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A Comparison of Memetic Algorithms, Tabu Search, and Ant Colonies for the Quadratic Assignment Problem
 Proc. Congress on Evolutionary Computation, IEEE
, 1999
"... A memetic algorithm (MA), i.e. an evolutionary algorithm making use of local search, for the quadratic assignment problem is presented. A new recombination operator for realizing the approach is described, and the behavior of the MA is investigated on a set of problem instances containing between 25 ..."
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Cited by 36 (4 self)
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A memetic algorithm (MA), i.e. an evolutionary algorithm making use of local search, for the quadratic assignment problem is presented. A new recombination operator for realizing the approach is described, and the behavior of the MA is investigated on a set of problem instances containing between 25 and 100 facilities/locations. The results indicate that the proposed MA is able to produce high quality solutions quickly. A comparison of the MA with some of the currently best alternative approaches  reactive tabu search, robust tabu search and the fast ant colony system  demonstrates that the MA outperforms its competitors on all studied problem instances of practical interest. 1 Introduction The problem of assigning a set of facilities (with given flows between them) to a set of locations (with given distances between them) in such a way that the sum of the product between flows and distances is minimized is known as the facilities location problem [1] or the quadratic assignment ...
A Unifying Objective Function for Topographic Mappings
, 1997
"... Many different algorithms and objective functions for topographic mappings have been proposed. We show that several of these approaches can be seen as particular cases of a more general objective function. Consideration of a very simple mapping problem reveals large differences in the form of the ma ..."
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Cited by 34 (4 self)
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Many different algorithms and objective functions for topographic mappings have been proposed. We show that several of these approaches can be seen as particular cases of a more general objective function. Consideration of a very simple mapping problem reveals large differences in the form of the map that each particular case favors. These differences have important consequences for the practical application of topographic mapping methods.
Nonlinear integer programming
 DISC. OPTIM
, 2009
"... Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reached when one considers nonlinear systems subject to integrality requirements for the variables. This chapt ..."
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Cited by 33 (10 self)
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Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reached when one considers nonlinear systems subject to integrality requirements for the variables. This chapter is dedicated to this topic. The primary goal is a study of a simple version of general nonlinear integer problems, where all constraints are still linear. Our focus is on the computational complexity of the problem, which varies significantly with the type of nonlinear objective function in combination with the underlying combinatorial structure. Numerous boundary cases of complexity emerge, which sometimes surprisingly lead even to polynomial time algorithms. We also cover recent successful approaches for more general classes of problems. Though no positive theoretical efficiency results are available, nor are they likely to ever be available, these seem to be the currently most successful and interesting approaches for solving practical problems. It is our belief that the study of algorithms motivated by theoretical considerations
Hierarchical Aligned Cluster Analysis for Temporal Clustering of Human Motion
, 2013
"... Temporal segmentation of human motion into plausible motion primitives is central to understanding and building computational models of human motion. Several issues contribute to the challenge of discovering motion primitives: the exponential nature of all possible movement combinations, the variab ..."
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Cited by 31 (2 self)
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Temporal segmentation of human motion into plausible motion primitives is central to understanding and building computational models of human motion. Several issues contribute to the challenge of discovering motion primitives: the exponential nature of all possible movement combinations, the variability in the temporal scale of human actions, and the complexity of representing articulated motion. We pose the problem of learning motion primitives as a temporal clustering one, and derive an unsupervised hierarchical bottomup framework called hierarchical aligned cluster analysis (HACA). HACA finds a partition of a given multidimensional time series into m disjoint segments such that each segment belongs to one of k clusters. HACA combines kernel kmeans with the generalized dynamic time alignment kernel to cluster time series data. Moreover, it provides a natural framework to find a lowdimensional embedding for the time series. HACA is efficiently optimized with a coordinate descent strategy and dynamic programming. Experimental results on motion capture and video data demonstrate the effectiveness of HACA for segmenting complex motions and as a visualization tool. We also compare the performance of HACA to stateoftheart algorithms for temporal clustering on data of a honey bee dance. The HACA code is available online.
Multilevel Mesh Partitioning for Heterogeneous Communication Networks
 Future Generation Comput. Syst
, 2001
"... Multilevel algorithms are a successful class of optimisation techniques which address the mesh partitioning problem for distributing unstructured meshes onto parallel computers. They usually combine a graph contraction algorithm together with a local optimisation method which refines the partition a ..."
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Cited by 31 (9 self)
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Multilevel algorithms are a successful class of optimisation techniques which address the mesh partitioning problem for distributing unstructured meshes onto parallel computers. They usually combine a graph contraction algorithm together with a local optimisation method which refines the partition at each graph level. To date these algorithms have been used almost exclusively to minimise the cut edge weight in the graph with the aim of minimising the parallel communication overhead, but recently there has been a perceived need to take into account the communications network of the parallel machine. For example the increasing use of SMP clusters (systems of multiprocessor compute nodes with very fast intranode communications but relatively slow internode networks) suggest the use of hierarchical network models. Indeed this requirement is exacerbated in the early experiments with metacomputers (multiple supercomputers combined together, in extreme cases over intercontinental networks). In this paper therefore, we modify a multilevel algorithm in order to minimise a cost function based on a model of the communications network. Several network models and variants of the algorithm are tested and we establish that it is possible to successfully guide the optimisation to reflect the chosen architecture. 2001 Elsevier Science B.V. All rights reserved.
