An interactive algorithm for solving multiobjective optimization problems based on a general scalarization technique

ýThe wide variety of available interactive methods brings the need for creating generalý ýinteractive algorithms enabling the decision maker (DM) to apply freely several convenient methods which best fit his/her preferencesý. ýTo this endý, ýin this paperý, ýwe propose a general scalarizing problem for multiobjective programming problemsý.
ýThe relation between optimal solutions of the introduced scalarizing problem and (weakly) efficient as well as properly efficient solutions of the main multiobjective optimization problem (MOP) is discussedý. ýIt is shown that some of the scalarizing problems used in different interactive methods can be obtained from proposed formulation by selecting suitable transformationsý. ýBased on the suggested scalarizing problemý, ýwe propose a general interactive algorithm (GIA) that enables the DM to specify his/her preferences in six different ways with capability to change his/her preferences any time during the iterations of the algorithmý.
ýFinallyý, ýa numerical example demonstrating the applicability of the algorithm is providedý.