不确定多目标优化问题的一类鲁棒标量化方法  

A Class of Robust Scalarization Methods for Uncertain Multi-Objective Optimization Problems

作　　者：张静 邓枘 赵克全 ZHANG Jing;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5期1-6,共6页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金面上项目(No.11991024,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：对不确定多目标优化问题的(近似)鲁棒弱有效解和(近似)鲁棒有效解的性质进行研究。通过对带松弛和剩余变量的鲁棒标量化问题(近似)最优解的研究,建立了(近似)鲁棒弱有效解和(近似)鲁棒有效解的一些充分条件和必要条件。将确定性多目标优化问题提出的带松弛和剩余变量标量化模型推广到鲁棒情形,提出了一类新的鲁棒标量化问题。所得结果是对最近一些研究工作的改进与推广。The properties of the(approximate)robust weak effective solutions and the(approximate)robust effective solutions of the uncertain multi-objective optimization problem are studied.Through the study of the(approximate)optimal solution of the robust scalarization problem with relaxation and residual variables,some sufficient conditions and necessary conditions for the(approximate)robust weak effective solution and the(approximate)robust effective solution are established.The scalarization model with relaxation and residual variables proposed by the deterministic multi-objective optimization problem is extended to the robust case,and a new class of robust scalarization problems is proposed.The results obtained are the improvement and promotion of some recent research work.

关 键 词：鲁棒多目标优化问题 鲁棒标量化问题 (近似)鲁棒弱有效解 (近似)鲁棒有效解 

分 类 号：O221.6[理学—运筹学与控制论]