A Branch-and-Cut Algorithm for the Symmetric Generalized Traveling Salesman Problem

Symmetri Generalized Travelling Salesman Problem Matteo Fis hetti Juan Jos e Salazar Gonz alezy Paolo Tothz January 1994; Revised May 1995 Abstra t We onsider a variant of the lassi al symmetri Travelling Salesman Problem in whi h the nodes are partitioned into lusters and the salesman has to visit at least one node for ea h luster. This NP-hard problem is known in the literature as the symmetri Generalized Travelling Salesman Problem (GTSP), and nds pra ti al appli ations in routing, s heduling and lo ation-routing. In a ompanion paper [5℄ we modeled GTSP as an integer linear program, and studied the fa ial stru ture of two polytopes asso iated with the problem. Here we propose exa t and heuristi separation pro edures for some lasses of fa et-de ning inequalities, whi h are used within a bran h-andut algorithm for the exa t solution of GTSP. Heuristi pro edures are also des ribed. Extensive omputational results for instan es taken from the literature and involving up to 442 nodes are reported.