An extension of the min-max method for approximate solutions of multi-objective optimization problems

Document Type : Research Paper

Authors

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

10.22128/gadm.2024.858.1117

Abstract

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.

Keywords


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Articles in Press, Accepted Manuscript
Available Online from 19 November 2024
  • Receive Date: 06 August 2024
  • Revise Date: 08 October 2024
  • Accept Date: 16 November 2024