Locating Objects in the Plane Using Global Optimization Techniques

We address the problem of locating objects in the plane such as segments, arcs of circumferences, arbitrary convex sets, their complements or their boundaries. Given a set of points, we seek the rotation and translation for such an object optimizing a very general performance measure, which includes...

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Bibliographic Details
Published in:Mathematics of operations research Vol. 34; no. 4; pp. 837 - 858
Main Authors: Blanquero, Rafael, Carrizosa, Emilio, Hansen, Pierre
Format: Journal Article
Language:English
Published: Linthicum INFORMS 01.11.2009
Institute for Operations Research and the Management Sciences
Subjects:
Algorithms
Analysis
Approximation
Branch & bound algorithms
Circumferences
computational metrology
DC optimization
Geometric planes
global optimization
location of objects
Location theory
Mathematical functions
Mathematical objects
Mathematical optimization
Mathematical sets
Objective functions
Optimization techniques
Studies
Vertices
United States
ISSN:0364-765X, 1526-5471
Online Access:Get full text
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Description
Summary:We address the problem of locating objects in the plane such as segments, arcs of circumferences, arbitrary convex sets, their complements or their boundaries. Given a set of points, we seek the rotation and translation for such an object optimizing a very general performance measure, which includes as a particular case the classical objectives in semi-obnoxious facility location. In general, the above-mentioned model yields a global optimization problem, whose resolution is dealt with using difference of convex (DC) techniques such as outer approximation or branch and bound.
Bibliography:ObjectType-Article-1
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ISSN:0364-765X
1526-5471
DOI:10.1287/moor.1090.0406