Competitive Facility Location in the Plane

Drezner, Tammy

doi:10.1007/978-1-4612-5355-6_14

Cited by 113 publications

(78 citation statements)

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“…the category points of one or even all the variables) and then in the case of a ¡ ¢ ¢ -like loss function find the the locations of the remaining points by calculating their multivariate medians (by solving the corresponding Weber problems). This goes towards the direction of facility location problems [5], which may provide interesting alternatives in visualizing categorical multivariate data. The resulting graph layout of the sleeping bags data set with the category points located on a square and the object points corresponding to the multivariate medians (Weber points) of the categories they belong to is shown in Figure 7 Figure 7, the patterns in the data are such that they give rise to a planar layout (edges do not intersect).…”

Section: The Structure Of the Optimal Solutionmentioning

confidence: 99%

Homogeneity analysis using absolute deviations

Michailidis

Leeuw

2005

Computational Statistics & Data Analysis

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ABSTRACT. Homogeneity analysis is a technique for making graphical representations of categorical multivariate data sets. Such data sets can also be represented by the adjacency matrix of a bipartite graph. Homogeneity analysis optimizes a weighted least squares criterion and the optimal graph drawing is computed by an alternating least squares algorithm. Heiser (1987) looked at homogeneity analysis under a weighted least absolute deviations criterion. In this paper, we take a closer look at the mathematical structure of this problem and show that the graph drawings are created by reciprocal computation of multivariate medians. Several algorithms for computing the solution are investigated and applications to actual data suggest that the resulting -dimensional drawings ¡ ¢ £ ¤ are degenerate, in the sense that all object points are clustered in ¥ ¦locations. We also examine some variations of the criterion used and conclude that the generate solutions observed are a consequence of the normalization constraint employed in this class of problems.

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Section: The Structure Of the Optimal Solutionmentioning

confidence: 99%

Homogeneity analysis using absolute deviations

Michailidis

Leeuw

2005

Computational Statistics & Data Analysis

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“…The unweighted and uncapacitated p-median problem is N P-hard [17]. Extensive references to works on this and related problems are contained in the main books, surveys and reviews in Location like [3,2,22,7].…”

Section: Algorithm Cnvnsmentioning

confidence: 99%

Parallel Variable Neighborhood Search

Moreno-Pérez

Hansen

Mladenović

2005

Parallel Metaheuristics

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Les textes publiés dans la série des rapports de recherche HEC n'engagent que la responsabilité de leurs auteurs. La publication de ces rapports de recherche bénéficie d'une subvention du Fonds québécois de la recherche sur la nature et les technologies. AbstractVariable Neighborhood Search (VNS) is a recent and effective metaheuristic for solving combinatorial and global optimization problems. It is capable of escaping from the local optima by systematic changes of the neighborhood structures within the search. In this paper several parallelization strategies for VNS have been proposed and compared on the large instances of the p-median problem. RésuméLa Rechercheà Voisinage Variable (RVV) est une métaheuristique récente et efficace pour la résolution de problèmes d'optimisation combinatoire ou globale. Elle permet de quitter un optimum local par des changements systématiques de structures de voisinageà l'intérieur de la recherche. Pour cet article plusieurs stratégies de parallélisation de RVV sont proposées et composées sur de grandes instances de problème de la p-médiane.

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“…The facility location problem and many of its variants are studied [5], [6]. In the basic facility location problem we are given (1) a set C of customers, (2) a set F of facilities, (3) an opening cost op( f ) for each f ∈ F, and (4) a connecting cost co(c, f ) for each c ∈ C and f ∈ F, then we open a subset F ⊆ F of facilities and find an assignment A of C to F such that a designated cost is minimized.…”

Section: Introductionmentioning

confidence: 99%

On <i>r</i>-Gatherings on the Line

Akagi

Nakano

2017

IEICE Trans. Inf. & Syst.

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SUMMARYIn this paper we study a recently proposed variant of the facility location problem, called the r-gathering problem. Given an integer r, a set C of customers, a set F of facilities, and a connecting cost co(c, f ) for each pair of c ∈ C and f ∈ F, an r-gathering of customers C to facilities F is an assignment A of C to open facilities F ⊆ F such that at least r customers are assigned to each open facility. We give an algorithm to find an r-gathering with the minimum cost, where the cost is max c∈C {co(c, A(c))}, when all C and F are on the real line.

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Competitive Facility Location in the Plane

Cited by 113 publications

References 0 publications

Homogeneity analysis using absolute deviations

Homogeneity analysis using absolute deviations

Parallel Variable Neighborhood Search

On <i>r</i>-Gatherings on the Line

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