mthsc810-lecture21-1x2

mthsc810-lecture21-1x2 - MthSc 810 Mathematical Programming...

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Unformatted text preview: MthSc 810: Mathematical Programming Lecture 21 Pietro Belotti Dept. of Mathematical Sciences Clemson University December 8, 2011 Reading for today: Section 6.3 Homework #13 due today, 6pm EST. The Traveling Salesperson Problem (TSP) A salesperson has to visit n cities and then return home. ◮ She/he would like to spend as little as possible in gas. ◮ Any pair of cities ( i , j ) is connected by a road, and the distance between them is denoted as d ij . This is a very well-known Optimization problem, with applications in the VLSI (chip manufacturing) industry: ◮ Punch a hole in n points on a printed circuit board ⇒ Minimize time spent moving robotic arm from point to point, i.e., the total distance travelled http://www.tsp.gatech.edu/pla85900 Formulation(s) ◮ Define the set of cities V = { 1 , 2 . . . , n } . ◮ Variables : x ij , binary; 1 if i → j in the tour , 0 otherwise ⇒ n ( n − 1 ) variables, one for each ( i , j ) ∈ V 2 : i 6 = j ◮ Objective function : The total distance travelled, X i ∈ V X j ∈ V : i 6 = j d ij x ij ◮ Constraints : each city i...
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mthsc810-lecture21-1x2 - MthSc 810 Mathematical Programming...

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