The 0-1 knapsack problem is technically an optimization problem: You’re trying to maximize the value of...
The 0-1 knapsack problem is technically an optimization problem: You’re trying to maximize the value of goods within a particular weight. Define a decision problem which can be used to solve the 0-1 knapsack optimization problem
Homework Answers
A Decision problem is a problem that can be posed as a yes-no
question of the input values.
Decision Problem for 0-1 Knapsack problem is as follow:
Given a particular value V, is there exist a combination that stays
within the weight limit W and has a value exceeding V?.
For a given value V ,we need to find a yes-no answer for the Question is there exist any combination that lies within the weight limit W and has a value exceeding V.
Add Answer to:
The 0-1 knapsack problem is technically an optimization problem:
You’re trying to maximize the value of...
Local Search Knapsack 0-1
Design a local search algorithm for the 0-1 knapsack problem. Assume there are n items x1 ... xn each with weight wi and value vi. The knapsack can have at most one of each item and the total weight cannot exceed W. You want to maximize the total value in the knapsack.Question 1: (7 points) Show the psuedocode/explanation for your algorithm.Question 2. (3 points) Is it guaranteed to find an optimal solution? Justify your answer.
Recall that in the "Knapsack Problem", there are n items having respective values V1..n) and weights...
Recall that in the "Knapsack Problem", there are n items having respective values V1..n) and weights W1..n), all greater than 0 and one needs to maximize the total value of the subset of the items placed in the knapsack limited by a weight capacity of W In the 0-1 Knapsack Problem, each item must be either be included or excluded in its entirety, in light of the fact that this problem is to be "NP-Complete", how can one solve the...
Solve the 0-1 knapsack problem given the following items, each labeled with weight and value. Assume...
Solve the 0-1 knapsack problem given the following items, each labeled with weight and value. Assume the total weight limit W is 8 lbs. Item 1 Value ($) 8 Weight (lb) 1 23 4 40 30 54 2 6 3
1) Use the Breadth-First-Search with Branch-and-Bound Pruning algorithm for the 0–1 Knapsack problem to maximize the...
1) Use the Breadth-First-Search with Branch-and-Bound Pruning
algorithm for the 0–1 Knapsack problem to maximize the profit for
the following problem instance. Show the actions step by step.
2) Use the Best-First Search with Branch-and-Bound Pruning
algorithm for the 0–1 Knapsack problem to maximize the profit for
the following problem instance. Show the actions step by step.
i PiPi 1 $20 210 2 $30 5 6 3 $35 75 4 $12 3 4 5 $3 13 wi Wー13
1. Fractional Knapsack Problem Algorithm Which best describes the tightest range of the number of items...
1. Fractional Knapsack Problem Algorithm Which best describes the tightest range of the number of items with only fractional inclusion (i.e. not entirely included or excluded) in the knapsack? (Let n denote the number of items for possible inclusion.) A) At least 0 items and at most n items B) At least 1 items and at most n items C) Exactly n items D) At least 0 items and at most n-1 items E) At least 1 items and at...
Formulate the followings into optimization problems. While you could use the integer constraints, the linear structure should be maintained. However, you shouldn’t use the integer constraints if you c...
Formulate the followings into optimization problems. While you
could use the integer constraints, the linear structure should be
maintained. However, you shouldn’t use the integer constraints if
you can formulate the problem without them. Describe the decision
variables, objective function and constraints carefully. You don’t
need to solve this problem.
(b) (5 pts) A KAIST student is planning a back-pack trip to Europe for this summer. There are 11 items (1 through n) that she is considering to carry to...
In 0-1 Knapsack Problem, what is maximized in the optimal solution? A.) Total Value B.) Total...
In 0-1 Knapsack Problem, what is maximized in the optimal solution? A.) Total Value B.) Total Weight C.) Total number of Items D.) Total Volume of Items E.) Total Value/ Total Weight
1. Apply the dynamic programming algorithm discussed in class to solve the knapsack problem. (10 points)...
1. Apply the dynamic programming algorithm discussed in class to solve the knapsack problem. (10 points) a. Show the completed table. b. Which items are included in the final configuration of the knapsack? c. What is the maximum value that can fit in the knapsack using a configuration of these items? item 1 2. 3 4 weight 3 2 value $25 $20 $15 1 capacity W = 6. 4 5 $40 $50 5
Use the Best-First Search with Branch-and-Bound Pruning algorithm for the 0–1 Knapsack problem to maximize the...
Use the Best-First Search with Branch-and-Bound Pruning
algorithm for the 0–1 Knapsack problem to maximize the profit for
the following problem instance. Show the actions step by step.
i P 1 $20 2 10 2 $30 5 6 3 $35 75 4 $12 3 4 5 $3 13
In weighted knapsack problem, given the knapsack capacity is 16 and the following items (Weight, Value),...
In weighted knapsack problem, given the knapsack capacity is 16 and the following items (Weight, Value), what is the maximum value we can take away. Explain shortly how and by what approach you arrived at this solution. Item 1 (4, 12) Item 2 (3, 14) Item 3 (7, 22) Item 4 (8, 32) Item 5 (4, 24) Item 6 (6, 20)
Recall that in the "Knapsack Problem", there are n items having respective values V1..n) and weights W1..n), all greater than 0 and one needs to maximize the total value of the subset of the items placed in the knapsack limited by a weight capacity of W In the 0-1 Knapsack Problem, each item must be either be included or excluded in its entirety, in light of the fact that this problem is to be "NP-Complete", how can one solve the...
Solve the 0-1 knapsack problem given the following items, each labeled with weight and value. Assume the total weight limit W is 8 lbs. Item 1 Value ($) 8 Weight (lb) 1 23 4 40 30 54 2 6 3
1) Use the Breadth-First-Search with Branch-and-Bound Pruning
algorithm for the 0–1 Knapsack problem to maximize the profit for
the following problem instance. Show the actions step by step.
2) Use the Best-First Search with Branch-and-Bound Pruning
algorithm for the 0–1 Knapsack problem to maximize the profit for
the following problem instance. Show the actions step by step.
i PiPi 1 $20 210 2 $30 5 6 3 $35 75 4 $12 3 4 5 $3 13 wi Wー13
Formulate the followings into optimization problems. While you
could use the integer constraints, the linear structure should be
maintained. However, you shouldn’t use the integer constraints if
you can formulate the problem without them. Describe the decision
variables, objective function and constraints carefully. You don’t
need to solve this problem.
(b) (5 pts) A KAIST student is planning a back-pack trip to Europe for this summer. There are 11 items (1 through n) that she is considering to carry to...
1. Apply the dynamic programming algorithm discussed in class to solve the knapsack problem. (10 points) a. Show the completed table. b. Which items are included in the final configuration of the knapsack? c. What is the maximum value that can fit in the knapsack using a configuration of these items? item 1 2. 3 4 weight 3 2 value $25 $20 $15 1 capacity W = 6. 4 5 $40 $50 5
Use the Best-First Search with Branch-and-Bound Pruning
algorithm for the 0–1 Knapsack problem to maximize the profit for
the following problem instance. Show the actions step by step.
i P 1 $20 2 10 2 $30 5 6 3 $35 75 4 $12 3 4 5 $3 13
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