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

作　　者：冯攀 夏远梅 赵克全 FENG Pan;XIA Yuanmei;ZHAO Kequan(School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《重庆师范大学学报（自然科学版）》2024年第2期2-6,共5页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金——重大项目(No.11991024),面上项目(No.12171063),青年科学基金项目(No.12101096);重庆市高校创新研究群体项目(No.CXQT20014);重庆市自然科学基金面上项目(No.cstc2022ycjh-bgzxm0114,No.cstc2021jcyj-msxmX0280);重庆市教育委员会科学技术研究青年项目(No.KJQN202100521)。

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。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 

分 类 号：TB472[一般工业技术—工业设计] F273.4[经济管理—企业管理]