Give the name of the algorithm that results from each of the following special cases: a. Local beam search with k = 1. b. Local beam search with one initial state and no limit on the number of states retained. c. Simulated annealing with T = 0 at all times (and omitting the termination test). d. Simulated annealing with T = ∞ at all times. e. Genetic algorithm with population size N = 1.

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Answer 1

Textbook Question

Chapter 4, Problem 1E

Give the name of the algorithm that results from each of the following special cases:

a. Local beam search with k = 1.
b. Local beam search with one initial state and no limit on the number of states retained.
c. Simulated annealing with T = 0 at all times (and omitting the termination test).
d. Simulated annealing with T = ∞ at all times.
e. Genetic algorithm with population size N = 1.

Expert Solution & Answer

Explanation of Solution

a.

The local beam search with “k=1” is hill-climbing search.

b.

Local beam search with one initial state and no limit on the number of states retained resembles with Breadth-First search.
In breadth first search, before adding the next layer it adds one complete layer nodes.
Starting from one state, the algorithm would be essentially identical to breadth-ﬁrst search except that each layer is generated all at once.

c.

Simulated annealing with “T=0” at all time:

There is a fact that termination step would be triggered immediately. Ignoring this fact, the search would be identical to first choice hill climbing.
This is because; every downward successor would be rejected with probability 1.

d.

Simulated annealing with “T = ∞” at all times is a random-walk search, it always accepts a new state.

e.

Generic algorithm with population size “N=1”:

The two selected parents will be same individual, if the population size is “1”.
The crossover yields an exact copy of individuals. Here, the mutation chance occurs.
Thus, the algorithm executes a random walk in the space of individuals.

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05:06

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(Dynamic Programming.) Recall the problem presented in Assign- ment 3 where given a list L of n ordered integers you're tasked with removing m of them such that the distance between the closest two remaining integers is maxi- mized. See Assignment 1 for further clarification and examples. As it turns out there is no (known) greedy algorithm to solve this problem. However, there is a dynamic programming solution. Devise a dynamic programming solution which determines the maximum distance between the closest two points after removing m numbers. Note, it doesn't need to return the resulting list itself. Hint 1: Your sub-problems should be of the form S(i, j), where S(i, j) returns the maximum distance of the closest two numbers when only considering removing j of the first i numbers in L. As an example if L [3, 4, 6, 8, 9, 12, 13, 15], then S(4, 1) = 2, since the closest two values of L' = [3,4,6,8] are 6 and 8 after removing 4 (note, 8-6 = = 2). = Hint 2: For the sub-problem S(i, j),…

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Answer 2

Textbook Question

Chapter 4, Problem 1E

Give the name of the algorithm that results from each of the following special cases:

a. Local beam search with k = 1.
b. Local beam search with one initial state and no limit on the number of states retained.
c. Simulated annealing with T = 0 at all times (and omitting the termination test).
d. Simulated annealing with T = ∞ at all times.
e. Genetic algorithm with population size N = 1.

Expert Solution & Answer

Explanation of Solution

a.

The local beam search with “k=1” is hill-climbing search.

b.

Local beam search with one initial state and no limit on the number of states retained resembles with Breadth-First search.
In breadth first search, before adding the next layer it adds one complete layer nodes.
Starting from one state, the algorithm would be essentially identical to breadth-ﬁrst search except that each layer is generated all at once.

c.

Simulated annealing with “T=0” at all time:

There is a fact that termination step would be triggered immediately. Ignoring this fact, the search would be identical to first choice hill climbing.
This is because; every downward successor would be rejected with probability 1.

d.

Simulated annealing with “T = ∞” at all times is a random-walk search, it always accepts a new state.

e.

Generic algorithm with population size “N=1”:

The two selected parents will be same individual, if the population size is “1”.
The crossover yields an exact copy of individuals. Here, the mutation chance occurs.
Thus, the algorithm executes a random walk in the space of individuals.

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05:06

Answer 3

Textbook Question

Chapter 4, Problem 1E

Give the name of the algorithm that results from each of the following special cases:

a. Local beam search with k = 1.
b. Local beam search with one initial state and no limit on the number of states retained.
c. Simulated annealing with T = 0 at all times (and omitting the termination test).
d. Simulated annealing with T = ∞ at all times.
e. Genetic algorithm with population size N = 1.

Expert Solution & Answer

Explanation of Solution

a.

The local beam search with “k=1” is hill-climbing search.

b.

Local beam search with one initial state and no limit on the number of states retained resembles with Breadth-First search.
In breadth first search, before adding the next layer it adds one complete layer nodes.
Starting from one state, the algorithm would be essentially identical to breadth-ﬁrst search except that each layer is generated all at once.

c.

Simulated annealing with “T=0” at all time:

There is a fact that termination step would be triggered immediately. Ignoring this fact, the search would be identical to first choice hill climbing.
This is because; every downward successor would be rejected with probability 1.

d.

