Improved ε-constraint method for multiobjective programming

In this paper, we revisit one of the most important scalarization techniques used in multiobjective programming, the epsilon-constraint method. We summarize the method and point out some weaknesses, namely the lack of easy-to-check conditions for properly efficient solutions and the inflexibility of the constraints. We present two modifications that address these weaknesses by first including slack variables in the formulation and second elasticizing the constraints and including surplus variables. We prove results on (weakly, properly) efficient solutions. The improved epsilon-constraint method that we propose combines both modifications.