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Operations Research Transactions >

2025 , Vol. 29 >Issue 2: 175 - 183

DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2025.02.013

Research Article

Generalized Tchebycheff norm scalarization in multi-objective optimization

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  • 1. School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China

Received date: 2022-02-21

  Online published: 2025-06-12

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, 2025, All rights reserved. Unauthorized reproduction is prohibited.
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Abstract

Scalarization method is one of the basic research subjects for multi-objective optimization problems. In this paper, we first study the properties of generalized Tchebycheff norm, and obtain some strict monotonicity results on the non-negative quadrant. Furthermore, two kinds of scalarization results of weakly efficient solutions, efficient solutions, strictly efficient solutions and properly efficient solutions of multi-objective optimization problems are studied by using the properties of the generalized Tchebycheff norm. Moreover, we point out that under the assumption of convexity of the objective function, the scalarization studied in this paper is equivalent to the weighted scalarization.

Key words： multi-objective optimization; generalized Tchebycheff norm; strict monotonicity; scalarization; (weakly, strictly, properly) efficient solutions

Cite this article

Yuanmei XIA, Dandan XIA, Kequan ZHAO . Generalized Tchebycheff norm scalarization in multi-objective optimization[J]. Operations Research Transactions, 2025 , 29(2) : 175 -183 . DOI: 10.15960/j.cnki.issn.1007-6093.2025.02.013

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