Simulated annealing with “T = ∞” at all times is a random-walk search, it always accepts a new state.

e.

Generic algorithm with population size “N=1”:

The two selected parents will be same individual, if the population size is “1”.
The crossover yields an exact copy of individuals. Here, the mutation chance occurs.
Thus, the algorithm executes a random walk in the space of individuals.

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05:06

Answer 4

Textbook Question

Chapter 4, Problem 1E

Give the name of the algorithm that results from each of the following special cases:

a. Local beam search with k = 1.
b. Local beam search with one initial state and no limit on the number of states retained.
c. Simulated annealing with T = 0 at all times (and omitting the termination test).
d. Simulated annealing with T = ∞ at all times.
e. Genetic algorithm with population size N = 1.

Expert Solution & Answer

Explanation of Solution

a.

The local beam search with “k=1” is hill-climbing search.

b.

Local beam search with one initial state and no limit on the number of states retained resembles with Breadth-First search.
In breadth first search, before adding the next layer it adds one complete layer nodes.
Starting from one state, the algorithm would be essentially identical to breadth-ﬁrst search except that each layer is generated all at once.

c.

Simulated annealing with “T=0” at all time:

There is a fact that termination step would be triggered immediately. Ignoring this fact, the search would be identical to first choice hill climbing.
This is because; every downward successor would be rejected with probability 1.

d.

Simulated annealing with “T = ∞” at all times is a random-walk search, it always accepts a new state.

e.

Generic algorithm with population size “N=1”:

The two selected parents will be same individual, if the population size is “1”.
The crossover yields an exact copy of individuals. Here, the mutation chance occurs.
Thus, the algorithm executes a random walk in the space of individuals.

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05:06

Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

Expert Solution & Answer

Explanation of Solution

a.

The local beam search with “k=1” is hill-climbing search.

b.

Local beam search with one initial state and no limit on the number of states retained resembles with Breadth-First search.
In breadth first search, before adding the next layer it adds one complete layer nodes.
Starting from one state, the algorithm would be essentially identical to breadth-ﬁrst search except that each layer is generated all at once.

c.

Simulated annealing with “T=0” at all time:

There is a fact that termination step would be triggered immediately. Ignoring this fact, the search would be identical to first choice hill climbing.
This is because; every downward successor would be rejected with probability 1.

d.

Simulated annealing with “T = ∞” at all times is a random-walk search, it always accepts a new state.

e.

Generic algorithm with population size “N=1”:

The two selected parents will be same individual, if the population size is “1”.
The crossover yields an exact copy of individuals. Here, the mutation chance occurs.
Thus, the algorithm executes a random walk in the space of individuals.

Answer 8

Expert Solution & Answer

Explanation of Solution

a.

The local beam search with “k=1” is hill-climbing search.

b.

Local beam search with one initial state and no limit on the number of states retained resembles with Breadth-First search.
In breadth first search, before adding the next layer it adds one complete layer nodes.
Starting from one state, the algorithm would be essentially identical to breadth-ﬁrst search except that each layer is generated all at once.

c.

Simulated annealing with “T=0” at all time:

There is a fact that termination step would be triggered immediately. Ignoring this fact, the search would be identical to first choice hill climbing.
This is because; every downward successor would be rejected with probability 1.

d.

Simulated annealing with “T = ∞” at all times is a random-walk search, it always accepts a new state.

e.

Generic algorithm with population size “N=1”:

The two selected parents will be same individual, if the population size is “1”.
The crossover yields an exact copy of individuals. Here, the mutation chance occurs.
Thus, the algorithm executes a random walk in the space of individuals.

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

Explanation of Solution

a.

The local beam search with “k=1” is hill-climbing search.

b.

Local beam search with one initial state and no limit on the number of states retained resembles with Breadth-First search.
In breadth first search, before adding the next layer it adds one complete layer nodes.
Starting from one state, the algorithm would be essentially identical to breadth-ﬁrst search except that each layer is generated all at once.

c.

Simulated annealing with “T=0” at all time:

There is a fact that termination step would be triggered immediately. Ignoring this fact, the search would be identical to first choice hill climbing.
This is because; every downward successor would be rejected with probability 1.

d.

Simulated annealing with “T = ∞” at all times is a random-walk search, it always accepts a new state.

e.

Generic algorithm with population size “N=1”:

The two selected parents will be same individual, if the population size is “1”.
The crossover yields an exact copy of individuals. Here, the mutation chance occurs.
Thus, the algorithm executes a random walk in the space of individuals.

Answer 12

Ch. 4 - Give the name of the algorithm that results from...Ch. 4 - Prob. 2E Ch. 4 - Prob. 3E Ch. 4 - Prob. 5E Ch. 4 - Prob. 6E Ch. 4 - Prob. 7E Ch. 4 - Prob. 8E Ch. 4 - Prob. 9E Ch. 4 - Prob. 10E Ch. 4 - Prob. 12E

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