CS621 : Artificial Intelligence Pushpak Bhattacharyya CSE Dept., IIT Bombay Lecture 5 – Other Search Algorithms

Iterative Deepening A* : 8-puzzle H(n) = SUM( Manhattan Distances ) = 2 +0 +3 +3 +1 +2 +0 +3 = 14 = threshhold 8 2 4 3 1 5 7 6 Start 1 2 3 4 5 6 Goal 7 8

Step-1 8 2 8 2 4 4 OL : 3 1 5 3 1 7 6 7 6 5 f = g + h = 1 + 13 = 14 f = g + h = 1 + 15 = 16 Exceeds threshold CL : empty

Step-2 8 2 8 2 4 4 OL : 3 5 3 1 5 7 1 6 7 6 f = g + h = 2 + 15 = 17 > threshold f = g + h = 2 + 15 = 19 Exceeds threshold 8 2 4 3 1 5 CL : 7 6

Revise Threshold Both Nodes in OL exceed threshold. Therefore, cannot extend search. Set new threshold to the minimum of f values exceeding threshold. New threshold = 17 Now conduct search by expanding the nodes on OL.

Minimax Search, α- β prnuning X : 1st player 0 : 2nd player e(p) = (rows + cols + diagonals open to ‘X’) – (Same to ‘0’) (1) Start e(p) = 0 X X’s Turn X X e = 8 – 4 = 4 e = 8 – 6 = 2 e = 8 – 5 = 3 X X 0’s Turn e = 5 – 4 = 1 e = 5 – 3 = 2

Minimax X tries to maximize his advantage At the root layer he tries to maximize 0’s disadvantage (minimize his advantage) So, minimax tree

AND OR Search S if B and C S if A A if D A if E B if E and F C if F C if G S A B C D E F G

AO* AO* has to operate like A* maintaining OL and CL. For AND connectors ALL the nodes have to be explored.