Generalized Traveling Salesman Problem
The symmetric Generalized Travelling Salesman Problem (GTSP) is
a variant of the classical symmetric Travelling
Salesman Problem, in which the nodes are partitioned into clusters and the
salesman has to visit at least one node for each cluster.
A different version of the problem, called E-GTSP, arises when
exactly one node for each cluster has to be visited.
Both GTSP and E-GTSP are NP-hard problems, and find practical
applications in routing and scheduling. In a
paper
we model GTSP and E-GTSP as integer linear programs, and study
the facial structure of the corresponding polytopes.
In another
paper
the previous results have been used to design
a branch-and-cut algorithm for the exact solution of instances
up to 442 nodes.
My contributions with P. Toth and M. Fischetti are:
The Symmetric Generalized Traveling Salesman Polytope,
Networks 26 (1995) 113-123.
A Branch-and-Cut Algorithm for the Symmetric Generalized
Traveling Salesman Polytope,
Operations Research 45/3 (1997) 378-394.