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TABU SEARCH
"... Tabu Search is a metaheuristic that guides a local heuristic search procedure to explore the solution space beyond local optimality. One of the main components of tabu search is its use of adaptive memory, which creates a more flexible search behavior. Memory based strategies are therefore the hallm ..."
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Cited by 822 (48 self)
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Tabu Search is a metaheuristic that guides a local heuristic search procedure to explore the solution space beyond local optimality. One of the main components of tabu search is its use of adaptive memory, which creates a more flexible search behavior. Memory based strategies are therefore the hallmark of tabu search approaches, founded on a quest for "integrating principles, " by which alternative forms of memory are appropriately combined with effective strategies for exploiting them. In this chapter we address the problem of training multilayer feedforward neural networks. These networks have been widely used for both prediction and classification in many different areas. Although the most popular method for training these networks is backpropagation, other optimization methods such as tabu search have been applied to solve this problem. This chapter describes two training algorithms based on the tabu search. The experimentation shows that the procedures provide high quality solutions to the training problem, and in addition consume a reasonable computational effort.
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.
Combinatorial auctions: A survey
, 2000
"... Many auctions involve the sale of a variety of distinct assets. Examples are airport time slots, delivery routes and furniture. Because of complementarities (or substitution effects) between the different assets, bidders have preferences not just for particular items but for sets or bundles of items ..."
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Cited by 215 (1 self)
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Many auctions involve the sale of a variety of distinct assets. Examples are airport time slots, delivery routes and furniture. Because of complementarities (or substitution effects) between the different assets, bidders have preferences not just for particular items but for sets or bundles of items. For this reason, economic efficiency is enhanced if bidders are allowed to bid on bundles or combinations of different assets. This paper surveys the state of knowledge about the design of combinatorial auctions. Second, it uses this subject as a vehicle to convey the aspects of integer programming that are relevant for the
A genetic algorithm for the set covering problem.
 European Journal of Operational Research
, 1996
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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.
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...
GRASP and path relinking for 2layer straight line crossing minimization
 INFORMS Journal on Computing
, 1999
"... ABSTRACT — In this paper, we develop a greedy randomized adaptive search procedure (GRASP) for the problem of minimizing straightline crossings in a 2layer graph. The procedure is fast and is particularly appealing when dealing with lowdensity graphs. When a modest increase in computational time ..."
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Cited by 100 (19 self)
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ABSTRACT — In this paper, we develop a greedy randomized adaptive search procedure (GRASP) for the problem of minimizing straightline crossings in a 2layer graph. The procedure is fast and is particularly appealing when dealing with lowdensity graphs. When a modest increase in computational time is allowed, the procedure may be coupled with a path relinking strategy to search for improved outcomes. Although the principles of path relinking have appeared in the tabu search literature, this search strategy has not been fully implemented and tested. We perform extensive computational experiments with more than 3,000 graph instances to first study the effect of changes in critical search parameters and then to compare the efficiency of alternative solution procedures. Our results indicate that graph density is a major influential factor on the performance of a solution procedure. Laguna and Martí / 2 The problem of minimizing straightline crossings in layered graphs has been the subject of study for at least 17 years, beginning with the Relative Degree Algorithm introduced by Carpano [2]. The problem consists of aligning the two shores V1 and V2 of a bipartite graph G = (V1, V2, E) on two parallel straight lines (layers) such that the number of crossing between the edges in E is minimized
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...
Probability distribution of solution time in GRASP: An experimental investigation
 J HEURISTIC
, 2000
"... A GRASP (greedy randomized adaptive search procedure) is a multistart metaheuristic for combinatorial optimization. We study the probability distributions of solution time to a suboptimal target value in five GRASPs that have appeared in the literature and for which source code is available. The ..."
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Cited by 60 (29 self)
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A GRASP (greedy randomized adaptive search procedure) is a multistart metaheuristic for combinatorial optimization. We study the probability distributions of solution time to a suboptimal target value in five GRASPs that have appeared in the literature and for which source code is available. The distributions are estimated by running 12,000 independent runs of the heuristic. Standard methodology for graphical analysis is used to compare the empirical and theoretical distributions and estimate the parameters of the distributions. We conclude that the solution time to a suboptimal target value fits a twoparameter exponential distribution. Hence, it is possible to approximately achieve linear speedup by implementing GRASP in parallel.