基于Kriging模型和条件风险值的多响应优化设计
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摘要
针对具有风险规避特性的多响应随机仿真优化问题,结合稳健参数设计思想和条件风险值准则,提出基于Kriging模型的均值—条件风险值优化策略。利用元建模技术,分别建立了均值响应和条件风险值响应的Kriging模型,在此基础上构建了具有风险参数描述的均值—条件风险值决策模型;采用bootstrap方法度量环境变量的不确定性对多响应优化Pareto前沿的影响,同时给出不同风险参数对Pareto前沿的影响。仿真实验结果表明所提方法能够有效处理具有风险规避特性的多响应随机仿真优化问题,验证了所提方法的有效性和合理性。
Aiming at the risk-averse stochastic simulation optimization problems with multiple responses,by combining robust design approach with conditional value at risk criterion,an optimal strategy of mean-conditional value at risk was proposed based on Kriging model was proposed.Kriging models for mean response and conditional value at risk response were constructed respectively with meta modeling technology,and the decision model of mean-conditional value at risk with risk parameter description was built on this basis.The influence of environment variable's uncertainty on Pareto frontier of multiple responses was measured by bootstrap method,and the influence of different risk parameters on Pareto frontier was also given.The simulation experiment results showed that the proposed approach could dispose the risk-averse stochastic simulation optimization problems with multiple responses effectively.
Aiming at the risk-averse stochastic simulation optimization problems with multiple responses,by combining robust design approach with conditional value at risk criterion,an optimal strategy of mean-conditional value at risk was proposed based on Kriging model was proposed.Kriging models for mean response and conditional value at risk response were constructed respectively with meta modeling technology,and the decision model of mean-conditional value at risk with risk parameter description was built on this basis.The influence of environment variable's uncertainty on Pareto frontier of multiple responses was measured by bootstrap method,and the influence of different risk parameters on Pareto frontier was also given.The simulation experiment results showed that the proposed approach could dispose the risk-averse stochastic simulation optimization problems with multiple responses effectively.
引文
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[3]SANTOS I R,ROBINSON P R.Simulation metamodels for modeling output distribution parameters[C]//Proceedings of the 2007 Winter Simulation Conference.Washington,D.C.,USA:IEEE,2007:910-918.
[4]KLEIJNEN J P C.Kriging metamodeling in simulation:a review[J].European Journal of Operational Research,2009,192(3):707-716.
[5]DELLINO G,KLEIGNEN J P C,MELONI C.Robust optimization in simulation:Taguchi and response surface methodology[J].International Journal of Production Economics,2010,125(1):52-59.
[6]OUYANG Linhan,MA Yizhong,LIU Liping,WANG Jianjun.Robust design modeling techniques based on improved Bayesian method[J].Computer Integrated Manufacturing Systems,2013,19(8):1967-1974(in Chinese).[欧阳林寒,马义中,刘利平,汪建均.基于改进贝叶斯方法的稳健性设计建模技术[J].计算机集成制造系统,2013,19(8):1967-1974.]
[7]SHANG J S,LI S,TADIKAMALIA P.Operational of supply chain system using the Taguchi method,response surface methodology,simulation,and optimization[J].International Journal of Production Research,2004,42(18):3823-3849.
[8]SHUKLA S K,TIWARI M K,WAN H D,SHANKER R.Optimization of the supply chain network:Taguchi and Psychoclonal algorithm embedded approach[J].Computers&Industrial Engineering,2010,58(1):29-39.
[9]SHI W,LIU Z,SHANG J,CUI Y.Multi-criteria robust design of a JIT-based cross docking distribution center for an auto parts supply chain[J].European Journal of Operational Research,2013,229(3):695-706.
[10]DELLINO G,KLEIJNEN J P C,MELONI C.Robust optimization in simulation:Taguchi and Krige combined[J].INFORMS Journal on Computing,2012,24(3):471-484.
[11]SHI Wen,LIU Zhixue,YANG Wei.Milk-run and cross-docking parts logistics system simulation optimization[J].Computer Integrated Manufacturing Systems,2012,18(12):2765-2776(in Chinese).[施文,刘志学,杨威.零部件循环取货越库物流系统仿真优化[J].计算机集成制造系统,2012,18(12):2765-2776.]
[12]ROCKAFELLAR R T,URYASEV S.Conditional value-atrisk for general loss distributions[J].Journal of Baking&Finance,2002,26(7):1443-1471.
[13]YIN Y,MADANAT S M,LU X Y.Robust improvement schemes for networks under demand uncertainty[J].European Journal of Operational Research,2009,198(2):470-479.
[14]GOTOH J Y,TAKANO Y C.Newsvendor solutions via conditional value-at-risk minimization[J].European Journal of Operational Research,2007,179(1):80-96.
[15]CHEN Y,XU M,ZHANG G.A risk-averse newsvendor model under the CVaR criterion[J].Operations Research,2009,57(4):1040-1044.
[16]LIU Yongmei,SUN Yuhua,FAN Chen.Strategic customer newsvendor model based on CVAR criterion[J].Computer Integrated Manufacturing Systems,2013,19(10):2572-2581(in Chinese).[刘咏梅,孙玉华,范辰.基于条件风险值准则的战略顾客报童模型[J].计算机集成制造系统,2013,19(10):2572-2581.]
[17]CHEN X,KIM K K.Building metamodels for quantile-based measures using sectioning[C]//Proceedings of the 2013Winter Simulation Conference.Washington,D.C.,USA:IEEE,2013:521-532.
[18]ANGUN E.A risk-averse approach to simulation optimization with multiple responses[J].Simulation Modelling Practice and Theory,2011,19(3):911-923.
[19]KLEIJNEN J P C.Design and analysis of simulation experiments[M].Berlin,Germany:Springer-Verlag,2008.
[20]HONG L J,LIU G.Simulating sensitivities of conditional value at risk[J].Management Science,2009,55(2):281-293.
[21]BASHYAM S,FU M C.Optimization of(s,S)inventory systems with lead times and a service level constraint[J].Management Science,1998,44(12):S243-S256.
[22]KLEINEN J P C,SARGENT R G.A methodology for fitting and validating metamodels in simulation[J].European Journal of Operational Research,2000,120(1):14-29.