Artificial Intelligence: A Modern Approach
3rd Edition
ISBN: 9780136042594
Author: Stuart Russell, Peter Norvig
Publisher: Prentice Hall
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Expert Solution & Answer
Chapter 5, Problem 1E
Explanation of Solution
- The translation uses the model of the opponent to fill in the opponent’s actions leaving the actions to be determined by the search algorithm.
- The search problem is given by
Initial state: P(S0) where S0 is the initial game state. P can be applied as the opponent may play first.
Actions: defined as in the game by ACTIONSs.
Successor function: RESULT′(s, a) = P(RESULT(s, a))
Goal test: goals are terminal states
Step cost: the cost of an action is zero.
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Hi please answer the following follow up questions as well, posted them as another question.
Question 4
For the 9-tile soring problem, assume that you start from this initial state
7
2
4
5
6
8
3
1
The Goal State is:
1
2
3
4
5
6
7
8
The cost of moving any tile is 1.
Let the heuristic function h(n) = number of misplaced tiles.
For the shown configuration, there are four options for the next move:
Move 5 to the right
Move 6 to the left
Move 2 down
Move 3 up
Each of these moves has a value f(n) = h(n) + g(n).
If we choose to Move 5 to the right, then
g(n) = 1. That is, it took us one step to reach this state from the initial state.
h(n) = number of misplaced tiles. The misplaced tiles are {7,4,8,3,1}. So the number of misplaced tiles = h(n) = 5.
If we choose to Move 6 to the left, g(n) is still = 1, but h(n) will change because the number of misplaced tiles is different.
A* works by computing f(n) = h(n) + g(n) for each of these possible moves. Then it…
Simulated annealing is an extension of hill climbing, which uses randomness to avoid getting stuck in local maxima and plateaux.
a) As defined in your textbook, simulated annealing returns the current state when the end of the annealing schedule is reached and if the annealing schedule is slow enough. Given that we know the value (measure of goodness) of each state we visit, is there anything smarter we could do?
(b) Simulated annealing requires a very small amount of memory, just enough to store two states: the current state and the proposed next state. Suppose we had enough memory to hold two million states. Propose a modification to simulated annealing that makes productive use of the additional memory.
In particular, suggest something that will likely perform better than just running simulated annealing a million times consecutively with random restarts. [Note: There are multiple correct answers here.]
(c) Gradient ascent search is prone to local optima just like hill climbing.…
This problem is taken from the delightful book "Problems for Mathematicians, Young and Old" by Paul R. Halmos.
Suppose that 931 tennis players want to play an elimination tournament. That means: they pair up, at random, for each round; if the number of players before the round begins is odd, one of them, chosen at
random, sits out that round. The winners of each round, and the odd one who sat it out (if there was an odd one), play in the next round, till, finally, there is only one winner, the champion. What is the total
number of matches to be played altogether, in all the rounds of the tournament?
Your answer:
Hint: This is much simpler than you think. When you see the answer you will say "of course".
Chapter 5 Solutions
Artificial Intelligence: A Modern Approach
Knowledge Booster
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