| 无穷多目标优化的Geoffrion真有效性及其在鲁棒优化中的应用 |
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| 引用本文： | 王峰,刘三阳.无穷多目标优化的Geoffrion真有效性及其在鲁棒优化中的应用[J].浙江大学学报(理学版),2018,45(3):294. |
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| 作者姓名： | 王峰 刘三阳 |
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| 作者单位： | 西安电子科技大学 数学与统计学院, 陕西 西安 710071 |
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| 基金项目： | 国家自然科学基金资助项目（61373174）. |
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| 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.
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| 关 键 词： | 无穷多个目标的优化问题 Pareto有效性 Geoffrion真有效性 鲁棒优化 Hurwicz准则 |
| 收稿时间： | 2017-08-24 |
Geoffrion proper efficiency in optimization with infinitely many objectives and its applications in robust optimization |
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| WANG Feng,LIU Sanyang.Geoffrion proper efficiency in optimization with infinitely many objectives and its applications in robust optimization[J].Journal of Zhejiang University(Sciences Edition),2018,45(3):294. |
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| Authors: | WANG Feng LIU Sanyang |
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| Affiliation: | School of Mathematics and Statistics, Xidian University, Xi'an 710071, China |
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| Abstract: | 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. |
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| Keywords: | optimization with infinitely many objectives Pareto efficiency Geoffrion proper efficiency robust optimization Hurwicz criterion |
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