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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 ..."
Abstract

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.
Greedy Randomized Adaptive Search Procedures For The Steiner Problem In Graphs
 QUADRATIC ASSIGNMENT AND RELATED PROBLEMS, VOLUME 16 OF DIMACS SERIES ON DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE
, 1999
"... We describe four versions of a Greedy Randomized Adaptive Search Procedure (GRASP) for finding approximate solutions of general instances of the Steiner Problem in Graphs. Di#erent construction and local search algorithms are presented. Preliminary computational results with one of the versions ..."
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Cited by 123 (31 self)
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We describe four versions of a Greedy Randomized Adaptive Search Procedure (GRASP) for finding approximate solutions of general instances of the Steiner Problem in Graphs. Di#erent construction and local search algorithms are presented. Preliminary computational results with one of the versions on a variety of test problems are reported. On the majority of instances from the ORLibrary, a set of standard test problems, the GRASP produced optimal solutions. On those that optimal solutions were not found, the GRASP found good quality approximate solutions.
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 64 (6 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...
Greedy randomized adaptive search procedures. In: Handbook of applied optimization (Eds.
 P.M. Pardalos, M.G.C. Resende). Oxford Univ.
, 2002
"... ..."
Intermodal transportation
, 2005
"... This Chapter focuses on Intermodal Freight Transportation, broadly defined as the transportation of a load from its origin to its destination by a sequence of at least two transportation modes, the transfer from one mode to the next being performed at an intermodal terminal. Containerbased transpor ..."
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Cited by 34 (3 self)
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This Chapter focuses on Intermodal Freight Transportation, broadly defined as the transportation of a load from its origin to its destination by a sequence of at least two transportation modes, the transfer from one mode to the next being performed at an intermodal terminal. Containerbased transportation services are an important part of intermodal transportation and the backbone of international trade. This importance is reflected in this Chapter. We also examine issues related other intermodal systems or components, such as postal services, intermodal rail transportation, and seaport container terminals. Compared to several other application areas, Operations Research models and methods for intermodal freight transportation is still a very young domain. The goal of the chapter is thus to be informative and provide a starting point for future research, by providing an overview of the evolution of the field and presenting methodological developments proposed to address a number of important operations and planning issues: system and service design, container fleet management, planning of container terminal operations, and national planning. We focus on models. Algorithmic developments are indicated but not examined in any depth.
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 (7 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.
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 22 (3 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.
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 18 (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.
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 15 (1 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...
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 &g ..."
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Cited by 14 (6 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...