一类特殊向量集的偏序性质与最优性  

Partial Order Properties and Optimality of a Special Class of Vector Sets

作　　者：赵克全 刘美含 夏远梅 ZHAO Kequan;LIU Meihan;XIA Yuanmei(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4期35-41,共7页Journal of Chongqing Normal University:Natural Science

基　　金：国家重点研发计划项目(No.2023YFA1011302);国家自然科学基金面上项目(No.12171063);重庆市高校创新研究群体项目(No.CXQT20014);重庆英才计划“包干制”项目(No.cstc2022ycjh-bgzxm0114)。

摘　　要：为研究一类具状态属性向量集的偏序性质和最优性,通过将大规模复杂电力系统抽象为具正常和故障状态属性的特殊向量集,考虑了一类加权和二元关系,证明了向量集中二元关系的一些偏序基本性质,进而获得了特殊向量集的一些最优性结果。针对一类具状态属性向量集,建立了其中二元关系的偏序性质、最优性等一系列定理。所得结果可对电力系统可靠性评估提供理论和方法支撑。The partial order property and optimality of a class of vector sets with state attributes are studied.By abstracting large-scale complex power systems into special vector sets with normal and fault state attributes,a class of weighted sum binary relations is considered.Some partial order basic properties of binary relations in vector sets are proved,and some optimality results of special vector sets are obtained.For a class of vector sets with state attributes,a series of theorems such as partial order properties and optimality of binary relations are established.The results can provide theoretical and methodological support for power system reliability assessment.

关 键 词：多目标优化问题 特殊向量集 偏序性质 最优性 

分 类 号：O221.6[理学—运筹学与控制论]