(2) (15 points) Use the Best-First Search with Branch-and-Bound Pruning algorithm for the 0-1 Knapsack problem...
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
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
Section 6.1 1. Use Algorithm 6.1 (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 i P t0 1 $20 2 10 2 830 56 3 835 75 4 812 3 4 5 83 1 3 W= 13
Solve 01 Knapsack problem using 1) Backtracking 2) Breath first search with branch and bound 3) Best fit search with branch bound. Find out maxprofit and solution vector X=(x1,x2,x3,x4,x5). You need to show how you solve it using pruned state space tree. plw $20* $30» $35.» $12* $3. pi/wi- 10» 60 5» 4° 30 2» 5* 2» 30 4° 30 W=12(Knapsack capacity)-
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.
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
8. EXTRA CREDIT (15 points] Solve the ILP problem below using the branch-and- bound method with LP relaxation, as illustrated on Slides 27-31 of the "ILP: Part II” lecture notes. Show your resulting search tree. You can use MATLAB to solve LP- relaxed subproblems as needed, or you can solve them graphically by hand. maximize subject to 17X1 10x1 + + + 12x2 7x2 X 1 X2 VI VAL 40 5 0 integers. X1, X2 X1, X2 10/3. Branch Hint:...
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...
Will rate. Must show all work (30 points. Use the MIP branch-and-bound algorithm to solve the following problem interactively. Use the graphical method to solver for each LP relaxation problem. Minimize Z = -x - y subject to 5x + 2y = 60 3x + 4y = 45 and X1 2 0,x2 > 0 integers. Show the graph for each LP relaxation problem.
3. Apply the dynamic programming algorithm discussed in class to solve the knapsack problem. (20 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 weighs 2 pounds and is worth $9.00 Item 2 weighs 3 pounds and is worth $12.00 Item 3 weighs 5 pounds and is worth $14.00 Item 4...