chap9_for_real

Chap9_for_real - Chapter 9 Integer Programming Outline Outline For Fun Introduction BIP Applications Modeling Tricks with Binary Variables Some

Info iconThis preview shows pages 1–11. Sign up to view the full content.

View Full Document Right Arrow Icon
Chapter 9: Integer Programming Outline Outline For Fun Introduction BIP Applications Modeling Tricks with Binary Variables Some Perspectives on Solving IPs Branch and Bound Chapter 9: Integer Programming 1
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Chapter 9: Integer Programming For Fun Outline For Fun Introduction BIP Applications Modeling Tricks with Binary Variables Some Perspectives on Solving IPs Branch and Bound Chapter 9: Integer Programming 2
Background image of page 2
Chapter 9: Integer Programming For Fun I Greg Hogan: I Class president, son of a Baptist minister, second cello in the Lehigh University orchestra, chaplain’s office assistant . .. I bank robber! Chapter 9: Integer Programming 3
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Chapter 9: Integer Programming For Fun The Traveling Bank Robber Problem I My mission: rob 8 specific banks as quickly as possible. I In what order do I rob the banks? I Objective: to minimize the total distance traveled. I Constraints: visit every bank. I Start and end at my house. I Information I need: the distance between every bank (can be found using maps.google.com). Chapter 9: Integer Programming 4
Background image of page 4
Chapter 9: Integer Programming For Fun My Daddy was a bank robber, but he never hurt nobody I One possible solution: Try every possible order. I How many different possible solutions are there? I n banks means n ! many possible solutions. Too hard. I I can use a heuristic method (try to find good, but maybe not optimal solutions). I Examples: “Nearest Neighbor” or “Cheapest-Intersection” Chapter 9: Integer Programming 5
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Chapter 9: Integer Programming For Fun An Integer Program I Good solutions are good, but every second is important (I am too pretty for jail). I Solution, use optimization techniques! I Step 1: Declare variables. I x ij = 1 means that rob bank i immediately before bank j . I Step 2: Objective Function. I Minimize i j c ij x ij Chapter 9: Integer Programming 6
Background image of page 6
Chapter 9: Integer Programming For Fun Continued I What are some constraints? I I must walk into every bank and walk out of every bank once (and only once): N X i =1 x ij = 1 for all j N X j =1 x ij = 1 for all i . I This is not enough! I As is, I can have the following solution 1 2 3 1 and 4 5 4. I We call these subtours . Chapter 9: Integer Programming 7
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Chapter 9: Integer Programming For Fun Subtour Elimination I We can prohibit this type of solution by adding the inequality x 12 + x 13 + x 21 + x 23 + x 31 + x 32 2 I For every subset of banks S the constraint: X i S , j S x ij ≤ | S | - 1 prohibits “beaming” (as in “Beam me up Scotty”). Chapter 9: Integer Programming 8
Background image of page 8
Chapter 9: Integer Programming For Fun The formulation min X i X j c ij x ij s.t. N X i =1 x ij = 1 j N X j =1 x ij = 1 i X i S , j S x ij ≤ | S | - 1 S N x ij = 0 or 1 Chapter 9: Integer Programming 9
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Chapter 9: Integer Programming For Fun Interesting facts I The previous problem is an Integer Program .
Background image of page 10
Image of page 11
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 03/12/2009 for the course MSCI 331 taught by Professor Ostrowski during the Winter '09 term at Waterloo.

Page1 / 74

Chap9_for_real - Chapter 9 Integer Programming Outline Outline For Fun Introduction BIP Applications Modeling Tricks with Binary Variables Some

This preview shows document pages 1 - 11. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online