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Locating Objects in the Plane Using Global Optimization Techniques

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
rblanquero{at}us.es
ecarrizosa{at}us.es
pierre.hansen{at}gerad.ca

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
History: Received: April 4, 2008; revision received: March 2, 2009;