A bilevel programming approach to the travelling salesman problem

Authors:
Patrice Marcotte;Gilles Savard;FréDéRic Semet
Affiliations:
DIRO, Université de Montréal and CRT, CP 6128, Succursale Centre-Ville, Montréal, QC, Canada H3C 3J7;ícole Polytechnique de Montréal and GERAD, C.P. 6079, Succursale Centre-Ville, Montréal, QC, Canada H3C 3A7, Canada;LAMIH, Université de Valenciennes, 59313 Valenciennes Cedex 9, France
Venue:
Operations Research Letters
Year:
2004

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Abstract

We show that the travelling salesman problem is polynomially reducible to a bilevel toll optimization program. Based on natural bilevel programming techniques, we recover the lifted Miller-Tucker-Zemlin constraints. Next, we derive an O(n^2) multi-commodity extension whose LP relaxation is comparable to the exponential formulation of Dantzig, Fulkerson and Johnson.