A BranchandBound Algorithm for the Quadratic Assignment Problem Based on the Hungarian Method
 European Journal of Operational Research
, 1996
"... This paper presents a new branchandbound algorithm for solving the Quadratic Assignment Problem (QAP). The algorithm is based on a Dual Procedure (DP) similar to the Hungarian method for solving the Linear Assignment Problem. Our DP solves the QAP in certain cases, i.e., for some small problems (N ..."
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Cited by 29 (5 self)
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This paper presents a new branchandbound algorithm for solving the Quadratic Assignment Problem (QAP). The algorithm is based on a Dual Procedure (DP) similar to the Hungarian method for solving the Linear Assignment Problem. Our DP solves the QAP in certain cases, i.e., for some small problems (N<7) and for numerous larger problems (7N16) that arise as subproblems of a larger QAP such as the Nugent 20. The DP, however, does not guarantee a solution. It is used in our algorithm to calculate lower bounds on solutions to the QAP. As a result of a number of recently developed improvements, the DP produces lower bounds that are as tight as any which might be useful in a branchandbound algorithm. These are produced relatively cheaply, especially on larger problems. Experimental results show that the computational complexity of our algorithm is lower than known methods, and that its actual runtime is significantly shorter than the best known algorithms for QAPLIB test instances of size 16 through 22. Our method has the potential for being improved and therefore can be expected to aid in solving even larger problems. Keywords Quadratic Assignment Problem, Branchandbound, Quadratic Programming, Integer Programming, Mathematical Programming. 2 1.
Quantifying Neighbourhood Preservation in Topographic Mappings
, 1996
"... Mappings that preserve neighbourhood relationships are important in many contexts, from neurobiology to multivariate data analysis. It is important to be clear about precisely what is meant by preserving neighbourhoods. At least three issues have to be addressed: how neighbourhoods are defined, how ..."
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Cited by 27 (5 self)
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Mappings that preserve neighbourhood relationships are important in many contexts, from neurobiology to multivariate data analysis. It is important to be clear about precisely what is meant by preserving neighbourhoods. At least three issues have to be addressed: how neighbourhoods are defined, how a perfectly neighbourhood preserving mapping is defined, and how an objective function for measuring discrepancies from perfect neighbourhood preservation is defined. We review several standard methods, and using a simple example mapping problem show that the different assumptionsof each lead to nontrivially different answers. We also introduce a particular measure for topographic distortion, which has the form of a quadratic assignmentproblem. Many previous methods are closely related to this measure, which thus serves to unify disparate approaches. 1 Introduction Problems of mapping occur frequently both in understanding biological processes and in formulating abstract methods of data an...
Solving Quadratic Assignment Problems Using Convex Quadratic Programming Relaxations
, 2000
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Topology Design for Service Overlay Networks With Bandwidth Guarantees
 IEEE IWQoS
, 2004
"... The Internet still lacks adequate support for QoS applications with realtime requirements. In great part, this is due to the fact that provisioning of endtoend QoS to traffic that traverses multiple autonomous systems (ASs) requires a level of cooperation between ASs that is difficult to achieve ..."
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Cited by 21 (0 self)
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The Internet still lacks adequate support for QoS applications with realtime requirements. In great part, this is due to the fact that provisioning of endtoend QoS to traffic that traverses multiple autonomous systems (ASs) requires a level of cooperation between ASs that is difficult to achieve in the current architecture. Recently, service overlay networks have been considered as an approach to QoS deployment that avoids these difficulties. In this study, we address the problem of the topological synthesis of a service overlay network, where endsystems and nodes of the overlay network (provider nodes) are connected through ISPs that supports bandwidth reservations. We express the topology design problem as an optimization problem. Even though the design problem is related to the (in general NPhard) quadratic assignment problem, we are able to show that relatively simple heuristic algorithms can deliver results that are sometimes close to the optimal solution.
An Analysis of Spectral Envelope Reduction via Quadratic Assignment Problems
 SIAM J. Matrix Anal. Appl
, 1994
"... . A new spectral algorithm for reordering a sparse symmetric matrix to reduce its envelope size was described in [2]. The ordering is computed by associating a Laplacian matrix with the given matrix and then sorting the components of a specified eigenvector of the Laplacian. In this paper we provide ..."
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Cited by 18 (0 self)
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. A new spectral algorithm for reordering a sparse symmetric matrix to reduce its envelope size was described in [2]. The ordering is computed by associating a Laplacian matrix with the given matrix and then sorting the components of a specified eigenvector of the Laplacian. In this paper we provide an analysis of the spectral envelope reduction algorithm. We describe related 1 and 2sum problems; the former is related to the envelope size, while the latter is related to an upper bound on the work in an envelope Cholesky factorization. We formulate the latter two problems as quadratic assignment problems, and then study the 2sum problem in more detail. We obtain lower bounds on the 2sum by considering a relaxation of the problem, and then show that the spectral ordering finds a permutation matrix closest to an orthogonal matrix attaining the lower bound. This provides stronger justification of the spectral envelope reduction algorithm than previously known. The lower bound on the 2...