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A greedy randomized adaptive search procedure for the 2partition problem
 Operations Research
, 1994
"... Abstract. Today, a variety of heuristic approaches are available to the operations research practitioner. One methodology that has a strong intuitive appeal, a prominent empirical track record, and is trivial to efficiently implement on parallel processors is GRASP (Greedy Randomized Adaptive Search ..."
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Cited by 478 (75 self)
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Abstract. Today, a variety of heuristic approaches are available to the operations research practitioner. One methodology that has a strong intuitive appeal, a prominent empirical track record, and is trivial to efficiently implement on parallel processors is GRASP (Greedy Randomized Adaptive Search Procedures). GRASP is an iterative randomized sampling technique in which each iteration provides a solution to the problem at hand. The incumbent solution over all GRASP iterations is kept as the final result. There are two phases within each GRASP iteration: the first intelligently constructs an initial solution via an adaptive randomized greedy function; the second applies a local search procedure to the constructed solution in hope of finding an improvement. In this paper, we define the various components comprising a GRASP and demonstrate, step by step, how to develop such heuristics for combinatorial optimization problems. Intuitive justifications for the observed empirical behavior of the methodology are discussed. The paper concludes with a brief literature review of GRASP implementations and mentions two industrial applications.
A Discrete LagrangianBased GlobalSearch Method for Solving Satisfiability Problems
 Journal of Global Optimization
, 1998
"... Satisfiability is a class of NPcomplete problems that model a wide range of realworld applications. These problems are difficult to solve because they have many local minima in their search space, often trapping greedy search methods that utilize some form of descent. In this paper, we propose a n ..."
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Cited by 60 (7 self)
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Satisfiability is a class of NPcomplete problems that model a wide range of realworld applications. These problems are difficult to solve because they have many local minima in their search space, often trapping greedy search methods that utilize some form of descent. In this paper, we propose a new discrete Lagrangemultiplierbased globalsearch method for solving satisfiability problems. We derive new approaches for applying Lagrangian methods in discrete space, show that equilibrium is reached when a feasible assignment to the original problem is found, and present heuristic algorithms to look for equilibrium points. Instead of restarting from a new starting point when a search reaches a local trap, the Lagrange multipliers in our method provide a force to lead the search out of a local minimum and move it in the direction provided by the Lagrange multipliers. One of the major advantages of our method is that it has very few algorithmic parameters to be tuned by users, and the se...
A Grasp For Satisfiability
 CLIQUES, COLORING, AND SATISFIABILITY: THE SECOND DIMACS IMPLEMENTATION CHALLENGE, VOLUME 26 OF DIMACS SERIES ON DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE
, 1996
"... A greedy randomized adaptive search procedure (Grasp) is a randomized heuristic that has been shown to quickly produce good quality solutions for a wide variety of combinatorial optimization problems. In this paper, we describe a Grasp for the satisfiability (SAT) problem. This algorithm can be also ..."
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Cited by 31 (6 self)
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A greedy randomized adaptive search procedure (Grasp) is a randomized heuristic that has been shown to quickly produce good quality solutions for a wide variety of combinatorial optimization problems. In this paper, we describe a Grasp for the satisfiability (SAT) problem. This algorithm can be also directly applied to both the weighted and unweighted versions of the maximum satisfiability (MAXSAT) problem. We review basic concepts of Grasp: construction and local search algorithms. The implementation of Grasp for the SAT problem is described in detail. Computational experience on a large set of test problems is presented.
Greedy Randomized Adaptive Search Procedures
 Handbook of Applied Optimization
, 2001
"... . GRASP (greedy randomized adaptive search procedure) is a metaheuristic for combinatorial optimization. GRASP usually is implemented as a multistart procedure, where each iteration is made up of a construction phase, where a randomized greedy solution is constructed, and a local search phase wh ..."
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Cited by 27 (4 self)
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. GRASP (greedy randomized adaptive search procedure) is a metaheuristic for combinatorial optimization. GRASP usually is implemented as a multistart procedure, where each iteration is made up of a construction phase, where a randomized greedy solution is constructed, and a local search phase which starts at the constructed solution and applies iterative improvement until a locally optimal solution is found. This chapter gives an overview of GRASP. Besides describing the basic building blocks of a GRASP, the chapter covers enhancements to the basic procedure, including reactive GRASP, hybrid GRASP, and intensification strategies. 1. Introduction Consider a combinatorial optimization problem, where one is given a discrete set X of solutions and an objective function f(x) : x # X # to be minimized and seeks a solution x # # X such that f(x # ) # f(x), for all x # X . Problems of this type are sometimes easy to solve, i.e. they can be solved in polynomial time, but mor...
Global Search Methods For Solving Nonlinear Optimization Problems
, 1997
"... ... these new methods, we develop a prototype, called Novel (Nonlinear Optimization Via External Lead), that solves nonlinear constrained and unconstrained problems in a unified framework. We show experimental results in applying Novel to solve nonlinear optimization problems, including (a) the lear ..."
