Abstarct: In this thesis, At first we introduce the efficient and weakly efficient solutions of a multiobjective optimization problem. Then, the scalarization method that is a method of solving multiobjective optimization problems, is expressed. In the following, with helping from geometric diuality theorem we show the correspondence between the primal and dual problems and using geometric duality theorem we express the Benson’s outer algorithm. The Benson’s algorithm outer find the Nondominated points of outcome set. After that, We explain The Benson’s algorithm dual and by applying changes on Benson’s algorithm dual we present approximation version of Benson’s algorithm dual. This algorithm by generating an outer approximation and inner approximation of Nondominated set, creates a set of ε-Nondominated points and we prove that the inner approximation is a set of ε-weakly Nondominated points. At the end, We describe the usage of algorithms in beam intensity optimization problems in Radiotherapy.