An interactive algorithm for solvingmultiobjective optimization problemsbased on a general scalarizationtechnique

The wide variety of available interactive methods brings the need for cre- ating general interactive algorithms enabling the decision maker (DM) to apply freely several convenient methods which best t his/her preference s. To this end, in this paper, we propose a general scalarizing problem for multi- objective programming problems. The relation between optimal solutions ofthe introduced scalarizing problem and (weakly) efficient as well as properly efficient solutions of the main multiobjective optimization problem (MOP) is discussed. It is shown that some of the scalarizing problems used in differentinteractive methods can be obtained from proposed formulation by selecting suitable transformations. Based on the suggested scalarizing problem, we propose a general interactive algorithm (GIA) that enables the DM to spec-ify his/her preferences in six different ways with capability to change his/her preferences any time during the iterations of the algorithm. Finally, a numer- ical example demonstrating the applicability of the algorithm is provided.

Keywords:

Multiobjective optimization , Interactive method , Scalarizingproblem , Proper efficiency , Preference information