Artificial Intelligence and Soft Computing: Behavioral ... - Arteimi.info

eductions. Constraint satisfaction techniques, being an emerging research
area, will be presented in detail in chapter 19. Means and ends analysis and
problem reduction techniques, on the other hand, are available in most text
books [7] and we omit these for lack of space.
Exercises
1. Using the Euclidean distance of a node (x, y) from a fixed node (2, 2),
i.e.,
h = [ (x –2) 2 + (y –2) 2 1 / 2
]
solve the water-jug problem by paper and pencil by A* algorithm. Does
this heuristic function return an optimal path? Consequently, can you call
it an admissible heuristic?
2. The 8-puzzle problem is similar to the 4-puzzle problem we discussed in
chapter 1. The only difference is that there exist 9 cells and 8 tiles instead
of the 4 cells and 3 tiles of a 4-puzzle problem. Can you select a heuristic
function for the 8-puzzle problem? Solve the 8-puzzle problem by the A*
algorithm with your selected heuristic function.
3. Show the computation for the first 3 ply moves in a tac-tac-toe game using
the α-β cut-off algorithm.
4. Consider a room whose floor space is partitioned into equal sized blocks.
Suppose there is a mobile robot (MR) in one block, and we want to move
to a distant block. Some of the blocks are occupied with obstacles. The
robot has to plan its trajectory so that it reaches the goal position from a
given initial position without touching the obstacles. Can you design a
heuristic function for the problem? If yes, solve the problem using the A*
algorithm on a graph paper. Assume the location of the obstacles and the
starting and the goal positions.
References
[1] Bender, E. A., Mathematical Methods in Artificial Intelligence, IEEE
Computer Society Press, Los Alamitos, pp. 33-84, 1996.
[2] Ginsberg, M., Essentials of Artificial Intelligence, Morgan Kaufmann,
San Mateo, CA, pp. 49-103, 1993.