Polyhedral Theory for the Asymmetric Traveling Salesman Problem

Abstract

The application of polyhedral methods to the TSP started in the mid-1970’s (see [396] and [402] for the first major breakthroughs). For more than a decade, until the late 1980’s, the main emphasis was on the symmetric TSP (STSP). There were several reasons for this: the traveling salesman paradigm suggests a geometric interpretation in which the costs are symmetric; some of the important real world applications, like in chip manufacturing, are symmetric; the polyhedral formulation of the symmetric TSP connects nicely to matching theory and borrows from the latter the family of facet defining 2-matching inequalities; finally, the asymmetric TSP (ATSP) can be reduced to a STSP on an undirected graph with twice as many nodes.