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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.
Tabu Search: A Tutorial
 Interfaces
, 1990
"... Tabu search is a "higher level " heuristic procedure for solving optimization problems, designed to guide other methods (or their component processes) to escape the trap of local optimality. Tabu search has obtained optimal and near optimal solutions to a wide variety of classical and prac ..."
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Cited by 145 (2 self)
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Tabu search is a "higher level " heuristic procedure for solving optimization problems, designed to guide other methods (or their component processes) to escape the trap of local optimality. Tabu search has obtained optimal and near optimal solutions to a wide variety of classical and practical problems in applications ranging from scheduling to telecommunications and from character recognition to neural networks. It uses flexible structures memory (to permit search information to be exploited more thoroughly than by rigid memory systems or memoryless systems), conditions for strategically constraining and freeing the search process (embodied in tabu restrictions and aspiration criteria), and memory functions of varying time spans for intensifying and diversifying the search (reinforcing attributes historically found good and driving the search into new regions). Tabu search can be integrated with branchandbound and cutting plane procedures, and it has the ability to start with a simple implementation that can be upgraded over time to incorporate more advanced or specialized elements. T abu search is a metaheuristic that can to prevent them from becoming trapped at be superimposed on other procedures locally optimal solutions. The method can
The Quadratic Assignment Problem: A Survey and Recent Developments
 In Proceedings of the DIMACS Workshop on Quadratic Assignment Problems, volume 16 of DIMACS Series in Discrete Mathematics and Theoretical Computer Science
, 1994
"... . Quadratic Assignment Problems model many applications in diverse areas such as operations research, parallel and distributed computing, and combinatorial data analysis. In this paper we survey some of the most important techniques, applications, and methods regarding the quadratic assignment probl ..."
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Cited by 109 (16 self)
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. Quadratic Assignment Problems model many applications in diverse areas such as operations research, parallel and distributed computing, and combinatorial data analysis. In this paper we survey some of the most important techniques, applications, and methods regarding the quadratic assignment problem. We focus our attention on recent developments. 1. Introduction Given a set N = f1; 2; : : : ; ng and n \Theta n matrices F = (f ij ) and D = (d kl ), the quadratic assignment problem (QAP) can be stated as follows: min p2\Pi N n X i=1 n X j=1 f ij d p(i)p(j) + n X i=1 c ip(i) ; where \Pi N is the set of all permutations of N . One of the major applications of the QAP is in location theory where the matrix F = (f ij ) is the flow matrix, i.e. f ij is the flow of materials from facility i to facility j, and D = (d kl ) is the distance matrix, i.e. d kl represents the distance from location k to location l [62, 67, 137]. The cost of simultaneously assigning facility i to locat...
A Tabu Search Approach to Task Scheduling on Heterogeneous Processors under Precedence Constraints
, 1994
"... Parallel programs may be represented as a set of interrelated sequential tasks. When multiprocessors are used to execute such programs, the parallel portion of the application can be speeded up by an appropriate allocation of processors to the tasks of the application. Given a parallel application d ..."
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Cited by 45 (9 self)
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Parallel programs may be represented as a set of interrelated sequential tasks. When multiprocessors are used to execute such programs, the parallel portion of the application can be speeded up by an appropriate allocation of processors to the tasks of the application. Given a parallel application defined by a task precedence graph, the goal of task scheduling (or processor assignment) is thus the minimization of the makespan of the application. In a heterogeneous multiprocessor system, task scheduling consists in determining which tasks will be assigned to each processor, as well as the execution order of the tasks assigned to each processor. In this work, we apply the tabu search metaheuristic to the solution of the task scheduling problem on a heterogeneous multiprocessor environment under precedence constraints. The topology of the Mean Value Analysis solution package for product form queueing networks is used as the framework for performance evaluation. We show that tabu search ob...
Genetic algorithms and tabu search: hybrids for optimization
 Comput. Oper. Res
, 1995
"... Scope and Purpo~The development of hybrid procedures for optimization focuses on enhancing the strengths and compensating for the weaknesses of two or more complementary approaches. The goal is to intelligently combine the key elements of competing methodologies to create a superior solution proce ..."
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Cited by 39 (1 self)
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Scope and Purpo~The development of hybrid procedures for optimization focuses on enhancing the strengths and compensating for the weaknesses of two or more complementary approaches. The goal is to intelligently combine the key elements of competing methodologies to create a superior solution procedure. Our paper explores the marriage between tabu search and genetic algorithms in the context of solving difficult optimization problems. Among other ideas, the procedure known as scatter search is revisited to create a unifying environment where tabu search and genetic algorithms can coexist. Overall, our objective is to demonstrate that it is possible to establish useful connections between methods whose search principles may superficially appear unrelated. AbstractGenetic algorithms and tabu search have a number of significant differences. They also have some common bonds, often unrecognized. We explore the nature of the connections between the methods, and show that a variety of opportunities exist for creating hybrid approaches to take advantage of their complementary features. Tabu search has pioneered the systematic exploration of memory functions in search processes, while genetic algorithms have pioneered the implementation of methods that exploit the idea of combining solutions. There is also another approach, related to both of these, that is frequently overlooked. The procedure called scatter search, whose origins overlap with those of tabu search (and
Algorithms for Maximum Independent Set Applied to Map Labelling
, 2000
"... We consider the following map labelling problem: given distinct points p 1 , p 2 , . . . , p n in the plane, and given #, find a maximum cardinality set of pairwise disjoint axisparallel # # squares Q 1 , Q 2 , . . . , Q r . This problem reduces to that of finding a maximum cardinality indepe ..."
