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 symmetr...

The Generalized Traveling Salesman Problem (GTSP) is a generalization of the well-known Traveling Salesman Problem (TSP), in which the set of cities is divided into mutually exclusive clusters. The objective of the GTSP consists in visiting each cluster exactly once in a tour, while minimizing the sum of the routing costs. This paper addresses the solution of the GTSP using a Memetic Algorithm....

The Travelling Salesmen Problem (TSP) is one of the most important and famous combinational optimization problems that aim to find the shortest tour. In this problem, the salesman starts to move from an arbitrary place called depot and after visiting all nodes, finally comes back to depot. Solving this problem seems hard because program statement is simple and leads this problem belonging to NP...

Given an edge-weighted graph G = (V, E), the Hamiltonian p-median problem (HpMP) asks for determining p cycles in G whose total length is minimized such that each node is contained in exactly one cycle. As the travelling salesman problem (TSP) corresponds to the choice p = 1, the HpMP can be interpreted as a generalization of the TSP. In this paper, we study the polytope associated with the HpM...

Given a graph ( , ) G N E  , the Covering Salesman Problem (CSP) is to identify the minimum length tour “covering” all the nodes. More specifically, it seeks the minimum length tour visiting a subset of the nodes in N such that each node i not on the tour is within a predetermined distance di of a node on the tour. In this paper, we define and develop a generalized version of the CSP, and refe...

The generalized traveling salesman problem (GTSP) is an extension of the well-known traveling salesman problem. In GTSP, we are given a partition of cities into groups and we are required to find a minimum length tour that includes exactly one city from each group. The aim of this paper is to present a new memetic algorithm for GTSP which clearly outperforms the state-of-the-art memetic algorit...

The graphical traveling salesman problem (GTSP) has been studied as a variant of the classical symmetric traveling salesman problem (STSP) suited particularly for sparse graphs. In addition, it can be viewed as a relaxation of the STSP and employed for solving the latter to optimality as originally proposed by Naddef and Rinaldi. There is a close natural connection between the two associated po...

It is shown how to transform the General Routing Problem (GRP) into a variant of the Graphical Travelling Salesman Problem (GTSP). This transformation yields a projective characterisation of the GRP polyhedron. Using this characterisation, it is shown how to convert facets of the GTSP polyhedron into valid inequalities for the GRP polyhedron. The resulting classes of inequalities subsume severa...