MULTIOBJECTIVE APPROACHES BASED ON VARIABLE ORDERING STRUCTURES FOR INTENSITY PROBLEMS IN RADIOTHERAPY TREATMENT

Abstract

Recently, in many papers intensity modulated radiotherapy treatment problems are studied as multi- criteria 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 an appropriate cone-valued mapping based on the goal of cancer treatment. We consider a mathematical formulation of beam intensity optimization equipped with this ordering structure. In addition, we investigate necessary optimality conditions for solutions of a vector-valued approximation problem with respect to a general ordering cone and the proposed variable ordering structure as well. Finally, we calculate in detail necessary optimality conditions for solutions of the mathematical model of beam intensity optimization in radiotherapy treatment