a. Solution A: There exists a variable corresponding to every “n 2 ” positions on the board. Solution B: There is a variable corresponding to every knight.

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Answer 1

Expert Solution & Answer

Chapter 6, Problem 2E

Explanation of Solution

a.

Solution A: There exists a variable corresponding to every “n²” positions on the board.

Solution B: There is a variable corresponding to every knight.

Explanation of Solution

b.

Solution A: Each of the variables can be taken one of two values. The values can be taken are, “occupied” and “vacant”.

Solution B: Domain of each variable is the set of squares.

Explanation of Solution

c.

Solution A: Each and every pair of square separated by knight’s move constrained, such that both cannot be occupied. The entire set of squares is constrained, such that the number of occupied squares should be “k”.

Solution B: Each and every pair of knights is constrained, such that no two knights can be on the same square or on squares separated by a knight’s move. The solution B may be preferable because there is no global constraint, although the solution A has the smaller state space when “k” is large.

Explanation of Solution

d.

The solutions must be describing a complete-state formulation. This is because the use of local search algorithm to find the solution. The successor function must be completely connecting the space for simulated annealing. The goal state must be reachable hillclimbing from initial state, for a random-restart. The two basic solutions are,

Solution C: Ensure that no attack at any time. Actions are to remove any knight, add a knight in any unattacked square, or move a knight to any unattacked square.

Solution D: allow attacks but try to get rid of them. Actions are to remove any knight, add a knight in any square, or move a knight to any square.

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Answer 2

Expert Solution & Answer

Chapter 6, Problem 2E

Explanation of Solution

a.

Solution A: There exists a variable corresponding to every “n²” positions on the board.

Solution B: There is a variable corresponding to every knight.

Explanation of Solution

b.

Solution A: Each of the variables can be taken one of two values. The values can be taken are, “occupied” and “vacant”.

Solution B: Domain of each variable is the set of squares.

Explanation of Solution

c.

Solution A: Each and every pair of square separated by knight’s move constrained, such that both cannot be occupied. The entire set of squares is constrained, such that the number of occupied squares should be “k”.

Solution B: Each and every pair of knights is constrained, such that no two knights can be on the same square or on squares separated by a knight’s move. The solution B may be preferable because there is no global constraint, although the solution A has the smaller state space when “k” is large.

Explanation of Solution

d.

The solutions must be describing a complete-state formulation. This is because the use of local search algorithm to find the solution. The successor function must be completely connecting the space for simulated annealing. The goal state must be reachable hillclimbing from initial state, for a random-restart. The two basic solutions are,

Solution C: Ensure that no attack at any time. Actions are to remove any knight, add a knight in any unattacked square, or move a knight to any unattacked square.

Solution D: allow attacks but try to get rid of them. Actions are to remove any knight, add a knight in any square, or move a knight to any square.

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Answer 3

Expert Solution & Answer

Chapter 6, Problem 2E

Explanation of Solution

a.

Solution A: There exists a variable corresponding to every “n²” positions on the board.

Solution B: There is a variable corresponding to every knight.

Explanation of Solution

b.

Solution A: Each of the variables can be taken one of two values. The values can be taken are, “occupied” and “vacant”.

Solution B: Domain of each variable is the set of squares.

Explanation of Solution

c.

Solution A: Each and every pair of square separated by knight’s move constrained, such that both cannot be occupied. The entire set of squares is constrained, such that the number of occupied squares should be “k”.

Solution B: Each and every pair of knights is constrained, such that no two knights can be on the same square or on squares separated by a knight’s move. The solution B may be preferable because there is no global constraint, although the solution A has the smaller state space when “k” is large.

Explanation of Solution

d.

The solutions must be describing a complete-state formulation. This is because the use of local search algorithm to find the solution. The successor function must be completely connecting the space for simulated annealing. The goal state must be reachable hillclimbing from initial state, for a random-restart. The two basic solutions are,

Solution C: Ensure that no attack at any time. Actions are to remove any knight, add a knight in any unattacked square, or move a knight to any unattacked square.

Solution D: allow attacks but try to get rid of them. Actions are to remove any knight, add a knight in any square, or move a knight to any square.

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Answer 4

Expert Solution & Answer

Chapter 6, Problem 2E

Explanation of Solution

a.

Solution A: There exists a variable corresponding to every “n²” positions on the board.

Solution B: There is a variable corresponding to every knight.

Explanation of Solution

b.

Solution A: Each of the variables can be taken one of two values. The values can be taken are, “occupied” and “vacant”.

Solution B: Domain of each variable is the set of squares.

Explanation of Solution

c.

Solution A: Each and every pair of square separated by knight’s move constrained, such that both cannot be occupied. The entire set of squares is constrained, such that the number of occupied squares should be “k”.

Solution B: Each and every pair of knights is constrained, such that no two knights can be on the same square or on squares separated by a knight’s move. The solution B may be preferable because there is no global constraint, although the solution A has the smaller state space when “k” is large.

Explanation of Solution

d.

