A box-uncertainty in multi-objective optimization: an ε-constraint approach

Subject Areas : Statistics

Shima Soleimani manesh ¹ , Mansour Saraj ² , Maryam Moemeni ³ , Mahmoud Alizadeh ⁴

1 - Department of mathematics, Islamic Azad University, Ahvaz branch, Ahvaz-Iran
2 - , Department of Mathematics , Faculty of Mathematical Sciences , and Computer, Shahid Chamran University of Ahvaz, , Ahvaz-IRAN
3 - Department of mathematics, Islamic Azad University, Ahvaz branch, Ahvaz-Iran
4 - Department of mathematics, Islamic Azad University, Ahvaz branch, Ahvaz-Iran

Received: 2020-11-09 Accepted : 2021-03-22 Published : 2022-06-22

Keywords: جواب کارای ضعیف استوار, برنامه‌ریزی کسری خطی چند هدفه, بهینه‌سازی استوار, عدم قطعیت جعبه‌ای, روش اپسیلون قید,

Abstract :

In the last few decades there has been lots of discussion in the literature regarding robust optimization. Since Epsilon constraint is one of the most important technique in interactive problems, therefore in this paper, due to the importance of robust optimization and multi-objective programming problems, we consider Multi-Objective Linear Fractional Programming (MOLFP) problem in the presence of box-uncertainty in the coefficients of the objective functions. We propose an approach based on ε-constraint and Charnes-Cooper methods to obtain weakly robust efficient solutions, that have special importance in the literature, for a MOLFP problems in the presence of uncertain data. Charnes-cooper method is applied to reduce a fractional programm to a non fractional programm. At the end we write the robust counterpart of the UMOLFP model in the presence of the box-uncertainty and it's equivalent linear programming problem: Finally a numerical example is used to show the usefulness of the proposed approach.

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