Multiobjective Programming with a Concave Vector Value Function

We consider the multiobjective optimization problem under certainty with partial information on the decision maker’s preferences structure by means of a vector value function with two components, which represents imprecision over his preferences. We introduce an approximation to the value efficient set which uses a vector value function with concave components on a convex feasible region. We propose an interactive algorithm to reduce the value efficient set and its approximation, based on information over the preferences revealed by the decision maker. Finally, a graphical example shows the method.