一类不确定多目标优化问题的鲁棒标量化

何瑜; 夏远梅; 郭辉

doi:10.21656/1000-0887.450194

一类不确定多目标优化问题的鲁棒标量化

doi: 10.21656/1000-0887.450194

何瑜¹,
夏远梅^1, ,,
郭辉²

1. 重庆师范大学数学科学学院，重庆 401331;
2. 河南工业大学理学院，郑州 450001

基金项目:

国家重点研发计划(2023YFA1011302)；国家自然科学基金(12171063；11991024；12101096)；

详细信息

作者简介:
何瑜（1998—），女，硕士生(E-mail: xiaohekaixin07@163.com)；夏远梅（1990—），女，副教授，博士，硕士生导师(通讯作者. E-mail: mathymxia@cqnu.edu.cn)；郭辉（1980—），女，副教授，博士，硕士生导师(E-mail: guoguofly@163.com).

通讯作者:
夏远梅（1990—），女，副教授，博士，硕士生导师(通讯作者. E-mail: mathymxia@cqnu.edu.cn)

中图分类号: O221.6
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出版历程
- 收稿日期: 2024-07-02
- 修回日期: 2024-10-22
- 网络出版日期: 2025-04-30

Robust Scalarization of a Class of Uncertain Multi-Objective Optimization Problems

HE Yu¹,
XIA Yuanmei^{1
, ,},
GUO Hui²

1. School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, P.R.China;
2. School of Sciences, Henan University of Technology, Zhengzhou 450001, P.R.China

Funds:

The National Science Foundation of China(12171063；11991024；12101096)

摘要

摘要: 标量化方法在不确定多目标优化问题求解中具有十分重要的作用.首先，基于鲁棒优化的思想，提出了不确定多目标优化问题的鲁棒Pascoletti-Serafini标量化，并得出了鲁棒弱有效解和鲁棒有效解的标量化性质.进一步，提出了不确定多目标优化问题的鲁棒弹性Pascoletti-Serafini标量化并得出了鲁棒弱有效解、鲁棒有效解和鲁棒真有效解的标量化性质.此外，也给出了一些例子对主要结果进行说明.
- 不确定多目标优化 /
- 鲁棒标量化 /
- Pascoletti-Serafini标量化
Abstract: Scalarization methods play an important role in solving uncertain multi-objective optimization problems. Firstly, based on the idea of robust optimization, a robust Pascoletti-Serafini scalarization for uncertain multi-objective optimization problems was proposed, and the scalarization properties of robust weakly efficient solutions and robust efficient solutions were established. Furthermore, a robust flexible Pascoletti-Serafini scalarization method for uncertain multi-objective optimization problems was proposed, and the scalarization properties of robust weakly efficient solutions, robust efficient solutions, and robust properly efficient solutions were established. Moreover, some examples were provided to illustrate the main results.
- uncertain multi-objective optimization /
- robust scalarization /
- Pascoletti-Serafini scalarization

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参考文献(21)

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一类不确定多目标优化问题的鲁棒标量化

doi: 10.21656/1000-0887.450194

作者简介:
何瑜（1998—），女，硕士生(E-mail: xiaohekaixin07@163.com)；夏远梅（1990—），女，副教授，博士，硕士生导师(通讯作者. E-mail: mathymxia@cqnu.edu.cn)；郭辉（1980—），女，副教授，博士，硕士生导师(E-mail: guoguofly@163.com).

通讯作者:
夏远梅（1990—），女，副教授，博士，硕士生导师(通讯作者. E-mail: mathymxia@cqnu.edu.cn)

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Robust Scalarization of a Class of Uncertain Multi-Objective Optimization Problems

计量

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留言板

一类不确定多目标优化问题的鲁棒标量化

doi: 10.21656/1000-0887.450194

作者简介: 何瑜（1998—），女，硕士生(E-mail: xiaohekaixin07@163.com)；夏远梅（1990—），女，副教授，博士，硕士生导师(通讯作者. E-mail: mathymxia@cqnu.edu.cn)；郭辉（1980—），女，副教授，博士，硕士生导师(E-mail: guoguofly@163.com).

通讯作者: 夏远梅（1990—），女，副教授，博士，硕士生导师(通讯作者. E-mail: mathymxia@cqnu.edu.cn)

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出版历程

Robust Scalarization of a Class of Uncertain Multi-Objective Optimization Problems

计量

出版历程

目录

作者简介:
何瑜（1998—），女，硕士生(E-mail: xiaohekaixin07@163.com)；夏远梅（1990—），女，副教授，博士，硕士生导师(通讯作者. E-mail: mathymxia@cqnu.edu.cn)；郭辉（1980—），女，副教授，博士，硕士生导师(E-mail: guoguofly@163.com).

通讯作者:
夏远梅（1990—），女，副教授，博士，硕士生导师(通讯作者. E-mail: mathymxia@cqnu.edu.cn)