混料D-最优近似设计的改进模拟退火算法  

Improved simulated annealing algorithm for D-optimal approximate design of mixture

作　　者：许秀钿 张崇岐 XU Xiu-tian;ZHANG Chong-qi(School of Economics and Statistics,Guangzhou University,Guangzhou 510006,China)

机构地区：[1]广州大学经济与统计学院,广东广州510006

出　　处：《高校应用数学学报（A辑）》2023年第4期389-397,共9页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(12071096)。

摘　　要：随着实际问题的不断细化,混料设计点的求解也越发困难,特别是高阶模型或是具有复杂约束的混料模型.传统的计算方法计算量大,灵活性不高,应用起来十分不便,已越发不适用于求解实际的混料试验设计.与传统的求解混料设计点的方法相比,使用计算机算法来求解混料设计点更为便利.文中研究一种改进的SA算法,该算法相比传统的SA算法,在步长以及马尔科夫链的设置上进行了改进.通过实例验证,该算法求解混料近似设计点时速度更快,精度更高.此外,该算法也可用于求解其他最优设计的设计点,由于篇幅限制,文中仅以D-最优设计为例进行展开.With the continuous refinement of practical problems,it is more and more dificult to solve the design points of the mixture,especially the high-order model or the mixture model with com-plex constraints.The traditional calculation method has a large amount of calculation,low flexibility,and is very inconvenient in application.It is more and more unsuitable for solving the practical mixing test design.Compared with the traditional method,it is more convenient to use computer algorithm to solve the mixing design point.This paper introduces an improved SA algorithm,which is improved in step size and Markov chain setting compared with the traditional SA algorithm.An example shows that the algorithm is faster and more accurate in solving approximate design points of mixture.In addition,this algorithm can also be used to solve the design points of other optimal designs.Due to space limitation,this paper only expands the D-optimal design as an example.

关 键 词：SA算法 改进SA算法 混料模型 D-最优设计 

分 类 号：O212.6[理学—概率论与数理统计]