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浙江大学学报(理学版)  2018, Vol. 45 Issue (3): 294-297,313    DOI: 10.3785/j.issn.1008-9497.2018.03.004
现代优化理论与算法专栏     
无穷多目标优化的Geoffrion真有效性及其在鲁棒优化中的应用
王峰, 刘三阳
西安电子科技大学 数学与统计学院, 陕西 西安 710071
Geoffrion proper efficiency in optimization with infinitely many objectives and its applications in robust optimization
WANG Feng, LIU Sanyang
School of Mathematics and Statistics, Xidian University, Xi'an 710071, China
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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.
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    
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.
Key words: optimization with infinitely many objectives    Pareto efficiency    Geoffrion proper efficiency    robust optimization    Hurwicz criterion
收稿日期: 2017-08-24 出版日期: 2018-03-15
CLC:  O221  
基金资助: 国家自然科学基金资助项目(61373174).
作者简介: 王峰(1985-),ORCID:http://orcid.org/0000-0002-1769-3398,男,博士研究生,主要从事鲁棒优化研究,E-mail:mathswf@163.com.
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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): 294-297,313.

WANG Feng, LIU Sanyang. Geoffrion proper efficiency in optimization with infinitely many objectives and its applications in robust optimization. Journal of Zhejiang University (Science Edition), 2018, 45(3): 294-297,313.

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https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2018.03.004        https://www.zjujournals.com/sci/CN/Y2018/V45/I3/294

[1] MARLER R T, ARORA J S. Survey of multi-objective optimization methods for engineering[J]. Structural and Multidisciplinary Optimization, 2004, 26(6):369-395.
[2] EHRGOTT M. Multicriteria Optimization[M]. Berlin:Springer Science & Business Media, 2005.
[3] CARRIZOSA E, PLASTRIA F. A characterization of efficient points in constrained location problems with regional demand[J].Operations Research Letters, 1996, 19(3):129-134.
[4] NDIAYE M, MICHELOT C. Efficiency in constrained continuous location[J]. European Journal of Operational Research, 1998, 104(2):288-298.
[5] KUHN H W, TUCKER A W. Nonlinear programming[C]//Proceedings of the second Berkeleg Symposium on Mathematical Statistics and Probability. Berkeley:University of California Press, 1951(01):481-492.
[6] HURWICZ L. Programming in linear spaces[C]//Studies in Linear and Nonlinear Programming. Stanford:Stanford University Press, 1958:38-102.
[7] KLINGER A. Improper solutions of the vector maximum problem[J].Operations Research, 1967, 15(3):570-572.
[8] GEOFFRION A M. Proper efficiency and the theory of vector maximization[J].Journal of Mathematical Analysis and Applications, 1968, 22(3):618-630.
[9] GUERRAGGIO A, MOLHO E, ZAFFARONI A. On the notion of proper efficiency in vector optimization[J]. Journal of Optimization Theory and Applications, 1994, 82(1):1-21.
[10] JAHN J. Vector Optimization:Theory, Applications, and Extensions[M]. Heidelberg:Springer, 2010.
[11] WINKLER K. Geoffrion proper efficiency in an infinite dimensional space[J]. Optimization, 2004, 53(4):355-368.
[12] WINKLER K. Characterizations of efficient points in convex vector optimization problems[J]. Mathematical Methods of Operations Research, 2001, 53(2):205-214.
[13] WINKLER K. A characterization of efficient and weakly efficient points in convex vector optimization[J]. SIAM Journal on Optimization, 2008, 19(2):756-765.
[14] ZHAO K Q, YANG X M. Characterizations of efficient and weakly efficient points in nonconvex vector optimization[J]. Journal of Global Optimization, 2015, 61(3):575-590.
[15] BEWLEY T F. Knightian decision theory:Part I[J]. Decisions in Economics and Finance, 2002, 25(2):79-110.
[16] RIGOTTI L, SHANNON C. Uncertainty and risk in financial markets[J]. Econometrica, 2005, 73(1):203-243.
[17] KOUVELIS P, YU G. Robust Discrete Optimization and Its Applications[M]. Berlin:Springer Science & Business Media, 1997.
[18] BEN-TAL A, EL GHAOUI L, NEMIROVSKI A.Robust Optimization[M]. Princeton:Princeton University Press, 2009.
[19] GOERIGK M, SCHÖBEl A. Algorithm engineering in robust optimization[C]//Algorithm Engineering. Berlin:Springer International Publishing, 2016:245-279.
[20] KLAMROTH K, KÖBIS E, SCHÖBEL A, et al. A unified approach to uncertain optimization[J]. European Journal of Operational Research, 2017, 260(2):403-420.
[21] HURWITZ L. Optimality criteria for decision making under ignorance[J]. Cowles Communication Discussion Paper, 1951,370:1-16.
[22] ARNOLD B F, GRÖßL I, STAHLECKER P. The minimax, the minimin, and the Hurwicz adjustment principle[J]. Theory and Decision, 2002, 52(3):233-260.
[23] ENGAU A. Definition and characterization of Geoffrion proper efficiency for real vector optimization with infinitely many criteria[J]. Journal of Optimization Theory and Applications, 2015, 165(2):439-457.
[24] ENGAU A. Proper efficiency and tradeoffs in multiple criteria and stochastic optimization[J]. Mathematics of Operations Research, 2016, 42(1):119-134.
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