摘要
在多目标优化中,Pareto有效性体现了目标之间的妥协与补偿,而Geoffrion真有效性能保证补偿是有界的.本文对有无穷多个目标的优化问题引入了真有效性,完整保留了Geoffrion的结构.基于一族锥,揭示了Geoffrion真有效性的特点及其与Pareto有效性的区别.并将Geoffrion真有效性的思想用于鲁棒优化,得到了著名的Hurwicz决策准则.
In multiobjective optimization,Pareto efficiency embodies the compromises and tradeoffs between objectives,while Geoffrion proper efficiency can guarantee bounded tradeoffs.In this paper,a proper efficiency which adheres to Geoffrion s structure is introduced for optimization problems with infinitely many objectives.In terms of a family of cones,Geoffrion proper efficiency is characterized and its difference from Pareto efficiency is highlighted.Finally,the famous Hurwicz decision criterion is derived by applying the idea of Geoffrion proper efficiency to robust optimization.
作者
王峰
刘三阳
WANG Feng;LIU Sanyang(School of Mathematics and Statistics,Xidian University,Xi an 710071,China)
出处
《浙江大学学报（理学版）》
CAS
CSCD
北大核心
2018年第3期294-297,313,共5页
Journal of Zhejiang University（Science Edition）
基金
国家自然科学基金资助项目(61373174)
