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

Abstract

???The wide variety of available interactive methods brings the need for creating general??? ???interactive algorithms enabling the decision maker (DM) to apply freely several convenient methods which best fit his/her preferences???. ???To this end???, ???in this paper???, ???we propose a general scalarizing problem for multiobjective programming problems???. ???The 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 discussed???. ???It is shown that some of the scalarizing problems used in different interactive 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 specify his/her preferences in six different ways with capability to change his/her preferences any time during the iterations of the algorithm???. ???Finally???, ???a numerical example demonstrating the applicability of the algorithm is provided???.