Will rate. Must show all work (30 points. Use the MIP branch-and-bound algorithm to solve the...
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:...
USE THE BRANCH AND BOUND (B&B) ALGORITHM!!!! Please show all the steps, including the branching and the graphs. 362 Chapter 9 nteger Linear Programming 9-56. Develop the B&B tree for each of the following problems. For coaseni xi as the branching variable at node 0. (a) Maximizez 3xi + 2r2 subject to x, x2 2 0 and integer (b) Maximizez2r, + 3x2 subject to 5x 7x2 s 35 x1, x2 0 and integer (c) Maximizezx + x2 subject to 2x1...
11. Dakin's algorithm (33%) Use the Dakin's algorithm presented in class to solve the following problem: D Please sketch (to scale) the feasible region for the integer program for each subproblem. Show the branch-and-bound tree. Alternatively, you can use LINGO to solve the subproblems Minimize z 2x,+3x1 subject to x,tx, 3 x1+3x226 and x,20, x20 x, x are integers 11. Dakin's algorithm (33%) Use the Dakin's algorithm presented in class to solve the following problem: D Please sketch (to scale)...
solve the following LP by hand using Branch-and-Bound. Can use any solver for the LPs. minimize tal que -7:01 - 2.02 -21 +2:02 < 4 5x1 + x2 < 20 -2.21 - 222 < -7 X1, X2 E ZI
3. (25 points) Solve the following MIP by branch-and-bound. You should not use simplex method to solve the (sub)LPs; they are simple enough to solve by inspection. Draw your branch-and-bound tree and tell why each node is pruned. Notice that variable y is allowed to take fractional values. max 2 +y s.t. v 20 i, r220;z1,32 integer 3. (25 points) Solve the following MIP by branch-and-bound. You should not use simplex method to solve the (sub)LPs; they are simple enough...
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
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
(2) (15 points) 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. Pi wi 1 $20 2 10 2 $30 5 6 3 S35 7 5 4 $12 3 4 5 $3 3 wi W 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
13.5 Show that the integrality gap of the relaxation for the following two variants of multiset multicover, based on LP (13.2), is not bounded by any function of n. 1. Remove the rest riction that M(S, e) <re 2. Impose the constraint that each set can be picked at most once. What is the best approximation guarantee you can establish for the greedy algorithm for the second variant. Σ(3)ES minimize (13.2) SES rs2 1, eeU subject to S: eES SES...