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The median cycle problem
, 2001
"... In the Median Cycle Problem the aim is to determine a simple cycle containing a subset of vertices of a graph, while considering two types of cost: routing costs associated with the cycle itself, and the cost of assigning vertices not on the cycle to vertices of the cycle. Two versions of the proble ..."
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In the Median Cycle Problem the aim is to determine a simple cycle containing a subset of vertices of a graph, while considering two types of cost: routing costs associated with the cycle itself, and the cost of assigning vertices not on the cycle to vertices of the cycle. Two versions of the problem are investigated. In the rst, the objective function is the sum of routing and assignment costs. In the second, routing costs are minimized, subject to an upper bound on the total assignment cost. The two versions are formulated as integer linear programs. The polyhedral structure of the rst model is analyzed and the second model is strengthened through the introduction of additional valid inequalities. Separation procedures are developed. Heuristic procedures and an exact branchandcut algorithm are described. Computational results on benchmark instances and on randomly generated problems con rm the e ciency of the proposed algorithms.
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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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.
Video–on–Demand Network Design And Maintenance Using Fuzzy Optimization
"... Video–on–Demand (VoD) is the entertainment source which, in the future, will likely overtake regular television in many aspects. Even though many companies have deployed working VoD services, some aspects of the VoD should still undergo further improvement, in order for it to reach to the foreseen p ..."
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Video–on–Demand (VoD) is the entertainment source which, in the future, will likely overtake regular television in many aspects. Even though many companies have deployed working VoD services, some aspects of the VoD should still undergo further improvement, in order for it to reach to the foreseen potentials. An important aspect of a VoD system is the underlying network in which it operates. According to the huge number of customers in this network, it should be carefully designed to fulfill certain performance criteria. This process should be capable of finding optimal locations for the nodes of the network as well as determining the content which should be cached in each one. While, this problem is categorized in the general group of network optimization problems, its specific characteristics demand a new solution to be sought for it. In this paper, inspired by the successful use of fuzzy optimization in similar problems in other fields, a fuzzy objective function is derived which is heuristically shown to minimize the communication cost in a VoD network, while also controlling the storage cost. Then, an iterative algorithm is proposed to find a locally optimal solution to the proposed objective function. Capitalizing on the unrepeatable tendency of the proposed algorithm, a heuristic method for picking a good solution, from a bundle of solutions produced by the proposed algorithm, is also suggested. This paper includes formal statement of the problem and its mathematical analysis. Also, different scenarios in which the proposed algorithm can be utilized are discussed
Corresponding Author's Institution: ENSTA ParisTech
, 2011
"... Abstract: Due to the emergence of bandwidthrequiring services, telecommunication operators are being compelled to renew their fix access network, most of them favoring the Fiber To The Home (FTTH) technology. This paper focuses on the optimization of FTTH deployment, which is of prime importance du ..."
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Abstract: Due to the emergence of bandwidthrequiring services, telecommunication operators are being compelled to renew their fix access network, most of them favoring the Fiber To The Home (FTTH) technology. This paper focuses on the optimization of FTTH deployment, which is of prime importance due to the economic stakes. The key design issue here is locating splitters and routing fibers in an existing network infrastructure to which is associated a graph with given capacities on the edges. No assumption is made on the structure of the graph. First we propose a mixed integer formulation for this decision problem. Then, valid inequalities and problem size reduction schemes are presented. Finally efficiency of solving approaches is assessed through extensive numerical tests performed on Orange reallife data. Research Highlights We propose an original model for a new real optical network design. The model is a linear program which is a generalization of a model of flow with multipliers (generalized flows). We give valid inequalities. We propose specific reductions of the graph and prove their validity. We test our model on real instances with up to thousand nodes: we use Cplex and obtain lower bounds within less than 2 % from the optimum. We prove the usefulness of the approach (cuts and reductions).Article pdf complet Click here to view linked References 1 2