( 25) 4 ( 7) 5 ( 9)

25. DR K Nagaiah IUR Bhilai 25 Merit and demerit of A* Algorithm Merits A* is both complete and admissible. Thus A* always finds an optimal path, if one exists. Demerits It is costly if the computation cost is high.

26. DR K Nagaiah IUR Bhilai 26 Problem Reduction

27. DR K Nagaiah IUR Bhilai 27 Problem Reduction Sometimes problems only seem hard to solve. A hard problem may be one that can be reduced to a number of simple problems...and, when each of the simple problems is solved, then the hard problem has been solved. Problem reduction may be defined as planning how best to solve a problem that can be recursively decomposed into subproblems in multiple ways.

28. AND or OR The complex problem and the sub problem , there exist two kinds of relationships. AND relationship OR relationship. In AND rela t ionship, t h e solution for the prob l em is obtained by solving all the sub problems. In O R rela t ions h ip, t h e solu t ion for the pr o blem is obtained by solving any of the sub problem. A n a r c ( ) conn e cting d i f fer e nt b r anches i s ca lled AND. DR K Nagaiah IUR Bhilai 28

29. DR K Nagaiah IUR Bhilai 29 AND/OR graphs Real life situations do not exactly decompose into either AND tree or OR tree but are always a combination of both. AND/OR graph is useful for representating the solutions of problem that can be solve by decomposing them into a set of smaller problems. A* algorithm is not adequate for AND/OR graphs. AO* algorithm is used for AND/OR graphs.

30. AND/OR tree 7 A DR K Nagaiah IUR Bhilai 30 B C D 5 4 6 9

31. E x ample DR K Nagaiah IUR Bhilai 31

32. DR K Nagaiah IUR Bhilai 32 AO* Algorithm 1. Initialize: set G * = {s}, f(s)= h(s) if s  T, label s as SOLVED Terminate: if s is SOLVED, then terminate. Select: select a non-terminal leaf node n from the marked sub tree. Expand: make explicit the successors of n For each new successor, m: set f(m)=h(m) if m is terminal, label m SOLVED Cost revision: call cost-revise(n) Loop: Go to step 2

33. Cost-revise(n) create Z={n} If Z={} return Select a node m from z such that m has no descendants in Z. If m is an AND node with successors. r 1 r 2 r 3 ………………….. r k Set f(m) = [f(r i ) + C(m, r i )] Mark the edge to each successor of m. If each successor is labeled SOLVED, then label m as SOLVED. 5. If m is an OR node with successors. r 1 r 2 r 3 ………………….. r k Set f(m) = min[f(r i ) + C(m, r i )] Mark the edge to best successor of m. If the marked successor is labeled SOLVED, then label m as SOLVED. 6. If the cost or label of m has changed, then insert those parents of m into z for which m is a marked successor. DR K Nagaiah IUR Bhilai 33

34. Example Illustrate the operation of AO* search upon the following search space. DR K Nagaiah IUR Bhilai 34

35. DR K Nagaiah IUR Bhilai 35 Games in Artificial Intelligence Why has game playing been a focus of AI? Games have well-defined rules, which can be implemented in programs Interfaces required are usually simple Many hu m a n expert e x ist t o as s ist i n t h e dev e l o ping of t h e programs. G a m es prov i de a stru c t u red task wh e rein success or fail u re can be measured with least effort.

36. DR K Nagaiah IUR Bhilai 36 Game Playing (Basic strategy) John von N eu m ann i s acknowl e d g ed as fa t her of theory. ga m e The term G a m e m e a ns a sor t of conflict i n which n individuals or groups (known as players) participate. Game theory denotes strategy for game. Grow a search tree Only one player move at each turn At the leaf position, when the game is finish, assign the utility to player.

37. DR K Nagaiah IUR Bhilai 37 Two-player games Usual conditions: Each player has a global view of the board Zero-sum game: any gain for one player is a loss for the other

38. DR K Nagaiah IUR Bhilai 38 Major components of a game playing program Two major components Plausible move generator: plausible move generator is used to generate the set of possible successor positions. Static evaluation function generator (utility function): based on heuristics, this generates the static evaluation function value for each and every move that is being made. The static evaluation function gives a snapshot of a particular move.

39. Game Tree The computer is Max . The opponent is Min . DR K Nagaiah IUR Bhilai 39 At the leaf nodes, the utility function is employed. Big value means good, small is bad. c omp u t e r ’ s turn oppo ne n t ’ s turn c omp u t e r ’ s turn oppo ne n t ’ s turn leaf nodes are evaluated

40. DR K Nagaiah IUR Bhilai 40 Game playing strategies Minimax strategy Alpha-Beta Pruning

41. DR K Nagaiah IUR Bhilai 41 Minimax Strategy It is a simple look ahead strategy for two person game playing. One player “maximizer” tries to maximize the utility function Other player “minimizer” tries to minimize the utility function The plausible move generator generates the necessary states for further evaluation and the static evaluation function “ranks” each of the positions. To decide one move, it explores the possibilities of winning by looking ahead to more than one stop. This is called ply. To decide the current move, game tree would be explored two levels farther.

