Download presentation

Presentation is loading. Please wait.

Published byLeslie Stallman Modified over 2 years ago

1
Branch and Bound See Beale paper

2
Example: Maximize z=x1+x2 x2 x1

3
Solve First LP problem: Solution is [1.5 2.5] x2 x1

4
[1.5 2.5] X1 <= 1 [1 1.5] x2 x1 X1 >= 2 [2 1.5], z=3.5, z=2.5

5
[1.5 2.5] X1 <= 1 [1 1.5] x2 x1 X1 >= 2 [2 1.5], z=3.5, z=2.5 X2 = 2 No solution [2.25, 1], z=3.25

6
[1 1.5] x2 x1 [2 1.5], z=3.5, z=2.5 X2 = 2 No solution [2.25, 1], z=3.25 X1 = 3 [2,1], z=3 No solution

8
Example: Maximize x1+x2 x2 x1

9
S Sbar Sums edges out of S >= 2

10
In TSP, we solve LP problem with constraint {each vertex has 2 edges incident to it} and we add just relevant ‘subtour inequalities’ to cut off any subtour solutions. So each time we solve LP and if we get a subtour solution, we add the specific subtour inequality to cut off that solution and resolve LP. This continues until we get a final tour solution.

11
Objective Function to be minimized Unbounded

12
Infeasible solution

13
LP feasible, but integer infeasible

Similar presentations

OK

Gomory Cuts Updated 25 March 2009. Example ILP Example taken from “Operations Research: An Introduction” by Hamdy A. Taha (8 th Edition)“Operations Research:

Gomory Cuts Updated 25 March 2009. Example ILP Example taken from “Operations Research: An Introduction” by Hamdy A. Taha (8 th Edition)“Operations Research:

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Converter pub to ppt online form Mobile ip seminar ppt on 4g Ppt on wheel balancing Ppt on power steering Ppt on fiscal policy in india 2010 Presentation ppt on motivation Ppt on power sharing in democracy who has the power Ppt on power line communication module Ppt on digital marketing Ppt on indian air force