多目标优化中ε-真有效解的一个注记  

A Note on ε-Properly Efficient Solutions in Multi-Objective Optimization

作　　者：夏丹丹 陈美杉 刘学文 XIA Dandan;CHEN Meishan;LIU Xuewen(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）》2021年第2期1-6,共6页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金重大项目(No.11991024)。

摘　　要：【目的】利用改进的约束标量化方法研究多目标优化ε-真有效解的标量化性质。【方法】首先对在已有研究的基础上,对ε-真有效解的标量化结果进行分析,通过严格的推理发现有两个条件是相互矛盾的。进一步地,引入新的条件对该结果进行修正。【结果】利用改进的约束标量化方法在新的条件下建立了多目标优化问题中ε-真有效解的标量化结果。此外,也举例对主要结果进行说明。【结论】获得的标量化结果不仅对已有文献中的结论进行了修正,同时也为研究多目标优化问题中解的性质提供新的思路。[Purposes]The scalarization properties ofε-properly efficient solutions for multi-objective optimization is studied by using the improved constraint scalarization method.[Methods]Based on the existing research,it firstly analyses the scalarization result ofε-properly efficient solutions,and two conditions are contradictory in the result.Furthermore,the result is modified by introducing new conditions.[Findings]Using the improved constrained scalarization method,the scalarization result of theε-properly efficient solutions in the multi-objective optimization problem are established under the new conditions.In addition,some examples are given to illustrate the main results.[Conclusions]The conclusion obtained not only revise the result in existing literature,but also provide new ideas for the study of the properties of solutions in multi-objective optimization problems.

关 键 词：改进的约束标量化方法 多目标优化问题 ε-真有效解 

分 类 号：O221.6[理学—运筹学与控制论]