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.

Keywords

• multiobjective optimization
• interactive method
• scalarizing problem
• proper efficiency
• preference information