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 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
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Linthicum
INFORMS
01.11.2009
Institute for Operations Research and the Management Sciences |
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| 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. |
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| 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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| 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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