含定性因子的二阶Scheff′e模型多目标最优设计  

Multi-objective optimal designs for second-order Scheff′e model with qualitative factors

作　　者：凌羚 李光辉[2] 张崇岐 LING Ling;LI Guang-hui;ZHANG Chong-qi(School of Economics and Statistics,Guangzhou University,Guangzhou 510006,China;School of science,Kaili University,Kaili 556011,China)

机构地区：[1]广州大学经济与统计学院,广东广州510006 [2]凯里学院理学院,贵州凯里556011

出　　处：《高校应用数学学报（A辑）》2022年第1期15-23,共9页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(12071096,11901260);贵州省科学技术基金(黔科合基础[2020]1Y010)。

摘　　要：在实际的很多情形中,混料试验都具有多个目标,且响应变量不仅受到各分量的影响,还会受到其他定性因子变量的影响.文中基于一类含定性因子的混料模型,通过求解效率和极值得到多目标最优设计,并证明了该设计满足相应组合最优性.实例证明,该方法同样适用于3个或更多目标优化设计问题.When applied to deal with practical problems, the regular mixture model is often endowed with multiple objectives. Its response variables are affected not only by each component, but also by other qualitative factors. Based on the research on a mixture model including qualitative factors,this paper aims to obtain the multi-objective optimal designs by solving the efficiency and realizing maximization, and to prove the design can realize the corresponding combinatorial optimality. In addition, through the examples of its application, it is shown that this method is also applicable to optimizing solutions to design with three or more objectives.

关 键 词：混料中心多项式 多目标 最优设计 定性因子 

分 类 号：O212.6[理学—概率论与数理统计]