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76
A polylogarithmic approximation algorithm for the group Steiner tree problem
 Journal of Algorithms
, 2000
"... The group Steiner tree problem is a generalization of the Steiner tree problem where we ae given several subsets (groups) of vertices in a weighted graph, and the goal is to find a minimumweight connected subgraph containing at least one vertex from each group. The problem was introduced by Reich a ..."
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Cited by 146 (9 self)
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The group Steiner tree problem is a generalization of the Steiner tree problem where we ae given several subsets (groups) of vertices in a weighted graph, and the goal is to find a minimumweight connected subgraph containing at least one vertex from each group. The problem was introduced by Reich and Widmayer and finds applications in VLSI design. The group Steiner tree problem generalizes the set covering problem, and is therefore at least as had. We give a randomized O(log 3 n log k)approximation algorithm for the group Steiner tree problem on an nnode graph, where k is the number of groups. The best previous ink)v/ (Bateman, Helvig, performance guarantee was (1 +  Robins and Zelikovsky).
Memetic Algorithms for Combinatorial Optimization Problems: Fitness Landscapes and Effective Search Strategies
, 2001
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A RandomKey Genetic Algorithm for the Generalized Traveling Salesman Problem
 European Journal of Operational research
, 2004
"... The Generalized Traveling Salesman Problem is a variation of the well known Traveling Salesman Problem in which the set of nodes is divided into clusters; the objective is to find a minimumcost tour passing through one node from each cluster. We present an effective heuristic for this problem. The ..."
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Cited by 47 (1 self)
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The Generalized Traveling Salesman Problem is a variation of the well known Traveling Salesman Problem in which the set of nodes is divided into clusters; the objective is to find a minimumcost tour passing through one node from each cluster. We present an effective heuristic for this problem. The method combines a genetic algorithm (GA) with a local tour improvement heuristic. Solutions are encoded using random keys, which circumvent the feasibility problems encountered when using traditional GA encodings. On a set of 41 standard test problems with symmetric distances and up to 442 nodes, the heuristic found solutions that were optimal in most cases and were within 1% of optimality in all but the largest problems, with computation times generally within 10 seconds. The heuristic is competitive with other heuristics published to date in both solution quality and computation time.
Approximation Algorithms for the Traveling Purchaser Problem and its Variants in Network Design
, 1999
"... . The traveling purchaser problem is a generalization of the traveling salesman problem with applications in a wide range of areas including network design and scheduling. The input consists of a set of markets and a set of products. Each market offers a price for each product and there is a cos ..."
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Cited by 26 (6 self)
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. The traveling purchaser problem is a generalization of the traveling salesman problem with applications in a wide range of areas including network design and scheduling. The input consists of a set of markets and a set of products. Each market offers a price for each product and there is a cost associated with traveling from one market to another. The problem is to purchase all products by visiting a subset of the markets in a tour such that the total travel and purchase costs are minimized. This problem includes many wellknown NPhard problems such as uncapacitated facility location, set cover and group Steiner tree problems as its special cases. We give an approximation algorithm with a polylogarithmic worstcase ratio for the traveling purchaser problem with metric travel costs. For a special case of the problem that models the ringstar network design problem, we give a constantfactor approximation algorithm. Our algorithms are based on rounding LP relaxation sol...
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 26 (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, arises when exactly one node for each cluster has to be visited. Both GTSP and EGTSP are NPhard problems, and find practical applications in routing and scheduling. In this paper we model GTSP and EGTSP as integer linear programs, and study the facial structure of the corresponding polytopes. In a companion paper (Fischetti, Salazar and Toth [5]), the results described in this work have been used to design a branchandcut algorithm for the exact solution of instances up to 442 nodes.
Generalized network design problems
 European Journal of Operational Research
, 2003
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An efficient composite heuristic for the symmetric generalized traveling salesman problem
 European Journal of Operational Research
, 1998
"... The main purpose of this paper is to introduce a new composite heuristic for solving the generalized traveling salesman problem. The proposed heuristic is composed of three phases: the construction of an initial partial solution, the insertion of a node from each nonvisited nodesubset, and a solut ..."
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Cited by 19 (1 self)
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The main purpose of this paper is to introduce a new composite heuristic for solving the generalized traveling salesman problem. The proposed heuristic is composed of three phases: the construction of an initial partial solution, the insertion of a node from each nonvisited nodesubset, and a solution improvement phase. We show that the heuristic performs very well on thirty six TSPLIB problems which have been solved to optimality by other researchers. We also propose some simple heuristics that can be used as basic blocks to construct more efficient composite heuristics.
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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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 consider different variations of a memetic algorithm approach to the GTSP. The aim of this paper is to present a new memetic algorithm for GTSP with a powerful local search procedure. The experiments show that the proposed algorithm clearly outperforms all of the known heuristics with respect 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.
The ring star problem: polyhedral analysis and exact algorithm
 NETWORKS
, 2004
"... In the Ring Star Problem, the aim is to locate a simple cycle through a subset of vertices of a graph with the objective of minimizing the sum of two costs: a ring cost proportional to the length of the cycle and an assignment cost from the vertices not in the cycle to their closest vertex on the cy ..."
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Cited by 17 (1 self)
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In the Ring Star Problem, the aim is to locate a simple cycle through a subset of vertices of a graph with the objective of minimizing the sum of two costs: a ring cost proportional to the length of the cycle and an assignment cost from the vertices not in the cycle to their closest vertex on the cycle. The problem has several applications in telecommunications network design and in rapid transit systems planning. It is an extension of the classical location–allocation problem introduced in the early 1960s, and closely related versions have been recently studied by several authors. This article formulates the problem as a mixedinteger linear program and strengthens it with the introduction of several families of valid inequalities. These inequalities are shown to be facetdefining and are used to develop a branchandcut algorithm. Computational results show that instances involving up to 300 vertices can be solved optimally using the proposed methodology.
Locating median cycles in networks
, 2005
"... In the median cycle problem the aim is to determine a simple cycle through a subset of vertices of a graph involving two types of costs: a routing cost associated with the cycle itself, and the cost of assigning vertices not on the cycle to visited vertices. The objective is to minimize the routing ..."
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Cited by 14 (1 self)
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In the median cycle problem the aim is to determine a simple cycle through a subset of vertices of a graph involving two types of costs: a routing cost associated with the cycle itself, and the cost of assigning vertices not on the cycle to visited vertices. The objective is to minimize the routing cost, subject to an upper bound on the total assignment cost. This problem arises in the location of a circularshaped transportation and telecommunication infrastructure. We present a mixed integer linear model, and strengthen it with the introduction of additional classes of nontrivial valid inequalities. Separation procedures are developed and an exact branchandcut algorithm is described. Computational results on instances from the classical TSP library and randomly generated ones confirm the efficiency of the proposed algorithm. An application related to the city of Milan (Italy) is also solved within reasonable computation time.