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40
Greedy Randomized Adaptive Search Procedures
, 2002
"... GRASP is a multistart metaheuristic for combinatorial problems, in which each iteration consists basically of two phases: construction and local search. The construction phase builds a feasible solution, whose neighborhood is investigated until a local minimum is found during the local search phas ..."
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Cited by 647 (82 self)
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GRASP is a multistart metaheuristic for combinatorial problems, in which each iteration consists basically of two phases: construction and local search. The construction phase builds a feasible solution, whose neighborhood is investigated until a local minimum is found during the local search phase. The best overall solution is kept as the result. In this chapter, we first describe the basic components of GRASP. Successful implementation techniques and parameter tuning strategies are discussed and illustrated by numerical results obtained for different applications. Enhanced or alternative solution construction mechanisms and techniques to speed up the search are also described: Reactive GRASP, cost perturbations, bias functions, memory and learning, local search on partially constructed solutions, hashing, and filtering. We also discuss in detail implementation strategies of memorybased intensification and postoptimization techniques using pathrelinking. Hybridizations with other metaheuristics, parallelization strategies, and applications are also reviewed.
An Efficient Implementation Of A Scaling MinimumCost Flow Algorithm
 Journal of Algorithms
, 1992
"... . The scaling pushrelabel method is an important theoretical development in the area of minimumcost flow algorithms. We study practical implementations of this method. We are especially interested in heuristics which improve reallife performance of the method. Our implementation works very well o ..."
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Cited by 139 (6 self)
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. The scaling pushrelabel method is an important theoretical development in the area of minimumcost flow algorithms. We study practical implementations of this method. We are especially interested in heuristics which improve reallife performance of the method. Our implementation works very well over a wide range of problem classes. In our experiments, it was always competitive with the established codes, and usually outperformed these codes by a wide margin. Some heuristics we develop may apply to other network algorithms. Our experimental work on the minimumcost flow problem motivated theoretical work on related problems. Supported in part by ONR Young Investigator Award N0001491J1855, NSF Presidential Young Investigator Grant CCR8858097 with matching funds from AT&T and DEC, Stanford University Office of Technology Licensing, and a grant form the Powell Foundation. 1 1. Introduction. Significant theoretical progress has been made recently in the area of minimumcost flow ...
A Case Study of Multiservice, Multipriority Traffic Engineering Design for Data Networks
 Proc. IEEE Int’l Global Telecomm. Conf. (GLOBECOM ’99
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A QMRbased interiorpoint algorithm for solving linear programs
 Mathematical Programming
, 1997
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A Truncated PrimalInfeasible DualFeasible Network Interior Point Method
, 1996
"... In this paper we introduce the truncated primalinfeasible dualfeasible interior point algorithm for linear programming and describe an implementation of this algorithm for solving the minimum cost network flow problem. In each iteration, the linear system that determines the search direction is co ..."
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Cited by 31 (3 self)
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In this paper we introduce the truncated primalinfeasible dualfeasible interior point algorithm for linear programming and describe an implementation of this algorithm for solving the minimum cost network flow problem. In each iteration, the linear system that determines the search direction is computed inexactly, and the norm of the resulting residual vector is used in the stopping criteria of the iterative solver employed for the solution of the system. In the implementation, a preconditioned conjugate gradient method is used as the iterative solver. The details of the implementation are described and the code, pdnet, is tested on a large set of standard minimum cost network flow test problems. Computational results indicate that the implementation is competitive with stateoftheart network flow codes.
Implementation of a Combinatorial Multicommodity Flow Algorithm
, 1992
"... The multicommodity flow problem involves simultaneously shipping multiple commodities through a single network so that the total amount of flow on each edge is no more than the capacity of the edge. This problem can be expressed as a large linear program, and most known algorithms for it, both theor ..."
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Cited by 22 (3 self)
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The multicommodity flow problem involves simultaneously shipping multiple commodities through a single network so that the total amount of flow on each edge is no more than the capacity of the edge. This problem can be expressed as a large linear program, and most known algorithms for it, both theoretical and practical, are linear programming algorithms designed to take advantage of the structure of multicommodity flow problems. The size of the linear programs, however, makes it prohibitively difficult to solve large multicommodity flow problems. In this paper, we describe and examine a multicommodity flow implementation based on the recent combinatorial approximation algorithm of Leighton et al. [13]. The theory predicts that the running time of the algorithm increases linearly with the number of commodities. Our experiments verify this behavior. The theory also predicts that the running time increases as the square of the desired precision. Our experiments show that the running time ...
Adaptive Use of Iterative Methods in PredictorCorrector Interior Point Methods for Linear Programming
 NUMERICAL ALGORITHMS
, 1999
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A Class of Preconditioners for Weighted Least Squares Problems
, 1999
"... We consider solving a sequence of weighted linear least squares problems where the changes from one problem to the next are the weights and the right hand side (or data). This is the case for primaldual interiorpoint methods. We derive a class of preconditioners based on a low rank correction to a ..."
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Cited by 19 (11 self)
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We consider solving a sequence of weighted linear least squares problems where the changes from one problem to the next are the weights and the right hand side (or data). This is the case for primaldual interiorpoint methods. We derive a class of preconditioners based on a low rank correction to a Cholesky factorization of a weighted normal equation coefficient matrix with the previous weight. Key Words. Weighted linear least squares, Preconditioners, Preconditioned conjugate gradient for least squares, Linear programming, Primaldual infeasibleinteriorpoint algorithms. 1 Introduction In this paper, we present a class of preconditioners based on low rank corrections to the Cholesky factorization of a weighted normal equation coefficient matrix. This class of preconditioners leads to good performance for interiorpoint methods for linear programming. Particularly, we have implemented primaldual Newton method to test this class of preconditioners. The numerical results on large scale...
INTERIOR POINT METHODS FOR COMBINATORIAL OPTIMIZATION
, 1995
"... Research on using interior point algorithms to solve combinatorial optimization and integer programming problems is surveyed. This paper discusses branch and cut methods for integer programming problems, a potential reduction method based on transforming an integer programming problem to an equivale ..."
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Cited by 16 (9 self)
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Research on using interior point algorithms to solve combinatorial optimization and integer programming problems is surveyed. This paper discusses branch and cut methods for integer programming problems, a potential reduction method based on transforming an integer programming problem to an equivalent nonconvex quadratic programming problem, interior point methods for solving network flow problems, and methods for solving multicommodity flow problems, including an interior point column generation algorithm.