具有范数结构多目标优化问题的近似方法及应用  

An Approximate Method for Multi-Objective Optimization Problems with Norm Structure and Its Application

作　　者：谭豫琳 杨春蓉 赵克全 TAN Yulin;YANG Chunrong;ZHAO Kequan(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）》2023年第2期28-33,共6页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金面上项目(No.11991024,12171063);重庆市高校创新研究群体项目(No.CXQT20014);重庆市自然科学基金面上项目(No.cstc2021jcyj-msxmX0280);重庆英才计划“包干制”项目(No.CQYC20210302270);重庆市教委科学技术研究项目(No.KJQN202100521)。

摘　　要：[目的]研究了一类特殊的具有范数结构的多目标优化问题,并应用于解决实际问题。[方法]针对这类多目标优化问题的求解,基于标量化思想,在适当假设条件下提出了一种近似方法。[结果]可以通过调整几类参数的取值范围获得多目标优化问题的Pareto解。[结论]利用具有范数结构的多目标优化模型和本文提出的近似求解方法于绩效管理中基础工作量的设置和电厂发电机的分配问题。[Purposes]A special kind of multi-objective optimization problem with norm structure is studied,which can be applied to the processing of many practical problems.[Methods]Based on the idea of scalarization,an approximate method is proposed to solve this kind of multi-objective optimization problem under some suitable assumptions.[Findings]It can obtain Pareto solutions of multiobjective optimization problems by adjusting the ranges of several parameters.[Conclusions]The multi-objective optimization model with norm structure and the approximate solution method are used in the setting of basic workload and the assignment of power plant generators in performance management.

关 键 词：多目标优化问题 范数结构 标量化思想 近似方法 

分 类 号：O221.6[理学—运筹学与控制论]