Abstract
In the Traveling Salesman Problem (TSP), a salesman wants to visit a set of cities and return home. There is a cost \(c_{ij}\) of traveling from city i to city j, which is the same in either direction for the Symmetric TSP. The objective is to visit each city exactly once, minimizing total travel costs. In the Graphical TSP, a city may be visited more than once, which may be necessary on a sparse graph. We present a new integer programming formulation for the Graphical TSP requiring only two classes of constraints that are either polynomial in number or polynomially separable, while addressing an open question proposed by Denis Naddef.
R. D. Carr—This material is based upon research supported in part by the U. S. Office of Naval Research under award number N00014-18-1-2099.
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Carr, R.D., Simonetti, N. (2021). A New Integer Programming Formulation of the Graphical Traveling Salesman Problem. In: Singh, M., Williamson, D.P. (eds) Integer Programming and Combinatorial Optimization. IPCO 2021. Lecture Notes in Computer Science(), vol 12707. Springer, Cham. https://doi.org/10.1007/978-3-030-73879-2_32
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