一类不确定多目标优化问题的鲁棒标量化  

Robust Scalarization of a Class of Uncertain Multi-Objective Optimization Problems

作　　者：何瑜 夏远梅 郭辉 HE Yu;XIA Yuanmei;GUO Hui(School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,P.R.China;School of Sciences,Henan University of Technology,Zhengzhou 450001,P.R.China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331 [2]河南工业大学理学院,郑州450001

出　　处：《应用数学和力学》2025年第4期542-550,共9页Applied Mathematics and Mechanics

基　　金：国家重点研发计划(2023YFA1011302);国家自然科学基金(12171063,11991024,12101096);重庆市自然科学基金(cstc2022ycjh-bgzxm0114,cstc2021jcyj-msxmX0280);重庆市教育委员会科学技术研究计划(KJQN202100521,KJZD-K202300509)。

摘　　要：标量化方法在不确定多目标优化问题求解中具有十分重要的作用.首先,基于鲁棒优化的思想,提出了不确定多目标优化问题的鲁棒Pascoletti-Serafini标量化,并得出了鲁棒弱有效解和鲁棒有效解的标量化性质.进一步,提出了不确定多目标优化问题的鲁棒弹性Pascoletti-Serafini标量化并得出了鲁棒弱有效解、鲁棒有效解和鲁棒真有效解的标量化性质.此外,也给出了一些例子对主要结果进行说明.Scalarization methods play an important role in solving uncertain multi-objective optimization problems.Firstly,based on the idea of robust optimization,a robust Pascoletti-Serafini scalarization for uncertain multi-objective optimization problems was proposed,and the scalarization properties of robust weakly efficient solutions and robust efficient solutions were established.Furthermore,a robust flexible Pascoletti-Serafini scalarization method for uncertain multi-objective optimization problems was proposed,and the scalarization properties of robust weakly efficient solutions,robust efficient solutions,and robust properly efficient solutions were established.Moreover,some examples were provided to illustrate the main results.

关 键 词：不确定多目标优化 鲁棒标量化 Pascoletti-Serafini标量化 

分 类 号：O221.6[理学—运筹学与控制论]