EXACT METHODS FOR THE ASYMMETRIC TRAVELING SALESMAN PROBLEM Matteo Fischetti D.E.I, University of Padova Via Gradenigo 6/A, 35100 Padova, Italy fisch@dei.unipd.it Abstract In the present chapter we concentrate on the exact solution methods for the Asymmetric TSP proposed in the literature after the writing of the survey of Balas and Toth [81]. In Section 2 two specific branch- and-bound methods, based on the solution of the assignment problem as a relaxation, are presented and compared. In Section 3 a branch- and-bound method based on the computation of an additive bound is described, while in Section 4 a branch-and-cut approach is discussed. Finally, in Section 5 all these methods are computationally tested on a large set of instances, and compared with an effective branch-and-cut code for the symmetric TSP. A formal definition of the problem is as follows. Let G = (V, A) be a given complete digraph, where is the vertex set and (2013)