A new integer programming formulation of the graphical traveling salesman problem
IPCO(2022)
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 polynomial-sized constraints while addressing an open question proposed by Denis Naddef. We generalize one of these classes, and present promising preliminary computational results.
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Key words
Linear program,Relaxation,TSP,Traveling Salesman Problem,GTSP,Graphical Traveling Salesman Problem
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