留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

多目标优化问题McRow最优解的刻画

赵春杰 高英 刘芙萍

赵春杰, 高英, 刘芙萍. 多目标优化问题McRow最优解的刻画[J]. 应用数学和力学, 2021, 42(6): 602-610. doi: 10.21656/1000-0887.410338
引用本文: 赵春杰, 高英, 刘芙萍. 多目标优化问题McRow最优解的刻画[J]. 应用数学和力学, 2021, 42(6): 602-610. doi: 10.21656/1000-0887.410338
ZHAO Chunjie, GAO Ying, LIU Fuping. Equivalent Characterization of McRow Optimal Solutions to Multiobjective Optimization Problems[J]. Applied Mathematics and Mechanics, 2021, 42(6): 602-610. doi: 10.21656/1000-0887.410338
Citation: ZHAO Chunjie, GAO Ying, LIU Fuping. Equivalent Characterization of McRow Optimal Solutions to Multiobjective Optimization Problems[J]. Applied Mathematics and Mechanics, 2021, 42(6): 602-610. doi: 10.21656/1000-0887.410338

多目标优化问题McRow最优解的刻画

doi: 10.21656/1000-0887.410338
基金项目: 

11991024)

重庆市高校创新研究群体项目(CXQT20014)

重庆市科学技术研究重点项目(KJZD-K202001104)

重庆市留学人员回国创业创新支持计划(cx2020096)

国家自然科学基金(11771064

详细信息
    作者简介:

    赵春杰(1995—),男,硕士生(E-mail: Zcj296020056@163.com);高英(1982—),女,教授,博士,硕士生导师(通讯作者. E-mail: gaoyingimu@163.com);刘芙萍(1975—),女,馆员,硕士(E-mail: lfp751214@163.com).

    通讯作者:

    高英(1982—),女,教授,博士,硕士生导师(通讯作者. E-mail: gaoyingimu@163.com)

  • 中图分类号: O221.6

Equivalent Characterization of McRow Optimal Solutions to Multiobjective Optimization Problems

Funds: 

11991024)

The National Natural Science Foundation of China(11771064

  • 摘要: 基于多目标优化问题的McRow模型,该文确定了W-鲁棒有效解(也称为McRow最优解)与弱有效解、有效解以及真有效解的关系.首先, 针对确定多目标优化问题,研究了W-鲁棒有效解与各种精确解的关系.随后,针对随机多目标优化问题,引进McRow最优解的概念,给出了它与其余各种解的关系.算例表明,利用McRow模型所得到的解更具有鲁棒性.
  • [2]KOOPMANS C. Analysis of Production as an Efficient Combination of Activities[M]. New York: John Wiley and Sons, 1951.
    PARETO V. Cours d’Economie Politique[M]. Lausanne: Librairie Droz, 1896.
    [3]KUHN H W, TUCKER A W. Nonlinear Programming[M]. Berkeley: University of California Press, 1951.
    [4]SAWARAGI Y, NAKAYAMA H, TANINO T. Theory of Multiobjective Optimization[M]. London: Academic Press, 1985.
    [5]HU J, MEHROTRA S. Robust andstochastically weighted multiobjective optimization models and reformulations[J]. Operations Research,2012,60(4): 936-953.
    [6]杨新民, 戎卫东. 广义凸性及其应用[M]. 北京: 科学出版社, 2016.(YANG Xinmin, RONG Weidong. Generalized Convexity With Applications[M]. Beijing: Science Press, 2016.(in Chinese))
    [7]杨新民, 陈光亚. 向量优化问题的线性标量化方法和Lagrange乘子研究[J]. 中国科学: 数学, 2020,50(2): 253-268.(YANG Xinmin, CHEN Guangya. The linear scalarizations and Lagrange multipliers for vector optimization[J]. Science China: Mathematics,2020,50(2): 253-268.(in Chinese))
    [8]JEYAKUMAR V. A generalization of a minimax theorem of Fan via a theorem of the alternative[J]. Journal of Optimization Theory and Applications,1986,48(3): 525-533.
    [9]HAYASHI M, KOMIYA H. Perfect duality for convexlike programs[J]. Journal of Optimization Theory and Applications,1982,38(2): 179-189.
    [10]仇秋生. 集值映射的广义凸性与集值最优化[D]. 博士学位论文. 上海: 上海大学, 2009.(QIU Qiusheng. The generalized convexity of set-valued maps and set-valued optimization[D]. PhD Thesis. Shanghai: Shanghai University, 2009.(in Chinese))
    [11]徐玖平, 李军. 多目标决策的理论与方法[M]. 北京: 清华大学出版社, 2005.(XU Jiuping, LI Jun. Multiple Objective Decision Making Theory and Methods[M]. Beijing: Tsinghua University Press, 2005.(in Chinese))
    [12]YANG X M, LI D, WANG S Y. Near-subconvexlikeness in vector optimization with set-valued functions[J]. Journal of Optimization Theory and Applications,2001,110(2): 413-427.
    [13]卢志义. 随机多目标规划有效解理论的研究[D]. 硕士学位论文. 西安: 西安建筑科技大学, 2005.(LU Zhiyi. Studies on the effecient solution theory for stochastic multiobjective programming[D]. Master Thesis. Xi’an: Xi’an University of Architecture and Technology, 2005.(in Chinese))
    [14]KORHONEN P, SALO S, STEURE R. A heuristic for estimating nadir criterion values in multiple objective linear programming[J]. Operations Research,1997,45(5): 751-757.
  • 加载中
计量
  • 文章访问数:  399
  • HTML全文浏览量:  95
  • PDF下载量:  36
  • 被引次数: 0
出版历程
  • 收稿日期:  2020-11-05
  • 修回日期:  2021-01-13

目录

    /

    返回文章
    返回