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Not every GTSP facet induces an STSP facet
 Integer Programming and Combinatorial Optimization 11, volume 3509 of LNCS
, 2005
"... Abstract. 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 o ..."
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Cited by 3 (2 self)
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Abstract. 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
The Symmetric Generalized Travelling Salesman Polytope
, 1995
"... 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 EGTSP, aris ..."
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Cited by 27 (4 self)
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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 EGTSP
The Generalized Traveling Salesman Problem
"... The Generalized Traveling Salesman Problem (GTSP) is an extension of the wellknown Traveling Salesman Problem (TSP), where the node set is partitioned into clusters, and the objective is to find the shortest cycle visiting each cluster exactly once. In this paper, we present a new hybrid Ant Colony ..."
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Colony System (ACS) algorithm for the symmetric GTSP. The proposed algorithm is a modification of a simple ACS for the TSP improved by an efficient GTSPspecific local search procedure. Our extensive computational experiments show that the use of the local search procedure dramatically improves
A Memetic Algorithm for the Generalized Traveling Salesman Problem
"... The generalized traveling salesman problem (GTSP) is an extension of the wellknown 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 recent studies on this subject ..."
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Cited by 17 (6 self)
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to both solution quality and running time. While the other memetic algorithms were designed only for the symmetric GTSP, our algorithm can solve both symmetric and asymmetric instances.
A BranchandCut Algorithm for the Symmetric Generalized Travelling Salesman Problem
, 1995
"... We consider 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. This NPhard problem is known in the literature as the symmetric Generalized Travelling Salesman Problem (GT ..."
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Cited by 76 (4 self)
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We consider 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. This NPhard problem is known in the literature as the symmetric Generalized Travelling Salesman Problem
Memetic algorithm for the generalized asymmetric traveling salesman problem
 PROCEEDINGS OF THE 2007 WORKSHOP ON NATURE INSPIRED COOPERATIVE STRATEGIES FOR OPTIMISATION. LECTURE NOTES IN COMPUTER SCIENCE (LNCS
"... The generalized traveling salesman problem (GTSP) is an extension of the wellknown 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 pres ..."
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Cited by 7 (3 self)
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times, but the running times still remain within reasonable bounds (at most a few minutes). While the SnyderDaskin memetic algorithm is designed only for the Symmetric GTSP, our algorithm can solve both symmetric and asymmetric instances. Unlike the SnyderDaskin heuristic, we use a simple machine
On the Graphical Relaxation of the Symmetric Traveling Salesman
, 2007
"... The Graphical Traveling Salesman Polyhedron (GTSP) has been proposed by Naddef and Rinaldi to be viewed as a relaxation of the Symmetric Traveling Salesman Polytope (STSP). It has also been employed by Applegate, Bixby, Chvátal, and Cook for solving the latter to optimality by the BranchandCut me ..."
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Cited by 3 (3 self)
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The Graphical Traveling Salesman Polyhedron (GTSP) has been proposed by Naddef and Rinaldi to be viewed as a relaxation of the Symmetric Traveling Salesman Polytope (STSP). It has also been employed by Applegate, Bixby, Chvátal, and Cook for solving the latter to optimality by the Branch
A TABU SEARCH ALGORITHM FOR THE SYMMETRIC GENERALIZED TRAVELING SALESMAN PROBLEM
"... The Generalized Traveling Salesman Problem (GTSP) consists of finding a least cost Hamiltonian circuit or cycle through several clusters of vertices. In this paper we propose a new tabu search algorithm which uses the problem’s configuration to guide the search and reduce the solution space. A new w ..."
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The Generalized Traveling Salesman Problem (GTSP) consists of finding a least cost Hamiltonian circuit or cycle through several clusters of vertices. In this paper we propose a new tabu search algorithm which uses the problem’s configuration to guide the search and reduce the solution space. A new
On the parsimonious property of relaxations of the symmetric traveling salesman polytope. arXiv/math.CO:blah, submitted
"... ABSTRACT. We relate the parsimonious property of relaxations of the Symmetric Traveling Salesman Polytope to a connectivity property of the ridge graph of the Graphical Traveling Salesman Polyhedron. This relationship is quite surprising. The proof is elegant and geometric: it makes use of recent re ..."
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Cited by 1 (1 self)
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ABSTRACT. We relate the parsimonious property of relaxations of the Symmetric Traveling Salesman Polytope to a connectivity property of the ridge graph of the Graphical Traveling Salesman Polyhedron. This relationship is quite surprising. The proof is elegant and geometric: it makes use of recent
ON THE FACIAL STRUCTURE OF SYMMETRIC AND GRAPHICAL TRAVELING SALESMAN POLYHEDRA
, 2009
"... The Symmetric Traveling Salesman Polytope Sn for a fixed number n of cities is a face of the corresponding Graphical Traveling Salesman Polyhedron Pn. This has been used to study facets of Sn using Pn as a tool. In this paper, we study the operation of “rotating” (or “lifting”) valid inequalities fo ..."
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The Symmetric Traveling Salesman Polytope Sn for a fixed number n of cities is a face of the corresponding Graphical Traveling Salesman Polyhedron Pn. This has been used to study facets of Sn using Pn as a tool. In this paper, we study the operation of “rotating” (or “lifting”) valid inequalities
Results 1  10
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126