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Universal Facility Location
 in Proc. of ESA ’03
, 2003
"... In the Universal Facility Location problem we are given a set of demand points and a set of facilities. ..."
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In the Universal Facility Location problem we are given a set of demand points and a set of facilities.
Valid inequalities and facets of the capacitated plant location problem
 Mathematical Programming
, 1989
"... Recently, several successful applications of strong cutting plane methods to combinatorial optimization problems have renewed interest in cutting plane methods, and polyhedral characterizations, of integer programming problems. In this paper, we investigate the polyhedral structure of the capacitate ..."
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Cited by 9 (1 self)
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Recently, several successful applications of strong cutting plane methods to combinatorial optimization problems have renewed interest in cutting plane methods, and polyhedral characterizations, of integer programming problems. In this paper, we investigate the polyhedral structure of the capacitated plant location problem. Our purpose is to identify facets and valid inequalities for a wide range of capacitated fixed charge problems that contain this prototype problem as a substructure. The first part of the paper introduces a family of facets for a version of the capacitated plant location problem with constant capacity K for all plants. These facet inequalities depend on K and thus differ fundamentally from the valid inequalities for the uncapacitated version of the problem. We also introduce a second formulation for a model with indivisible customer demand and show that it is equivalent to a vertex packing problem on a derived graph. We identify facets and valid inequalities for this version of the problem by applying known results for the vertex packing polytope.
The pmedian problem: A survey of metaheuristic approaches
 European J Operational Research 179 927
, 2007
"... The pmedian problem, like most location problems, is classified as NPhard, and so, heuristic methods are usually used for solving it. The pmedian problem is a basic discrete location problem with real application that have been widely used to test heuristics. Metaheuristics are frameworks for bui ..."
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Cited by 6 (1 self)
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The pmedian problem, like most location problems, is classified as NPhard, and so, heuristic methods are usually used for solving it. The pmedian problem is a basic discrete location problem with real application that have been widely used to test heuristics. Metaheuristics are frameworks for building heuristics. In this survey, we examine the pmedian, with the aim of providing an overview on advances in solving it using recent procedures based on metaheuristic rules.
AFFINITY PROPAGATION: CLUSTERING DATA BY PASSING MESSAGES
, 2009
"... Clustering data by identifying a subset of representative examples is important for detecting patterns in data and in processing sensory signals. Such “exemplars ” can be found by randomly choosing an initial subset of data points as exemplars and then iteratively refining it, but this works well on ..."
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Clustering data by identifying a subset of representative examples is important for detecting patterns in data and in processing sensory signals. Such “exemplars ” can be found by randomly choosing an initial subset of data points as exemplars and then iteratively refining it, but this works well only if that initial choice is close to a good solution. This thesis describes a method called “affinity propagation ” that simultaneously considers all data points as potential exemplars, exchanging realvalued messages between data points until a highquality set of exemplars and corresponding clusters gradually emerges. Affinity propagation takes as input a set of pairwise similarities between data points and finds clusters on the basis of maximizing the total similarity between data points and their exemplars. Similarity can be simply defined as negative squared Euclidean distance for compatibility with other algorithms, or it can incorporate richer domainspecific models (e.g., translationinvariant distances for comparing images). Affinity propagation’s computational and memory requirements scale linearly with the number of similarities input; for nonsparse problems where all possible similarities are computed, these requirements scale quadratically with the number of data points. Affinity propagation is demonstrated on several applications