运筹学学报 >
2025 , Vol. 29 >Issue 2: 175 - 183
DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2025.02.013
多目标优化的广义Tchebycheff范数标量化
收稿日期: 2022-02-21
网络出版日期: 2025-06-12
基金资助
国家自然科学基金(11991024);国家自然科学基金(12171063);国家自然科学基金(12101096);国家自然科学基金(11971084);重庆市高校创新研究群体项目(CXQT20014);重庆市自然科学基金面上项目(cstc2021jcyj-msxmX0280);重庆英才计划“包干制”项目(CQYC20210302270);重庆英才计划“包干制”项目(Nos. CQYC20210302270, CQYC20210309536);重庆市教委科学技术研究项目(KJQN202100521);重庆师范大学博士启动项目(20XLB028)
版权
Generalized Tchebycheff norm scalarization in multi-objective optimization
Received date: 2022-02-21
Online published: 2025-06-12
Copyright
标量化方法是多目标优化问题研究的基本内容之一。本文首先对广义Tchebycheff范数的性质进行研究, 获得了其在非负象限上的严格单调性等结果。进一步, 利用广义Tchebycheff范数的这些性质研究了多目标优化问题弱有效解、有效解、严有效解和真有效解的两类标量化结果。同时也指出, 在目标函数的凸性假设下, 本文研究的标量化与加权标量化等价。
关键词： 多目标优化; 广义Tchebycheff范数; 严格单调性; 标量化; (弱, 严, 真) 有效解
夏远梅, 夏丹丹, 赵克全 . 多目标优化的广义Tchebycheff范数标量化[J]. 运筹学学报, 2025 , 29(2) : 175 -183 . DOI: 10.15960/j.cnki.issn.1007-6093.2025.02.013
Scalarization method is one of the basic research subjects for multi-objective optimization problems. In this paper, we first study the properties of generalized Tchebycheff norm, and obtain some strict monotonicity results on the non-negative quadrant. Furthermore, two kinds of scalarization results of weakly efficient solutions, efficient solutions, strictly efficient solutions and properly efficient solutions of multi-objective optimization problems are studied by using the properties of the generalized Tchebycheff norm. Moreover, we point out that under the assumption of convexity of the objective function, the scalarization studied in this paper is equivalent to the weighted scalarization.
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