Multiobjective approaches based on variable ordering structures for intensity problems in radiotherapy treatment / Le Thanh Tam

Abstract

Recently, in many papers Intensity Modulated Radiotherapy Treatment problems are studied as multicriteria optimization problems with respect to a constant ordering cone. In these problems, the goal is to maximize the dose delivered to cancer tumor as well as to reduce side effects. However, from a practical perspective, it is more convenient to consider such problems with respect to a variable ordering structure. In this paper, we introduce a special cone-valued mapping based on the goal of cancer treatment. We consider a mathematical formulation of intensity problems equipped with this ordering structure. In addition, we derive necessary conditions for solutions of a vector-valued approximation problem with respect to a general ordering cone. Finally, we calculate in detail necessary conditions for minimal solutions of the intensity problem in radiotherapy treatment.