A combined scalarizing method for multiobjective programming problems

In this paper, a new general scalarization technique for solving multiobjective optimization problems is presented. After studying the properties of this formulation, two problems as special cases of this general formula are considered. It is shown that some well-known methods such as the weighted sum method, the ∊-constraint method, the Benson method, the hybrid method and the elastic ∊-constraint method can be subsumed under these two problems. Then, considering approximate solutions, some relationships between ε-(weakly, properly) efficient points of a general (without any convexity assumption) multiobjective optimization problem and ∊-optimal solutions of the introduced scalarized problem are achieved.