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DNA computers in vitro and vivo
, 1996
"... We show how DNA molecules and stan dard lab techniques may be used to create a nondeterministic Turing machine. This is the first scheme that shows how to make a universal computer with DNA. We claim that both our scheme and previous ones will work but they probably cannot be scaled up to be of pra ..."
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Cited by 28 (0 self)
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We show how DNA molecules and stan dard lab techniques may be used to create a nondeterministic Turing machine. This is the first scheme that shows how to make a universal computer with DNA. We claim that both our scheme and previous ones will work but they probably cannot be scaled up to be of practical computational importance. In vivo,
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.
Efficient Separation Routines for the Symmetric Traveling Salesman Problem II: Separating multi Handle Inequalities
, 2001
"... This paper is the second in a series of two papers dedicated to the separation problem in the symmetric traveling salesman polytope. The first one gave the basic ideas behind the separation procedures and applied them to the separation of Comb inequalities. We here address the problem of separating ..."
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Cited by 8 (2 self)
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This paper is the second in a series of two papers dedicated to the separation problem in the symmetric traveling salesman polytope. The first one gave the basic ideas behind the separation procedures and applied them to the separation of Comb inequalities. We here address the problem of separating inequalities which are all, in a way or another, a generalization of Comb inequalities. These are namely Clique Trees, Path, Ladder inequalities. Computational results are reported for the solution of instances of the TSPLib using the branch and cut framework ABACUS.
SYMPHONY: A Parallel Framework for Branch and Cut
, 1999
"... This white paper introduces SYMPHONY (Single or MultiProcess Optimization over Networks), a powerful environment for implementing branch, cut, and price algorithms. SYMPHONY is a stateoftheart solver which is designed to be completely modular and is easy to port to various problem settings. All ..."
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Cited by 6 (4 self)
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This white paper introduces SYMPHONY (Single or MultiProcess Optimization over Networks), a powerful environment for implementing branch, cut, and price algorithms. SYMPHONY is a stateoftheart solver which is designed to be completely modular and is easy to port to various problem settings. All library subroutines are generictheir implementation does not depend on the the problemsetting. To develop a fullscale, parallel branch, cut, and price algorithm, the user has only to specify a few problemspeci c functions such as preprocessing and separation. The vast majority of the computation takes place within a \black box, &quot; of which the user need have no knowledge. SYMPHONY communicates with the user's routines through welldened interfaces and performs all the normal functions of branch and cuttree management, LP solution, cut pool management, as well as interprocess communication. Although there are default options, the user can also assert control over the behavior of SYMPHONY through a myriad of parameters and optional subroutines. SYMPHONY can be built in a variety of congurations, ranging from completely sequential to fully parallel with independently functioning cut generators, cut pools, and LP solvers. The distributed version currently runs in any environment supported by the PVM message passing protocol. The same source code can also be compiled for sharedmemory architectures using any OpenMP compliant compiler.
Interactive Genetic Algorithms for the Traveling Salesman Problem
 In Genetic and Evolutionary Computation Conf
, 1999
"... We use an interactive genetic algorithm to divide and conquer large traveling salesperson problems. Current genetic algorithm approaches are computationally intensive and may not produce acceptable tours within the time available. Instead of applying a genetic algorithm to the entire problem, we let ..."
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Cited by 3 (0 self)
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We use an interactive genetic algorithm to divide and conquer large traveling salesperson problems. Current genetic algorithm approaches are computationally intensive and may not produce acceptable tours within the time available. Instead of applying a genetic algorithm to the entire problem, we let the user interactively decompose a problem into subproblems, let the genetic algorithm separately solve these subproblems and then interactively connect subproblem solutions to get a global tour for the original problem. Our approach significantly reduces the computing time to find high quality solutions for large traveling salesperson problems. We believe that an interactive approach can be extended to other visually decomposable problems. 1 INTRODUCTION The traveling salesperson problem (TSP) is a classical example of an NPHard combinatorial optimization problem (Garey and Johnson, 1979). Given N cities and distances among them, the aim is to find the shortest tour that visits each cit...
Cuttingplane proofs in polynomial space
 Mathematical Programming
, 1990
"... Following Chvfital, cutting planes may be viewed as a proof system for establishing that a given system of linear inequalities has no integral solution. We show that such proofs may be carried out in polynomial workspace. Key words: Integer programming, cutting planes. The integer programming proble ..."
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Cited by 2 (0 self)
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Following Chvfital, cutting planes may be viewed as a proof system for establishing that a given system of linear inequalities has no integral solution. We show that such proofs may be carried out in polynomial workspace. Key words: Integer programming, cutting planes. The integer programming problem is to decide if a given system of linear inequalities has an integral solution. Recent progress on this algorithmic question has involved techniques from the geometry of numbers, in the celebrated paper of Lenstra [20] and in results of Babai [1], Gr6tschel, Lovfisz and Schrijver [14] and Kannan [16]. One of the things that is apparent in these results is the importance of the fact that if a polyhedron contains no integral vectors then there must be some direction in which it is not very 'wide'. This idea has been developed more fully by Kannan and Lovfisz [17], who obtained a theorem which provides much more information on the appearance of such polyhedra. These 'width ' results have consequences for the construction and analysis of proof systems for verifying that a polyhedron contains no integral vectors. Whereas the integer programming problem is directly
Branch, Cut, and Price: Sequential and Parallel
"... Branch, cut, and price (BCP) is an LPbased branch and bound technique for solving largescale discrete optimization problems (DOPs). In BCP, both cuts and variables can be generated dynamically throughout the search tree. The ability to handle constantly changing sets of cuts and variables allows t ..."
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Branch, cut, and price (BCP) is an LPbased branch and bound technique for solving largescale discrete optimization problems (DOPs). In BCP, both cuts and variables can be generated dynamically throughout the search tree. The ability to handle constantly changing sets of cuts and variables allows these algorithms to undertake the solution of very largescale DOPs; however, it also leads to interesting implementational challenges. These lecture notes, based on our experience over the last six years with implementing a generic framework for BCP called SYMPHONY (Single or MultiProcess Optimization over Networks), address these challenges. They are an attempt to summarize some of what we and others have learned about implementing BCP, both sequential and parallel, and to provide a useful reference for those who wish to use BCP techniques in their own research.