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Very LargeScale Neighborhood Search for the Quadratic Assignment Problem
 DISCRETE APPLIED MATHEMATICS
, 2002
"... The Quadratic Assignment Problem (QAP) consists of assigning n facilities to n locations so as to minimize the total weighted cost of interactions between facilities. The QAP arises in many diverse settings, is known to be NPhard, and can be solved to optimality only for fairly small size instances ..."
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Cited by 146 (14 self)
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The Quadratic Assignment Problem (QAP) consists of assigning n facilities to n locations so as to minimize the total weighted cost of interactions between facilities. The QAP arises in many diverse settings, is known to be NPhard, and can be solved to optimality only for fairly small size instances (typically, n < 25). Neighborhood search algorithms are the most popular heuristic algorithms to solve larger size instances of the QAP. The most extensively used neighborhood structure for the QAP is the 2exchange neighborhood. This neighborhood is obtained by swapping the locations of two facilities and thus has size O(n²). Previous efforts to explore larger size neighborhoods (such as 3exchange or 4exchange neighborhoods) were not very successful, as it took too long to evaluate the larger set of neighbors. In this paper, we propose very largescale neighborhood (VLSN) search algorithms where the size of the neighborhood is very large and we propose a novel search procedure to heuristically enumerate good neighbors. Our search procedure relies on the concept of improvement graph which allows us to evaluate neighbors much faster than the existing methods. We present extensive computational results of our algorithms on standard benchmark instances. These investigations reveal that very largescale neighborhood search algorithms give consistently better solutions compared the popular 2exchange neighborhood algorithms considering both the solution time and solution accuracy.
Semidefinite Programming and Combinatorial Optimization
 DOC. MATH. J. DMV
, 1998
"... We describe a few applications of semide nite programming in combinatorial optimization. ..."
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Cited by 111 (1 self)
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We describe a few applications of semide nite programming in combinatorial optimization.
Handbook of semidefinite programming
"... Semidefinite programming (or SDP) has been one of the most exciting and active research areas in optimization during the 1990s. It has attracted researchers with very diverse backgrounds, including experts in convex programming, linear algebra, numerical optimization, combinatorial optimization, con ..."
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Cited by 84 (2 self)
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Semidefinite programming (or SDP) has been one of the most exciting and active research areas in optimization during the 1990s. It has attracted researchers with very diverse backgrounds, including experts in convex programming, linear algebra, numerical optimization, combinatorial optimization, control theory, and statistics. This tremendous research activity was spurred by the discovery of important applications in combinatorial optimization and control theory, the development of efficient interiorpoint algorithms for solving SDP problems, and the depth and elegance of the underlying optimization theory. This book includes nineteen chapters on the theory, algorithms, and applications of semidefinite programming. Written by the leading experts on the subject, it offers an advanced and broad overview of the current state of the field. The coverage is somewhat less comprehensive, and the overall level more advanced, than we had planned at the start of the project. In order to finish the book in a timely fashion, we have had to abandon hopes for separate chapters on some important topics (such as a discussion of SDP algorithms in the
An Enabling Framework for MasterWorker Applications on the Computational Grid
 Cluster Computing
, 2000
"... We describe MW  a software framework that allows users to quickly and easily parallelize scientific computations using the masterworker paradigm on the computational grid. MW provides both a "top level" interface to application software and a "bottom level" interface to exi ..."
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Cited by 82 (10 self)
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We describe MW  a software framework that allows users to quickly and easily parallelize scientific computations using the masterworker paradigm on the computational grid. MW provides both a "top level" interface to application software and a "bottom level" interface to existing grid computing toolkits. Both interfaces are briefly described. We conclude with a case study, where the necessary Grid services are provided by the Condor highthroughput computing system, and the MWenabled application code is used to solve a combinatorial optimization problem of unprecedented complexity. This work was supported in part by Grants No. CDA9726385 and CDA9623632 from the National Science Foundation. y Department of Electrical and Computer Engineering, Northwestern University, and Mathematics and Computer Science Division, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, Illinois 60439, goux@mcs.anl.gov z Computer Sciences Department, University of Wisconsin  Madison, 1210 West Dayton Street, Madison, WI 53706, fsanjeevk,yodermeg@cs.wisc.edu x Mathematics and Computer Science Division, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, Illinois 60439, linderot@mcs.anl.gov 1 1
Functional Maps: A Flexible Representation of Maps Between Shapes
"... Figure 1: Horse algebra: the functional representation and map inference algorithm allow us to go beyond pointtopoint maps. The source shape (top left corner) was mapped to the target shape (left) by posing descriptorbased functional constraints which do not disambiguate symmetries (i.e. without ..."
