鲁棒多目标优化问题的约束标量化方法  

A Constraint Scaling Method for Robust Multi-Objective Optimization Problems

作　　者：邓枘 赵克全 DENG Rui;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）》2024年第3期20-25,共6页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金项目——重大项目(No.11991024),自由申请项目(No.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项目(No.cstc2022ycjh-bgzxm0114)。

摘　　要：为了研究带约束鲁棒标量化问题的最优解与多目标优化问题的鲁棒有效解和鲁棒弱有效解之间的关系,获得鲁棒解的性质。利用鲁棒标量化方法将带约束的确定性多目标优化问题推广到鲁棒多目标优化问题,并在不同参数条件下,对鲁棒有效解和鲁棒弱有效解进行研究。建立了鲁棒有效解和鲁棒弱有效解的一些充分条件,并给出具体例子对主要结果进行解释。所得结果是对最近一些研究工作的改进与推广。In order to study the relationship between the optimal solution of constrained robust scalarization problems and the robust effective solution and robust weak effective solution of multi-objective optimization problems,and to obtain the properties of robust solutions.Using robust scalarization methods,the constrained deterministic multi-objective optimization problem is extended to robust multi-objective optimization problems,and robust effective solutions and robust weak effective solutions are studied under different parameter conditions.Some sufficient conditions for robust efficient solutions and robust weak efficient solutions are established,and specific examples are given to explain the main results.The results are an improvement and replication of some recent research work.

关 键 词：鲁棒多目标优化问题 鲁棒标量化问题 鲁棒弱有效解 鲁棒有效解 

分 类 号：O221.6[理学—运筹学与控制论]