title: Calculating and controlling the error of discrete representations of Pareto surfaces in convex multi-criteria optimization.
abstract: A discrete set of points and their convex combinations can serve as a sparse representation of the Pareto surface in multiple objective convex optimization. We develop a method to evaluate the quality of such a representation, and show by example that in multiple objective radiotherapy planning, the number of Pareto optimal solutions needed to represent Pareto surfaces of up to five dimensions grows at most linearly with the number of objectives. The method described is also applicable to the representation of convex sets.
authors.affiliation: Department of Radiation Oncology, Massachusetts General Hospital and Harvard Medical School, Boston, MA 02114, USA. dcraft@partners.org
authors.forename: David
authors.initials: D
authors.lastname: Craft
mesh_terms: D006801:Humans; D008297:Male; D009369:Neoplasms / Q000532:radiotherapy; D011880:Radiotherapy Planning, Computer-Assisted / Q000379:methods*; D050397:Radiotherapy, Intensity-Modulated