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Here we assume that we have a situation analyzer that converts all judgments about board situations into a single, over all quality number.

In many applications there might be multiple agents or persons searching for solutions in the same solution space. So traveling further from S D A B to some other node will make the path longer. We proceed in this manner.

So we explore D.

## Artificial Intelligence (CS607)

For example, in a game of tic-tac-toe player one might want that he should complete a line with crosses while at the same time hhandouts two wants to complete a line of zeros.

The maximizer wishes to maximize the score so apparently 7 being the maximum score, the maximizer should go to C and then to G. All nandouts heuristically informed procedures are considered better but they do not guarantee the optimal solution, as they are dependent on the quality of heuristic being used.

Next we visit E, then we visit B the child of E, we bound the sub-tree below B. Search the history of over billion web pages on the Internet.

The values on the nodes shown in yellow are the underestimates of the distance of a specific node from G. Now A and E are equally good nodes so we arbitrarily choose amongst them, and we move to A. Dynamic Programming The idea of estimates is that we can travel in the solution space using a heuristic hhandouts.

Hence we block all the further sub-trees along this path, as shown in the diagram below. The maximizer has to keep in view that what choices hajdouts be available to the minimizer on the next step. The simple idea of branch and bound is the following: Hence maximizer will end up with a score of 2 if he goes to C from A. This approach is analogous to the brute force method and is also called the British museum procedure.

To clarify the concept of adversarial search let us discuss a procedure called the minimax procedure. We construct the tree corresponding to the graph above. The player hoping for positive numbers is called maximizing player or maximizer. We will discuss the technique with the same example as that in branch-and- bound.

Both have their advantages and disadvantages.

Support your answer with examples of a few trees. Fs607 problem here is that if we go with an overestimate of the remaining distance then we might loose a solution that is somewhere nearby.

As all the sub-trees emerging from B make our path length more than 9 units so we bound this path, as shown in the next diagram. Run the MiniMax procedure on the bandouts tree. The readers are required to go though the last portion of Lecture 10 for the explanation of this example, if required.

Notice further that if player one puts a cross in any box, player-two will intelligently try to make a move that would leave player-one with minimum chance to win, that is, he will try to stop player- one from handotus a line of crosses and at hanndouts same time will try to complete his line of zeros. The length of the complete path from S to G is 9.

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The other player is called minimizing player or minimizer. Hence the right most branch of the tree will be pruned and won’t be evaluated for static evaluation. Negative numbers indicate favor to the other player.

Now, since the choice is between scores of 3 or 2, the maximizer will go to node B from A. The numbers on the nodes are the estimated distance on the node from the goal state. There is no need to look at any other paths to or from Expanded f Never Expanded In the diagram you can see that we can reach node D directly from S with a cost of 3 and via S A D with a cost of 6 hence we will never expand the path with the larger cost of reaching the same node.

Clearly identify the four components of problem solving in the above statement, i. Q5 Discuss the problems in Hill Climbing.

Handoust static evaluation scores for each leaf node are written under it. Positive numbers, by convention indicate favor to one player. Hence using dynamic programming we will ignore the whole sub-tree beneath D the child of A as shown in the next diagram. Consider the following diagram.

We have shown the sequence of steps in the diagrams below. We have discussed a detailed example on Alpha Beta Pruning in the lectures.