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Cited by 18 (0 self)
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We consider the following map labelling problem: given distinct points p 1 , p 2 , . . . , p n in the plane, and given #, find a maximum cardinality set of pairwise disjoint axisparallel # # squares Q 1 , Q 2 , . . . , Q r . This problem reduces to that of finding a maximum cardinality independent set in an associated graph called the conflict graph. We describe several heuristics for the maximum cardinality independent set problem, some of which use an LP solution as input. Also, we describe a branchandcut algorithm to solve it to optimality. The standard independent set formulation has an inequality for each edge in the conflict graph which ensures that only one of its endpoints can belong to an independent set. To obtain good starting points for our LPbased heuristics and good upper bounds on the optimal value for our branchandcut algorithm we replace this set of inequalities by the set of inequalities describing all maximal cliques in the conflict graph. For this streng...
Artificial intelligence, heuristic frameworks and tabu search
 Managerial & Decision Economics 11
, 1990
"... This paper examines some of the characteristics of Albased heuristic procedures that have emerged as frameworks for solving difficult optimization problems. Consideration of attributes shared to some degree by human prohlem solvers leads to focusing in greater detail on one of the moreituccessful ..."
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Cited by 15 (1 self)
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This paper examines some of the characteristics of Albased heuristic procedures that have emerged as frameworks for solving difficult optimization problems. Consideration of attributes shared to some degree by human prohlem solvers leads to focusing in greater detail on one of the moreituccessful procedures, tabu search, which employs a flexible memory system (in contrast to 'memoryless ^ systems, as in simulated annealing and genetic algorithms, and rigid memory systems as in branch and bound and A * search). Specific attention is given to the shortterm memory component of tahu search, which has provided solutions superior to the best obtained by other methods for a variety of problems. Our development emphasizes the principles underlying the interplay between restricting tbe searcb to avoid unproductive retracing of patbs (by tneans of tabu conditions) and freeing the search to explore otherwise forbidden avenues (by aspiration criteria). Finally, we discuss briefly the relevance of a supplementary framework, called target analysis, which is a method for determining good decision rules to enable heuristics to perform more effectively.
Tutorial on surrogate constraint approaches for optimization in graphs
 Journal of Heuristics
, 2003
"... Surrogate constraint methods have been embedded in a variety of mathematical programming applications over the past thirty years, yet their potential uses and underlying principles remain incompletely understood by a large segment of the optimization community. In a number of significant domains of ..."
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Cited by 11 (4 self)
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Surrogate constraint methods have been embedded in a variety of mathematical programming applications over the past thirty years, yet their potential uses and underlying principles remain incompletely understood by a large segment of the optimization community. In a number of significant domains of combinatorial optimization, researchers have produced solution strategies without recognizing that they can be derived as special instances of surrogate constraint methods. Once the connection to surrogate constraint ideas is exposed, additional ways to exploit this framework become visible, frequently offering opportunities for improvement. We provide a tutorial on surrogate constraint approaches for optimization in graphs, illustrating the key ideas by reference to independent set and graph coloring problems, including constructions for weighted independent sets which have applications to associated covering and weighted maximum clique problems. In these settings, the surrogate constraints can be generated relative to wellknown packing and covering formulations that are convenient for exposing key notions. The surrogate constraint approaches yield widely used heuristics for
Constructive Genetic Algorithm and Column Generation: an Application to Graph Coloring
, 2000
"... We present a combined use of Genetic Algorithms (GAs) and column generation to approximately solve graphcoloring problems. The proposed method is divided in two phases. The constructive phase builds the initial pool of columns using a Constructive Genetic Algorithm (CGA). Each column forms an in ..."
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Cited by 11 (2 self)
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We present a combined use of Genetic Algorithms (GAs) and column generation to approximately solve graphcoloring problems. The proposed method is divided in two phases. The constructive phase builds the initial pool of columns using a Constructive Genetic Algorithm (CGA). Each column forms an independent set. The second phase solves by column generation the set covering formulation. The columns are generated solving weighted independent set problems. Some computational experience is given.
Breakout local search for maximum clique problems
 Computers & Operations Research
"... The maximum clique problem (MCP) is one of the most popular combinatorial optimization problems with various practical applications. An important generalization of MCP is the maximum weight clique problem (MWCP) where a positive weight is associate to each vertex. In this paper, we present Breakout ..."
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Cited by 9 (8 self)
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The maximum clique problem (MCP) is one of the most popular combinatorial optimization problems with various practical applications. An important generalization of MCP is the maximum weight clique problem (MWCP) where a positive weight is associate to each vertex. In this paper, we present Breakout Local Search (BLS) which can be applied to both MC and MWC problems without any particular adaptation. BLS explores the search space by a joint use of local search and adaptive perturbation strategies. Extensive experimental evaluations using the DIMACS and BOSHLIB benchmarks show that the proposed approach competes favourably with the current stateofart heuristic methods for MCP. Moreover, it is able to provide some new improved results for a number of MWCP instances. This paper also reports for the first time a detailed landscape analysis, which has been missing in the literature. This analysis not only explains the difficulty of several benchmark instances, but also justifies to some extent the behaviour of the proposed approach and the used parameter settings.