The solutions must be describing a complete-state formulation. This is because the use of local search algorithm to find the solution. The successor function must be completely connecting the space for simulated annealing. The goal state must be reachable hillclimbing from initial state, for a random-restart. The two basic solutions are,

Solution C: Ensure that no attack at any time. Actions are to remove any knight, add a knight in any unattacked square, or move a knight to any unattacked square.

Solution D: allow attacks but try to get rid of them. Actions are to remove any knight, add a knight in any square, or move a knight to any square.

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Answer 5

Expert Solution & Answer

Answer 6

Expert Solution & Answer

Answer 7

Chapter 6, Problem 2E

Explanation of Solution

a.

Solution A: There exists a variable corresponding to every “n²” positions on the board.

Solution B: There is a variable corresponding to every knight.

Explanation of Solution

b.

Solution A: Each of the variables can be taken one of two values. The values can be taken are, “occupied” and “vacant”.

Solution B: Domain of each variable is the set of squares.

Explanation of Solution

c.

Solution A: Each and every pair of square separated by knight’s move constrained, such that both cannot be occupied. The entire set of squares is constrained, such that the number of occupied squares should be “k”.

Solution B: Each and every pair of knights is constrained, such that no two knights can be on the same square or on squares separated by a knight’s move. The solution B may be preferable because there is no global constraint, although the solution A has the smaller state space when “k” is large.

Explanation of Solution

d.

The solutions must be describing a complete-state formulation. This is because the use of local search algorithm to find the solution. The successor function must be completely connecting the space for simulated annealing. The goal state must be reachable hillclimbing from initial state, for a random-restart. The two basic solutions are,

Solution C: Ensure that no attack at any time. Actions are to remove any knight, add a knight in any unattacked square, or move a knight to any unattacked square.

Solution D: allow attacks but try to get rid of them. Actions are to remove any knight, add a knight in any square, or move a knight to any square.

Answer 8

Chapter 6, Problem 2E

Explanation of Solution

a.

Solution A: There exists a variable corresponding to every “n²” positions on the board.

Solution B: There is a variable corresponding to every knight.

Answer 9

Chapter 6, Problem 2E

Explanation of Solution

a.

Solution A: There exists a variable corresponding to every “n²” positions on the board.

Solution B: There is a variable corresponding to every knight.

Answer 10

Explanation of Solution

b.

Solution A: Each of the variables can be taken one of two values. The values can be taken are, “occupied” and “vacant”.

Solution B: Domain of each variable is the set of squares.

Answer 11

Explanation of Solution

b.

Solution A: Each of the variables can be taken one of two values. The values can be taken are, “occupied” and “vacant”.

Solution B: Domain of each variable is the set of squares.

Answer 12

Explanation of Solution

c.

Solution A: Each and every pair of square separated by knight’s move constrained, such that both cannot be occupied. The entire set of squares is constrained, such that the number of occupied squares should be “k”.

Solution B: Each and every pair of knights is constrained, such that no two knights can be on the same square or on squares separated by a knight’s move. The solution B may be preferable because there is no global constraint, although the solution A has the smaller state space when “k” is large.

Answer 13

Explanation of Solution

c.

Solution A: Each and every pair of square separated by knight’s move constrained, such that both cannot be occupied. The entire set of squares is constrained, such that the number of occupied squares should be “k”.

Solution B: Each and every pair of knights is constrained, such that no two knights can be on the same square or on squares separated by a knight’s move. The solution B may be preferable because there is no global constraint, although the solution A has the smaller state space when “k” is large.

Answer 14

Explanation of Solution

d.

The solutions must be describing a complete-state formulation. This is because the use of local search algorithm to find the solution. The successor function must be completely connecting the space for simulated annealing. The goal state must be reachable hillclimbing from initial state, for a random-restart. The two basic solutions are,

Solution C: Ensure that no attack at any time. Actions are to remove any knight, add a knight in any unattacked square, or move a knight to any unattacked square.

Solution D: allow attacks but try to get rid of them. Actions are to remove any knight, add a knight in any square, or move a knight to any square.

Answer 15

Explanation of Solution

d.

The solutions must be describing a complete-state formulation. This is because the use of local search algorithm to find the solution. The successor function must be completely connecting the space for simulated annealing. The goal state must be reachable hillclimbing from initial state, for a random-restart. The two basic solutions are,

Solution C: Ensure that no attack at any time. Actions are to remove any knight, add a knight in any unattacked square, or move a knight to any unattacked square.

Solution D: allow attacks but try to get rid of them. Actions are to remove any knight, add a knight in any square, or move a knight to any square.

Answer 16

Ch. 6 - Prob. 2E Ch. 6 - Prob. 3E Ch. 6 - Prob. 4E Ch. 6 - Prob. 5E Ch. 6 - Show how a single ternary constraint such as A + B...Ch. 6 - Prob. 7E Ch. 6 - Prob. 8E Ch. 6 - Prob. 9E Ch. 6 - Prob. 10E Ch. 6 - Prob. 11E

a. Solution A: There exists a variable corresponding to every “n 2 ” positions on the board. Solution B: There is a variable corresponding to every knight.

Explanation of Solution