多目标优化的广义Pascoletti-Serafini标量化  

Generalized Pascoletti-Serafini scalarization for multi-objectiveoptimization

作　　者：夏远梅 赵克全 高英 Yuanmei Xia;Kequan Zhao;Ying Gao

机构地区：[1]重庆师范大学数学科学学院,重庆401331 [2]内蒙古大学数学科学学院,呼和浩特010021

出　　处：《中国科学：数学》2024年第2期231-244,共14页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:12171063,11991024和12101096);重庆市高校创新研究群体(批准号:CXQT20014);重庆市自然科学基金(批准号:cstc2022ycjh-bgzxm0114和cstc2021jcyj-msxm X0280);重庆市教育委员会科学技术研究计划(批准号:KJQN202100521和KJZD-K202300509)资助项目。

摘　　要：广义Tchebycheff范数是研究多目标优化问题各类解性质的重要工具之一.本文基于广义Tchebycheff范数的推广形式提出多目标优化问题的一类广义Pascoletti-Serafini标量化模型,进而基于这类标量化模型并在模型参数范围的恰当限制下获得了一般多目标优化问题弱有效解、有效解、严有效解和真有效解的一些标量化刻画结果.The generalized Tchebycheff norm is an important tool for studying the properties of various solutions of multi-objective optimization problems.In this paper,based on the extended generalized Tchebycheff norm,a generalized Pascoletti-Serafini scalarization model for multi-objective optimization problems is proposed,and then based on this kind of scalarization model,some scalarization characterization results of weakly efficient solutions,efficient solutions,strictly efficient solutions,and properly efficient solutions are obtained for a class of general multi-objective optimization problems under the appropriate constraints of the model parameter range.

关 键 词：多目标优化 广义Tchebycheff范数 Pascoletti-Serafini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]