A combined scalarization method for multi-objective optimization problems

Yuan-mei Xia; Xin-min Yang; Ke-quan Zhao

doi:10.3934/jimo.2020088

Article Contents

2021, Volume 17, Issue 5: 2669-2683. Doi: 10.3934/jimo.2020088

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A combined scalarization method for multi-objective optimization problems

1.
Department of Mathematics, College of Sciences, Shanghai University, Shanghai 200444, China
2.
School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China

^* Corresponding author: Xin-min Yang
^* Corresponding author: Xin-min Yang

Received: September 30, 2019

Revised: December 31, 2019

Early access: April 2020

Published: September 2021

This research was partially supported by the major program of National Natural Science Foundation of China (No.11991024), the National Natural Science Foundation of China (Nos. 11971084, 11671062, 11771064), the Science Foundation of Chongqing (Nos. cstc2015jcyjA00027, cstc2017jcyj-yszxX0008, cstc2018jcyj-yszx0007) and the Open Project Funded by the Key Lab for OCME, School of Mathematical Sciences, Chongqing Normal University (CSSXKFKTQ201810)

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Abstract

In this paper, we propose a new combined scalarization method of multi-objective optimization problems by using the surplus variables and the generalized Tchebycheff norm and then use it to obtain some equivalent scalarization characterizations of (weakly, strictly, properly) efficient solutions by adjusting the range of parameters. These scalarization results do not need any convexity assumption conditions of objective functions. Furthermore, we establish some scalarization results of approximate solutions by means of the method. Moreover, we also present some examples to illustrate the main results.

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Mathematics Subject Classification: 90C26, 90C29, 90C30, 90C46.

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