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The ABACUS System for BranchandCutandPrice Algorithms in Integer Programming and Combinatorial Optimization
, 1998
"... The development of new mathematical theory and its application in software systems for the solution of hard optimization problems have a long tradition in mathematical programming. In this tradition we implemented ABACUS, an objectoriented software framework for branchandcutandprice algorithms ..."
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Cited by 20 (0 self)
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for the solution of mixed integer and combinatorial optimization problems. This paper discusses some difficulties in the implementation of branchandcutandprice algorithms for combinatorial optimization problems and shows how they are managed by ABACUS.
FFTW: An Adaptive Software Architecture For The FFT
, 1998
"... FFT literature has been mostly concerned with minimizing the number of floatingpoint operations performed by an algorithm. Unfortunately, on presentday microprocessors this measure is far less important than it used to be, and interactions with the processor pipeline and the memory hierarchy have ..."
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Cited by 602 (4 self)
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, with over 40 implementations of the FFT on 7 machines. Our tests show that FFTW's selfoptimizing approach usually yields significantly better performance than all other publicly available software. FFTW also compares favorably with machinespecific, vendoroptimized libraries. 1. INTRODUCTION
Chaff: Engineering an Efficient SAT Solver
, 2001
"... Boolean Satisfiability is probably the most studied of combinatorial optimization/search problems. Significant effort has been devoted to trying to provide practical solutions to this problem for problem instances encountered in a range of applications in Electronic Design Automation (EDA), as well ..."
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Cited by 1350 (18 self)
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Boolean Satisfiability is probably the most studied of combinatorial optimization/search problems. Significant effort has been devoted to trying to provide practical solutions to this problem for problem instances encountered in a range of applications in Electronic Design Automation (EDA), as well
A BRANCHANDCUT ALGORITHM FOR THE RESOLUTION OF LARGESCALE SYMMETRIC TRAVELING SALESMAN PROBLEMS
, 1991
"... An algorithm is described for solving largescale instances of the Symmetric Traveling Salesman Problem (STSP) to optimality. The core of the algorithm is a "polyhedral" cuttingplane procedure that exploits a subset of the system of linear inequalities defining the convex hull of the in ..."
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Cited by 205 (7 self)
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, as opposed to branchandbound, keeps on producing cuts after branching. The algorithm has been implemented in FORTRAN. Two different linear programming (LP) packages have been used as the LP solver. The implementation of the algorithm and the interface with one of the LP solvers is described in sufficient
Branchandprice: Column generation for solving huge integer programs
 OPER. RES
, 1998
"... We discuss formulations of integer programs with a huge number of variables and their solution by column generation methods, i.e., implicit pricing of nonbasic variables to generate new columns or to prove LP optimality at a node of the branchandbound tree. We present classes of models for which t ..."
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Cited by 360 (13 self)
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this approach decomposes the problem, provides tighter LP relaxations, and eliminates symmetry. We then discuss computational issues and implementation of column generation, branchandbound algorithms, including special branching rules and efficient ways to solve the LP relaxation. We also discuss
Study of the implementation of BranchandCut as applied to Ising Spin Glasses
, 2007
"... Combinatorial Optimisation is a branch of Mathematics involved in finding the optimal (according to some criteria) combination among a finite set of possibilities. One such problem is finding the lowest energy state of the Ising Spin Glass, a model of disordered systems used in Statistical Physics. ..."
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Simplex algorithms. In an integer linear programming problem we have an additional constraint, that all the variables are integers: in this case we cannot use the simple Simplex/DualSimplex anymore but require an extension: the BranchandCut algorithm. We have implemented the BranchandCut algorithm to solve
A branchandcut algorithm for quadratic assignment problems based on linearizations.”
 Computers & Operations Research,
, 2007
"... Abstract The quadratic assignment problem (QAP) is one of the hardest combinatorial optimization problems known. Exact solution attempts proposed for instances of size larger than 15 have been generally unsuccessful even though successful implementations have been reported on some test problems fro ..."
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Cited by 7 (0 self)
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that require fewer variables and yield stronger lower bounds than existing formulations. We strengthen the formulations with valid inequalities and report computational experience with a branchandcut algorithm. The proposed method performs quite well on QAPLIB instances for which certain metrics (indices
A branchandcut algorithm for the equicut problem
, 1993
"... We describe an algorithm for solving the equicut problem on complete graphs. The core of the algorithm is a cuttingplane procedure that exploits a subset of the linear inequalities defining the convex hull of the incidence vectors of the edge sets that define an equicut. The cuts are generated by s ..."
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Cited by 18 (0 self)
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by several separation procedures that will be described in the paper. Whenever the cuttingplane procedure does not terminate with an optimal solution the algorithm uses a branchandcut strategy. We also describe the implementation of the algorithm and the interface with the LP solver. We then report on our
BRANCHANDCUT ALGORITHMS FOR INTEGER PROGRAMMING
, 1998
"... Branchandcut methods are exact algorithms for integer programming problems. They consist of a combination of a cutting plane method with a branchandbound algorithm. These methods work by solving a sequence of linear programming relaxations of the integer programming problem. Cutting plane method ..."
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Cited by 7 (1 self)
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as good introductions to the area of branchandcut algorithms are [21, 32]. A more recent work on the branchandcut approach to the traveling salesman problem is [1]. Branchandcut methods have also been used to solve other combinatorial optimization problems; recent references
A branchandcut algorithm with betweenness variables for . . .
, 2010
"... The subject of this thesis is the Minimum Linear Arrangement Problem, a classical problem in combinatorial optimization. It consists in finding a positioning p of the vertices V of some graph G on a line, that minimizes the weighted sum of the resulting edge lengths: min p ij∈E cij p(i) − p(j) Som ..."
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Cited by 2 (0 self)
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graphs. We present here a novel approach to solving the Minimum Linear Arrangement Problem with a branchandcut algorithm using so called betweenness variables. The lower bounds are improved and many instances could be solved to proven
Results 1  10
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