42. MiniMax Example 192 DR K Nagaiah IUR Bhilai

43. MiniMax Example DR K Nagaiah IUR Bhilai 43

44. MiniMax Example DR K Nagaiah IUR Bhilai 44

45. MiniMax Example DR K Nagaiah IUR Bhilai 45

46. MiniMax Example DR K Nagaiah IUR Bhilai 46

47. Minimax Algorithm Illustrated 2 7 1 8 MAX 2 1 2 7 1 8 2 1 2 2 1 2 2 7 1 8 Move selected by minimax Static evaluation Value returned M I N DR K Nagaiah IUR 2 7 1 8 47 B hilai

48. DR K Nagaiah IUR Bhilai 48 Minimax Algorithm function MINIMAX(N) is begin if N is a leaf then return the estimated score of this leaf else Let N1, N2, .., Nm be the successors of N; if N is a Min node then return min{MINIMAX(N1), .., MINIMAX(Nm)} else return max{MINIMAX(N1), .., MINIMAX(Nm)} end MINIMAX;

49. Example 1: Considering the following game tree search space Which move should be chosen under min-max search procedure, if the first move is a maximizing move? DR K Nagaiah IUR Bhilai 49

50. – If the first player is a maximizing player, what move should be chosen under the min-max strategy? Example 2: Considering the following game tree search space DR K Nagaiah IUR Bhilai 50

51. Example 3: Considering the following game tree search space Find out optimal path and value of the following example with the help of min-max algorithm DR K Nagaiah IUR Bhilai 51

52. DR K Nagaiah IUR Bhilai 52 Alpha-Beta Pruning The problem with Mini-Max algorithm is that the number of game states it has to examine is exponential in the number of moves. The Alpha-Beta Pruning helps to arrive at correct Min-Max algorithm decision without looking at every node of the game tree. Applying an alpha-cutoff means we stop search of a particular branch because we see that we already have a better opportunity elsewhere. Applying a beta cutoff means we stop search of a particular branch because we see that the opponent already has a better opportunity elsewhere. Applying both forms is alpha beta pruning.

53. DR K Nagaiah IUR Bhilai 53 Alpha Beta Procedure Depth first search of game tree, keeping track of: Alpha: Highest value seen so far on maximizing level Beta: Lowest value seen so far on minimizing level Pruning When Maximizing, do not expand any more sibling nodes once a node has been seen whose evaluation is smaller than Alpha When Minimizing, do not ex pa nd any sib l i n g nodes once a no d e has been s e en w h ose ev a lu at ion is great e r than Be t a

54. α-β pruning example DR K Nagaiah IUR Bhilai 54

55. α-β pruning example alpha cutoff DR K Nagaiah IUR Bhilai 55  = 3

56. α-β pruning example DR K Nagaiah IUR Bhilai 56

57. α-β pruning example DR K Nagaiah IUR Bhilai 57

58. α-β pruning example DR K Nagaiah IUR Bhilai 58

59. DR K Nagaiah IUR Bhilai 59 Alpha-beta algorithm function MAX-VALUE (state, game, alpha, beta) ;; alpha = best MAX so far; beta = best MIN if CUTOFF-TEST (state) then return EVAL (state) for each s in SUCCESSORS (state) do alpha := MAX (alpha, MIN-VALUE (state, game, alpha, beta)) if alpha >= beta then return beta end return alpha function MIN-VALUE (state, game, alpha, beta) if CUTOFF-TEST (state) then return EVAL (state) for each s in SUCCESSORS (state) do beta := MIN (beta, MAX-VALUE (s, game, alpha, beta)) if beta <= alpha then return alpha end return beta

60. α-β pruning example DR K Nagaiah IUR Bhilai 60

61. Example 1: Prune this tree DR K Nagaiah IUR Bhilai 61

62. Example 2: Considering the following game tree search space W hat node would not be n e eded t o be e x a m in e d using a lph a -b e ta pruning technique? DR K Nagaiah IUR Bhilai 62

63. – W hat nod e s sho u ld not b e ne e d e d t o b e e xa m in e d using alpha-beta pruning technique? Example 3: Considering the following game tree search space DR K Nagaiah IUR Bhilai 63

64. DR K Nagaiah IUR Bhilai 64 Games of chance In real life, many unpredictable external events can put us into unforeseen situations. Many games mirror this unpredictability by including a random element, such as the throwing of STOCHASTIC GAMES dice. We call these stochastic games or games of chance. Backgammon is a typical game that combines luck and skill. Dice are rolled at the beginning of a player's rum to determine the legal moves in the backgammon position. In game tree in backgammon must include chance nodes in addition to MAX and MIN nodes.

65. Schematic game tree for a backgammon position The DR K Nagaiah IUR Bhilai 65

66. DR K Nagaiah IUR Bhilai 66 Games of chance The next step is to understand how to make correct decisions. Obviously, we still want to pick the move that leads to the best position. However, positions do not have definite minimax values. instead, we can only calculate the expected value of a position: the average over all possible outcomes of the chance nodes. This leads us to generalize the minimax value for deterministic games to an expecti_minimax value for games with chance nodes. Terminal nodes and MAX and MIN nodes (for which the dice roll is known) work exactly the same way as before. For chance nodes we compute the expected value, which is the sum of the value over all outcomes, weighted by the probability of each chance action.