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mthsc810-lecture21-2x2

# mthsc810-lecture21-2x2 - The Traveling Salesperson...

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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 = j Objective function : The total distance travelled, i V j V : i = j d ij x ij Constraints : eachcity i is visited once, i.e., one arc leaves i : j V : i = j x ij = 1 i V

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mthsc810-lecture21-2x2 - The Traveling Salesperson...

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