重庆师范大学学报(自然科学版)2024,Vol.41Issue(2) :2-6.DOI:10.11721/cqnuj20240213

多目标优化问题统一解的加权Tchebycheff标量化

Weighted Tchebycheff Scalarization for Unified Solutions of Multi-Objective Optimization Problems

冯攀 夏远梅 赵克全
重庆师范大学学报(自然科学版)2024,Vol.41Issue(2) :2-6.DOI:10.11721/cqnuj20240213

多目标优化问题统一解的加权Tchebycheff标量化

Weighted Tchebycheff Scalarization for Unified Solutions of Multi-Objective Optimization Problems

冯攀 1夏远梅 1赵克全1
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作者信息

  • 1. 重庆师范大学数学科学学院,重庆 401331
  • 折叠

摘要

为研究多目标优化问题(C,ε)-型、E-型统一解的标量化性质,利用Bowman等人提出的加权Tchebycheff标量化方法建立多目标优化问题(C,ε)-弱有效解和E-弱有效解的标量化结果.进一步,建立基于加权Tchebycheff标量化方法多目标优化问题(C,ε)-有效解和E-有效解的标量化结果.通过调整标量化模型参数范围得到了多目标优化问题(C,ε)-(弱)有效解、E-(弱)有效解的一些加权Tchebycheff标量化结果,为求解多目标优化问题的算法设计提供了理论基础.

Abstract

The scalarization properties of(C,ε)-type and E-type unified solutions for multi-objective optimization problems are studied.First,the weighted Tchebycheff scalarization method proposed by Bowman et al.is employed to establish the scalarization results of(C,ε)-weakly efficient solutions and E-weakly efficient solutions for multi-objective optimization problems.Furthermore,based on the weighted Tchebycheff scalarization method,the scalarization results of(C,ε)-efficient solutions and E-efficient solutions for multi-objective optimization problems are established.Some weighted Tchebycheff scalarization results of(C,ε)-(weakly)efficient solutions and E-(weakly)efficient solutions for multi-objective optimization problems are obtained by adjusting parameters range of the scalarization model.The obtained scalarization results are an extension of some existing work and provide a theoretical basis for algorithm design for solving multi-objective optimization problems.

关键词

多目标优化问题/(C,ε)-(弱)有效解/E-(弱)有效解/加权Tchebycheff标量化方法

Key words

multi-objective optimization problems/(C,ε)-(weakly)efficient solutions/E-(weakly)efficient solutions/weighted Tchebycheff scalarization method

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基金项目

国家自然科学基金——重大项目(11991024)

国家自然科学基金——面上项目(12171063)

国家自然科学基金——青年科学基金项目(12101096)

重庆市高校创新研究群体项目(CXQT20014)

重庆市自然科学基金面上项目(cstc2022ycjhbgzxm0114)

重庆市自然科学基金面上项目(cstc2021jcyjmsxmX0280)

重庆市教育委员会科学技术研究青年项目(KJQN202100521)

出版年

2024
重庆师范大学学报(自然科学版)
重庆师范大学

重庆师范大学学报(自然科学版)

CSTPCD北大核心
影响因子:0.652
ISSN:1672-6693
参考文献量3
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