A global optimization procedure for the location of a median line in the three-dimensional space

A global optimization procedure is proposed to find a line in the Euclidean three-dimensional space which minimizes the sum of distances to a given finite set of three-dimensional data points. Although we are using similar techniques as for location problems in two dimensions, it is shown that the p...

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Bibliographic Details
Authors: Blanquero Bravo, Rafael, Carrizosa Priego, Emilio José, Schöbel, Anita, Scholz, Daniel
Format: article
Status:Published version
Publication Date:2011
Country:España
Institution:Universidad de Sevilla (US)
Repository:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/107475
Online Access:https://hdl.handle.net/11441/107475
https://doi.org/10.1016/j.ejor.2011.05.030
Access Level:Open access
Keyword:Geometric branch-and-bound methods
Global optimization
Line location
Description
Summary:A global optimization procedure is proposed to find a line in the Euclidean three-dimensional space which minimizes the sum of distances to a given finite set of three-dimensional data points. Although we are using similar techniques as for location problems in two dimensions, it is shown that the problem becomes much harder to solve. However, a problem parameterization as well as lower bounds are suggested whereby we succeeded in solving medium-size instances in a reasonable amount of computing time.