Locating Objects in the Plane Using Global Optimization Techniques

• 成果类型: Article
• 署名作者: Blanquero, Rafael; Carrizosa, Emilio; Hansen, Pierre
• 署名单位: University of Sevilla; Universite de Montreal; Universite de Montreal; HEC Montreal
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.1090.0406
• 发表日期: 2009
• 页码: 837-858
• 关键词: linear facility location; polygonal curves; approximation; set; hyperplanes; points; models; circle; distances; algorithm

摘要

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.