Polyhedral Theory for the Asymmetric Traveling Salesman Problem

AbstractThe 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.KeywordsTraveling Salesman ProblemIncidence VectorLift ProcedureClique TreeAsymmetric Travel Salesman ProblemThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.