多目标优化问题McRow最优解的刻画  

Equivalent Characterization of McRow Optimal Solutions to Multiobjective Optimization Problems

作　　者：赵春杰 高英 刘芙萍 ZHAO Chunjie;GAO Ying;LIU Fuping(School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,P.R.China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《应用数学和力学》2021年第6期602-610,共9页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11771064;11991024);重庆市科学技术研究重点项目(KJZD⁃K202001104);重庆市高校创新研究群体项目(CXQT20014);重庆市留学人员回国创业创新支持计划(cx2020096)。

摘　　要：基于多目标优化问题的McRow模型,该文确定了W⁃鲁棒有效解(也称为McRow最优解)与弱有效解、有效解以及真有效解的关系.首先,针对确定多目标优化问题,研究了W⁃鲁棒有效解与各种精确解的关系.随后,针对随机多目标优化问题,引进McRow最优解的概念,给出了它与其余各种解的关系.算例表明,利用McRow模型所得到的解更具有鲁棒性.Based on the McRow model for multiobjective optimization problems,the relationships between the W⁃robust efficient solution(also known as the McRow optimal solution)and the weakly efficient solution,the efficient solution and the properly efficient solution were established.Firstly,the relationship between the W⁃robust efficient solution and various exact solutions to multiobjective optimization problems was studied.Then,the concept of the McRow optimal solution to stochastic multiobjective optimization problems was introduced,and the relationship between the McRow optimal solution and other solutions was given.The examples show that,the solutions obtained with the McRow model are of better robustness.

关 键 词：多目标优化 随机多目标优化 鲁棒优化 McRow最优解 

分 类 号：O221.6[理学—运筹学与控制论]