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Global Analysis and Discrete Mathematics، جلد ۸، شماره ۲، صفحات ۱۲۱-۱۳۲
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عنوان انگلیسی An extension of the min-max method for approximate solutions of multi-objective optimization problems
چکیده انگلیسی مقاله It is a common characteristic of many multiobjective optimization problems that the efficient solution set can only be identified approximately. This study addresses scalarization techniques for solving multiobjective optimization problems. The min-max scalarization technique is considered, and efforts are made to overcome its weaknesses in studying approximate efficient solutions. To this end, two modifications of the min-max scalarization technique are proposed. First, an alternative form of the min-max method is introduced. Additionally, by using slack and surplus variables in the constraints and penalizing violations in the objective function, we obtain easy-to-check conditions for approximate efficiency. The established theorems clarify the relationship between varepsilon-(weakly and properly) efficient solutions of the multiobjective optimization problem and epsilon-optimal solutions of the proposed scalarized problems, without requiring any assumptions of convexity.
کلیدواژه‌های انگلیسی مقاله multi-objective programming,scalarization,min-max method,approximate solutions
نویسندگان مقاله Hossein Salmei |
Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.

Mehran Namjoo |
Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.

نشانی اینترنتی https://ansne.du.ac.ir/article_441_9a55b2fbc1d9b5727be119bd114d9845.pdf
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