多目标优化问题的完全标量化  

Complete scalarization of multi-objective optimization problems

作　　者：赵克全 杨新民 夏远梅 Kequan Zhao;Xinmin Yang;Yuanmei Xia

机构地区：[1]重庆师范大学数学科学学院,重庆401331 [2]上海大学数学系,上海200444

出　　处：《中国科学：数学》2021年第2期411-424,共14页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11431004,11671062和11771064);重庆市基础与前沿研究计划(批准号:cstc2015jcyjA00027,cstc2017jcyj-yszxX0008和cstc2018jcyj-yszxX0009)资助项目。

摘　　要：本文首先利用松弛变量和广义Tchebycheff范数的推广形式提出一类新的标量化优化问题.进一步,通过调整几种参数范围获得一般多目标优化问题弱有效解、有效解和真有效解的一些完全标量化刻画.此外,本文提出例子对主要结果进行说明,利用相应的标量化方法判定给定的多目标优化问题的可行解是否是弱有效解、有效解和真有效解.In this paper,we first propose a kind of new scalarization optimization problem by using the slack variables and the extension of generalized Tchebycheff norm.Furthermore,we obtain some complete scalarization characterizations of weakly efficient solutions,efficient solutions and properly efficient solutions for a general multi-objective optimization problem by adjusting the ranges of several kinds of parameters.Moreover,we give an example to illustrate our main results,which verifies that whether a given feasible solution of multi-objective optimization problems is a weakly efficient solution,an efficient solution and a properly efficient solution by using the corresponding scalarization procedures.

关 键 词：多目标优化 广义Tchebycheff范数 完全标量化 有效解 弱有效解 真有效解 

分 类 号：O224[理学—运筹学与控制论]