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Reformulation and decomposition of integer programs
"... In this survey we examine ways to reformulate integer and mixed integer programs. Typically, but not exclusively, one reformulates so as to obtain stronger linear programming relaxations, and hence better bounds for use in a branchandbound based algorithm. First we cover in detail reformulations b ..."
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Cited by 29 (2 self)
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In this survey we examine ways to reformulate integer and mixed integer programs. Typically, but not exclusively, one reformulates so as to obtain stronger linear programming relaxations, and hence better bounds for use in a branchandbound based algorithm. First we cover in detail reformulations based on decomposition, such as Lagrangean relaxation, DantzigWolfe and the resulting column generation and branchandprice algorithms. This is followed by an examination of Benders ’ type algorithms based on projection. Finally we discuss in detail extended formulations involving additional variables that are based on problem structure. These can often be used to provide strengthened a priori formulations. Reformulations obtained by adding cutting planes in the original variables are not treated here. 1
A Hybrid Multistart Heuristic for the Uncapacitated Facility Location Problem
, 2003
"... We present a multistart heuristic for the uncapacitated facility location problem, based on a very successful method we originally developed for the pmedian problem. ..."
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Cited by 17 (3 self)
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We present a multistart heuristic for the uncapacitated facility location problem, based on a very successful method we originally developed for the pmedian problem.
Design and dimensioning of a novel compositestar WDM network with TDM channel partitioning
 Proceedings of IEEE Third International Conference on Broadband Communications, Networks and Systems
, 2006
"... Abstract — This paper presents the design and dimensioning optimization of a novel optical network structure, called the Petaweb, having a total capacity of several Pb/s (10 15 bit/s). Its topology is a superimposition of stars that drastically eases signaling and switching operations. Firstly, we d ..."
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Abstract — This paper presents the design and dimensioning optimization of a novel optical network structure, called the Petaweb, having a total capacity of several Pb/s (10 15 bit/s). Its topology is a superimposition of stars that drastically eases signaling and switching operations. Firstly, we deal with the network model, focusing on the insertion of the timesharing of the optical channel in network components and in lightpath provisioning. The design problem is jointly a network dimensioning and an assignment problem; we propose for the dimensioning an integer linear programming formulation and a linear resolution algorithm for the assignment. We also propose the use of a quasiregular topology extracted from the optimized regular topology to reduce costs and improve the network utilization. I.
Valid inequalities and facets of the capacitated plant location problem
 Mathematical Programming
, 1989
"... Recently, several successful applications of strong cutting plane methods to combinatorial optimization problems have renewed interest in cutting plane methods, and polyhedral characterizations, of integer programming problems. In this paper, we investigate the polyhedral structure of the capacitate ..."
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Cited by 9 (1 self)
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Recently, several successful applications of strong cutting plane methods to combinatorial optimization problems have renewed interest in cutting plane methods, and polyhedral characterizations, of integer programming problems. In this paper, we investigate the polyhedral structure of the capacitated plant location problem. Our purpose is to identify facets and valid inequalities for a wide range of capacitated fixed charge problems that contain this prototype problem as a substructure. The first part of the paper introduces a family of facets for a version of the capacitated plant location problem with constant capacity K for all plants. These facet inequalities depend on K and thus differ fundamentally from the valid inequalities for the uncapacitated version of the problem. We also introduce a second formulation for a model with indivisible customer demand and show that it is equivalent to a vertex packing problem on a derived graph. We identify facets and valid inequalities for this version of the problem by applying known results for the vertex packing polytope.
Primaldual variable neighborhood search for the simple plant location problem
 INFORMS Journal on Computing
"... doi 10.1287/ijoc.1060.0196 ..."
Optimization of a Dedicated Path Protected TDM/WDM Petaweb Architecture
 Riva Del Garda, Italy
, 2006
"... This paper deals with the insertion of a dedicated path protection strategy in the design of a novel optical network structure, called PetaWeb, that can reach a total capacity of several Pb/s (10 15 bit/s). Prior studies of the same authors have tackled the optimization of a PetaWeb network architec ..."
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Cited by 5 (5 self)
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This paper deals with the insertion of a dedicated path protection strategy in the design of a novel optical network structure, called PetaWeb, that can reach a total capacity of several Pb/s (10 15 bit/s). Prior studies of the same authors have tackled the optimization of a PetaWeb network architecture with a regular compositestar topology and with a quasiregular topology. In this paper, a protection strategy is added to the network model modifying the optimization algorithm. The results show that the optimized PetaWeb architecture is reliable and that every edge node is connected to at least two switching sites. We highlight the strength of the proposed network model for this compositestar architecture: a fastswitching backbone that eases signaling and switching operations at a competitive network cost. The network cost is evaluated on real physical costs and on a virtual cost due to lightpaths propagation delays. 1 1
Design Optimization of a New Network Structure for the Next Generation Internet
, 2004
"... Les textes publiés dans la série des rapports de recherche HEC n’engagent que la responsabilité de leurs auteurs. La publication de ces rapports de recherche bénéficie d’une subvention du Fonds québécois de la recherche sur la nature et les technologies. ..."
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Les textes publiés dans la série des rapports de recherche HEC n’engagent que la responsabilité de leurs auteurs. La publication de ces rapports de recherche bénéficie d’une subvention du Fonds québécois de la recherche sur la nature et les technologies.
A BranchandCut Algorithm for the Index Selection Problem
, 1996
"... The Index Selection Problem (ISP) is a phase of fundamental importance in the physical design of databases, calling for a set of indexes to be built in a database so as to minimize the overall execution time for a given database workload. The problem is a generalization of the wellknown Uncapaci ..."
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Cited by 2 (0 self)
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The Index Selection Problem (ISP) is a phase of fundamental importance in the physical design of databases, calling for a set of indexes to be built in a database so as to minimize the overall execution time for a given database workload. The problem is a generalization of the wellknown Uncapacitated Facility Location Problem (UFLP). We formulate ISP as a set packing problem, showing that our mathematical model contains all the clique inequalities (whose number is polynomial). The upper bound provided by solving the LP relaxation of this model turns out to be quite bad for some instances. We therefore face the problem of strengthening this relaxation by means of additional valid inequalities. In particular, we describe an effective exact separation procedure for a suitablydefined family of lifted oddhole inequalities, obtained by applying a ChvatalGomory derivation to the clique inequalities. These results are used within a branchandcut algorithm for the exact soluti...
2003b. Solving the simple plant location problem using data correcting approach
 J. Global Optim
"... The Data Correcting Algorithm is a branch and bound algorithm in which the data of a given problem instance is ‘corrected ’ at each branching in such a way that the new instance will be as close as possible to a polynomially solvable instance and the result satisfies an acceptable accuracy (the diff ..."
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The Data Correcting Algorithm is a branch and bound algorithm in which the data of a given problem instance is ‘corrected ’ at each branching in such a way that the new instance will be as close as possible to a polynomially solvable instance and the result satisfies an acceptable accuracy (the difference between optimal and current solution). In this paper the data correcting algorithm is applied to determining exact and approximate optimal solutions to the simple plant location problem. Implementations of the algorithm are based on a pseudoBoolean representation of the goal function of the SPLP and a new reduction rule. We study the efficiency of the data correcting approach using two different bounds, the combinatorial bound and the Erlenkotter bound. We present computational results on several benchmark instances of the simple plant location problem, which confirm the efficiency of the datacorrecting approach.
Simulation and Optimization
 of the Power Distribution Network in VLSI circuits,” ICCAD00
, 2000
"... projections onto grids and finite resolution images ..."
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projections onto grids and finite resolution images