多目标优化问题统一解的加权Tchebycheff标量化
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青年科学基金项目(No.12101096);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.cstc2022ycjh-bgzxm0114, No.cstc2021jcyj-msxmX0280);重庆市教育委员会科学技术研究青年项目(No.KJQN202100521)国家自然科学基金——重大项目(No.11991024),面上项目(No.12171063),


Weighted Tchebycheff Scalarization for Unified Solutions of Multi-Objective Optimization Problems
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    摘要:

    为研究多目标优化问题(C,ε)-型、E-型统一解的标量化性质,利用Bowman等人提出的加权Tchebycheff标量化方法建立多目标优化问题(C,ε)-弱有效解和E-弱有效解的标量化结果。进一步,建立基于加权Tchebycheff标量化方法多目标优化问题(C,ε)-有效解和E-有效解的标量化结果。通过调整标量化模型参数范围得到了多目标优化问题(C,ε)-(弱)有效解、E-(弱)有效解的一些加权Tchebycheff标量化结果,为求解多目标优化问题的算法设计提供了理论基础。

    Abstract:

    The scalarization properties of (C,ε)-type and E-type unified solutions for multi-objective optimization problems are studied. First, the weighted Tchebycheff scalarization method proposed by Bowman et al. is employed to establish the scalarization results of (C,ε)-weakly efficient solutions and E-weakly efficient solutions for multi-objective optimization problems. Furthermore, based on the weighted Tchebycheff scalarization method, the scalarization results of (C,ε)-efficient solutions and E-efficient solutions for multi-objective optimization problems are established. Some weighted Tchebycheff scalarization results of (C,ε)- (weakly) efficient solutions and E- (weakly) efficient solutions for multi-objective optimization problems are obtained by adjusting parameters range of the scalarization model. The obtained scalarization results are an extension of some existing work and provide a theoretical basis for algorithm design for solving multi-objective optimization problems.

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冯攀,夏远梅,赵克全.多目标优化问题统一解的加权Tchebycheff标量化[J].重庆师范大学学报自然科学版,2024,41(2):2-6

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  • 在线发布日期: 2024-06-12