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Unformatted text preview: Traveling Salesperson Covering and Packing Quadratic Assignment IE426: Optimization Models and Applications: Lecture 16 Jeff Linderoth Department of Industrial and Systems Engineering Lehigh University October 26, 2006 Jeff Linderoth IE426:Lecture 16 Traveling Salesperson Covering and Packing Quadratic Assignment Homework Like all great parents, I caved in to the smallest amount of whining, and I am granting you a two day homework extension. Homework now due 11/2 at 4:30 NO LATE HOMEWORK will be accepted. Quiz #2 is still on 11/5. Jeff Linderoth IE426:Lecture 16 Traveling Salesperson Covering and Packing Quadratic Assignment Background Formulation Solving It QAP “Quadratic” Assignment Problem Set of facilities F Set of locations L d ij distance from i ∈ L to j ∈ L f kl flow from k ∈ F to l ∈ F Jeff Linderoth IE426:Lecture 16 Traveling Salesperson Covering and Packing Quadratic Assignment Background Formulation Solving It QAP x ij = 1 assign facility i to location j Otherwise min k ∈ F i ∈ L l ∈ F j ∈ L d ij f kl x ki x lj i ∈ F x ij = 1 ∀ j ∈ L j ∈ L x ij = 1 ∀ i ∈ F x ij ∈ { , 1 } ∀ i ∈ F, ∀ j ∈ L Jeff Linderoth IE426:Lecture 16 Traveling Salesperson Covering and Packing Quadratic Assignment Background Formulation Solving It QAP – The Home Version Try it Yourself http://wwwunix.mcs.anl.gov/otc/Guide/CaseStudies/ qap/ I have put a Mosel QAP model (and data) on the web site Jeff Linderoth IE426:Lecture 16 Traveling Salesperson Covering and Packing Quadratic Assignment Background Formulation Solving It QAP x ki x lj is nonlinear! What you really want it is to count d ij f kl towards your objective if and only if you assign facility f → i and facility k → j For this, you need a “trick” from last time (that I skipped), when you are multiplying two binary variables. δ 3 = 1 ⇔ δ 1 = 1 ,δ 2 = 1 δ 3 = 1 ⇔ δ 1 = 1 ,δ 2 = 1 δ 3 ≤ δ 1 δ 3 ≤ δ 2 δ 1 + δ 2 δ 3 ≤ 1 Jeff Linderoth IE426:Lecture 16 Traveling Salesperson Covering and Packing Quadratic Assignment Background Formulation Solving It A Final Trick Modeling Trick : Linearizing product of two binaries z kilj = 1 ⇔ x ki = 1 ,x lj = 1 z kilj ≤ x ki ∀ k ∈ F,i ∈ L,l ∈ F,j ∈ L z...
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This note was uploaded on 02/29/2008 for the course IE 426 taught by Professor Linderoth during the Spring '08 term at Lehigh University .
 Spring '08
 Linderoth
 Optimization

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