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Cited by 15 (1 self)
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... these new methods, we develop a prototype, called Novel (Nonlinear Optimization Via External Lead), that solves nonlinear constrained and unconstrained problems in a unified framework. We show experimental results in applying Novel to solve nonlinear optimization problems, including (a) the learning of feedforward neural networks, (b) the design of quadraturemirrorfilter digital filter banks, (c) the satisfiability problem, (d) the maximum satisfiability problem, and (e) the design of multiplierless quadraturemirrorfilter digital filter banks. Our method achieves better solutions than existing methods, or achieves solutions of the same quality but at a lower cost.
Combinatorial Optimization In Telecommunications
, 2001
"... Combinatorial optimization problems are abundant in the telecommunications industry. In this paper, we present four realworld telecommunications applications where combinatorial optimization plays a major role. The first problem concerns the optimal location of modem pools for an internet servi ..."
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Cited by 13 (2 self)
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Combinatorial optimization problems are abundant in the telecommunications industry. In this paper, we present four realworld telecommunications applications where combinatorial optimization plays a major role. The first problem concerns the optimal location of modem pools for an internet service provider. The second problem deals with the optimal routing of permanent virtual circuits for a frame relay service. In the third problem, one seeks to optimally design a SONET ring network. The last problem comes up when planning a global telecommunications network.
Computing Approximate Solutions Of The Maximum Covering Problem With Grasp
 J. of Heuristics
, 1998
"... . We consider the maximum covering problem, a combinatorial optimization problem that arises in many facility location problems. In this problem, a potential facility site covers a set of demand points. With each demand point, we associate a nonnegative weight. The task is to select a subset of p > ..."
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Cited by 8 (4 self)
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. We consider the maximum covering problem, a combinatorial optimization problem that arises in many facility location problems. In this problem, a potential facility site covers a set of demand points. With each demand point, we associate a nonnegative weight. The task is to select a subset of p > 0 sites from the set of potential facility sites, such that the sum of weights of the covered demand points is maximized. We describe a greedy randomized adaptive search procedure (GRASP) for the maximum covering problem that finds good, though not necessarily optimum, placement configurations. We describe a wellknown upper bound on the maximum coverage which can be computed by solving a linear program and show that on large instances, the GRASP can produce facility placements that are nearly optimal. 1. INTRODUCTION We consider the maximum covering problem (MCP) [11], a combinatorial optimization problem that has been applied to numerous facility location problems, including rural health c...
Consumer choice in competitive location models: Formulations and heuristics
, 1998
"... A new direction of research in Competitive Location theory incorporates theories of Consumer Choice Behavior in its models. Following this direction, this paper studies the importance of consumer behavior with respect to distance or transportation costs in the optimality of locations obtained by tra ..."
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Cited by 8 (2 self)
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A new direction of research in Competitive Location theory incorporates theories of Consumer Choice Behavior in its models. Following this direction, this paper studies the importance of consumer behavior with respect to distance or transportation costs in the optimality of locations obtained by traditional Competitive Location models. To do this, it considers different ways of defining a key parameter in the basic Maximum Capture model (MAXCAP). This parameter will reflect various ways of taking into account distance based on several Consumer Choice Behavior theories. The optimal locations and the deviation in demand captured when the optimal locations of the other models are used instead of the true ones, are computed for each model. A metaheuristic based on GRASP and Tabu search procedure is presented to solve all the models. Computational experience and an application to 55node network are also presented. Keywords: distance, competitive location models, consumer choice behavior, GRASP, tabu.
Location Models for Airline Hubs Behaving as M/D/c Queues
 Computers & Operations Research
"... Models are presented for the optimal location of hubs in airline networks, that take into consideration the congestion effects. Hubs, which are the most congested airports, are modeled as M/D/c queuing systems, that is, Poisson arrivals, deterministic service time, and c servers. A formula is derive ..."
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Cited by 6 (0 self)
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Models are presented for the optimal location of hubs in airline networks, that take into consideration the congestion effects. Hubs, which are the most congested airports, are modeled as M/D/c queuing systems, that is, Poisson arrivals, deterministic service time, and c servers. A formula is derived for the probability of a number of customers in the system, which is later used to propose a probabilistic constraint. This constraint limits the probability of b airplanes in queue, to be lesser than a value a. Due to the computational complexity of the formulation, The model is solved using a metaheuristic based on tabu search. Computational experience is presented. Keywords: Hub location, Congestion, Tabusearch Introduction Networks involving hubs are important in transportation and telecommunications. In both cases, when there is traffic between several origins and several destinations, there are economical benefits if this traffic is concentrated on some arcs of the network. A hu...
A Bibliography of GRASP
"... This document contains references related to GRASP (greedy randomized adaptive search procedure) that have either appeared in the literature or as technical reports. If you are aware of any uncited reference, incorrectly cited reference, or update to a cited reference, please contact Mauricio G. C. ..."
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Cited by 2 (2 self)
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This document contains references related to GRASP (greedy randomized adaptive search procedure) that have either appeared in the literature or as technical reports. If you are aware of any uncited reference, incorrectly cited reference, or update to a cited reference, please contact Mauricio G. C. Resende at the address given at the end of this document.