An Extension of the Min-Max Method for Approximate Solutions of Multiobjective Optimization Problems

It is a common characteristic of many multiobjective optimization problems that the efficient solution set can only be identified approximately. this study addresses scalarization techniques for solving multiobjective optimization problems. the min-max scalarization technique is considered, and efforts are made to overcome its weaknesses in studying approximate efficient solutions. to this end, two modifications of the min-max scalarization technique are proposed. first, an alternative form of the min-max method is introduced. additionally, by using slack and surplus variables in the constraints and penalizing violations in the objective function, we obtain easy-to-check conditions for approximate efficiency. the established theorems clarify the relationship between ε-(weakly and properly) efficient solutions of the multiobjective optimization problem and ϵ-optimal solutions of the proposed scalarized problems, without requiring any assumptions of convexity.