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

Iranian Journal of Numerical Analysis and Optimization

مقاله 5، دوره 6، شماره 1 - شماره پیاپی 9، اردیبهشت 2016، صفحه 79-101   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.v6i1.44631

نویسندگان

m. Ghaznavi^{* 1}؛ M. Ilati²؛ E. Khorram²

¹Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran.

²Faculty of Mathematics and Computer Science, Amirkabir University of Technology, 424, Hafez Avenue, 15914 Tehran, Iran.

چکیده

‎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.

کلیدواژه‌ها

Multiobjective optimization؛ Interactive method؛ Scalarizing problem؛ Proper efficiency؛ Preference information

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