A Revised Pascoletti–Serafini Scalarization Method for Multiobjective Optimization Problems

The presented study deals with the scalarization techniques for solving multiobjective optimization problems. The Pascoletti–Serafini scalarization technique is considered, and it is attempted to sidestep two weaknesses of this method, namely the inflexibility of the constraints and the difficulties of checking proper efficiency. To this end, two modifications for the Pascoletti–Serafini scalarization technique are proposed. First, by including surplus variables in the constraints and penalizing the violations in the objective function, the inflexibility of the constraints is resolved. Moreover, by including slack variables in the constraints, easy-to-check statements on proper efficiency are obtained. Thereafter, the two proposed modifications are combined to obtain the revised Pascoletti–Serafini scalarization method. Theorems are provided on the relation of (weakly, properly) efficient solutions of the multiobjective optimization problem and optimal solutions of the proposed scalarized problems. All the provided results are established with no convexity assumption. Moreover, the capability of the proposed approaches is demonstrated through numerical examples.