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Cited by 50 (12 self)
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Figure 1: Horse algebra: the functional representation and map inference algorithm allow us to go beyond pointtopoint maps. The source shape (top left corner) was mapped to the target shape (left) by posing descriptorbased functional constraints which do not disambiguate symmetries (i.e. without landmark constraints). By further adding correspondence constraints, we obtain a near isometric map which reverses orientation, mapping left to right (center). The representation allows for algebraic operations on shape maps, so we can subtract this map from the ambivalent map, to retrieve the orientation preserving nearisometry (right). Each column shows the first 20x20 block of the functional map representation (bottom), and the action of the map by transferring colors from the source shape to the target shape (top). We present a novel representation of maps between pairs of shapes that allows for efficient inference and manipulation. Key to our approach is a generalization of the notion of map that puts in correspondence realvalued functions rather than points on the shapes. By choosing a multiscale basis for the function space on each shape, such as the eigenfunctions of its LaplaceBeltrami operator, we obtain a representation of a map that is very compact, yet fully suitable for global inference. Perhaps more remarkably, most
Frequency Assignment Problems
 HANDBOOK OF COMBINATORIAL OPTIMIZATION
, 1999
"... The ever growing number of wireless communications systems deployed around the globe have made the optimal assignment of a limited radio frequency spectrum a problem of primary importance. At issue are planning models for permanent spectrum allocation, licensing, regulation, and network design. Furt ..."
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Cited by 41 (3 self)
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The ever growing number of wireless communications systems deployed around the globe have made the optimal assignment of a limited radio frequency spectrum a problem of primary importance. At issue are planning models for permanent spectrum allocation, licensing, regulation, and network design. Further at issue are online algorithms for dynamically assigning frequencies to users within an established network. Applications include aeronautical mobile, land mobile, maritime mobile, broadcast, land fixed (pointto point), and satellite systems. This paper surveys research conducted by theoreticians, engineers, and computer scientists regarding the frequency assignment problem (FAP) in all of its guises. The paper begins by defining some of the more common types of FAPs. It continues with a discussion on measures of optimality relating to the use of spectrum, models of interference, and mathematical representations of the many FAPs, both in graph theoretic terms, and as mathematical pro...
Copositive and semidefinite relaxations of the quadratic assignment problem
 DISCRETE OPTIM
, 2009
"... Semidefinite relaxations of the quadratic assignment problem (QAP) have recently turned out to provide good approximations to the optimal value of QAP. We take a systematic look at various conic relaxations of QAP. We first show that QAP can equivalently be formulated as a linear program over the co ..."
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Cited by 31 (3 self)
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Semidefinite relaxations of the quadratic assignment problem (QAP) have recently turned out to provide good approximations to the optimal value of QAP. We take a systematic look at various conic relaxations of QAP. We first show that QAP can equivalently be formulated as a linear program over the cone of completely positive matrices. Since it is hard to optimize over this cone, we also look at tractable approximations and compare with several relaxations from the literature. We show that several of the wellstudied models are in fact equivalent. It is still a challenging task to solve the strongest of these models to reasonable accuracy on instances of moderate size.
MultiStart Tabu Search and Diversification Strategies for the Quadratic Assignment Problem
, 2006
"... The quadratic assignment problem (QAP) is a well known combinatorial optimization problem most commonly used to model the facilitylocation problem. The widely acknowledged difficulty of the QAP has made it the focus of many metaheuristic solution approaches. In this study, we introduce several mul ..."
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Cited by 15 (1 self)
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The quadratic assignment problem (QAP) is a well known combinatorial optimization problem most commonly used to model the facilitylocation problem. The widely acknowledged difficulty of the QAP has made it the focus of many metaheuristic solution approaches. In this study, we introduce several multistart tabu search variants and show the benefit of utilizing strategic diversification within the tabu search framework for the QAP. Computational results for a set of problems obtained from QAPLIB demonstrate the ability of our TS multistart variants to improve on the classic tabu search approach that is one of the principal and most widely used methods for the QAP. We also show that our new procedures are highly competitive with the best recently introduced methods from the literature, including more complex hybrid approaches that incorporate a classic tabu search method as a subroutine.