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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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
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Abstract 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.
AbstractList 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.
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. [PUBLICATION ABSTRACT]
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. Key words: global optimization; DC optimization; location of objects; computational metrology MSC2000 subject classification: Primary: 90B85; secondary: 90C26 OR/MS subject classification: Primary: facilities/equipment planning, location/continuous; secondary: programming, nonlinear History: Received April 4, 2008; revised November 2, 2008, and March 2, 2009. Published online in Articles in Advance October 7, 2009. DOI 10.1287/moor.1090.0406
Audience Academic
Author Blanquero, Rafael
Carrizosa, Emilio
Hansen, Pierre
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Snippet We address the problem of locating objects in the plane such as segments, arcs of circumferences, arbitrary convex sets, their complements or their boundaries....
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SubjectTerms 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
Title Locating Objects in the Plane Using Global Optimization Techniques
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Volume 34
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