Locating Objects in the Plane Using Global Optimization Techniques

Authors:
Rafael Blanquero;Emilio Carrizosa;Pierre Hansen
Affiliations:
Facultad de Matemáticas, Universidad de Sevilla, 41012 Sevilla, Spain;Facultad de Matemáticas, Universidad de Sevilla, 41012 Sevilla, Spain;GERAD and HEC Montréal, Montréal, Québec H3T 2A7, Canada
Venue:
Mathematics of Operations Research
Year:
2009

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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.