lecture16

lecture16 - Traveling Salesperson Covering and Packing...

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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://www-unix.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. 3 = 1 1 = 1 , 2 = 1 3 = 1 1 = 1 , 2 = 1 3 1 3 2 1 + 2- 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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lecture16 - Traveling Salesperson Covering and Packing...

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