面向产品族协同优化设计的模糊层次优化模型与方法研究
|
摘要
产品族设计是大规模定制中的关键问题。以往的研究,对于产品族主要功能参数及其关联的从属功能参数的设计多采取各自独立的方式而忽略其间的主从关联关系,缺乏对各功能参数的协同设计的研究,特别是具有模糊参数的情形。模糊多层次优化问题由于其广泛的实际应用背景而成为近年来研究的热点,但由于其求解的难度而主要停留在理论层面。本文针对这一现实背景,对面向产品族协同优化设计的模糊双层规划模型与方法进行了系统的研究,主要工作如下:
第一,基于对目前产品族参数设计的研究综述,分析并指出了研究中的不足;提出了基于主从关联结构的产品族协同优化设计的理念,将具有主从结构的产品族协同优化设计问题分为两类:全局-局部协同优化和关键-从属协同优化。
第二,对于全局-局部协同优化和关键-从属协同优化两类问题,研究了其概念模型和数学模型建立的全过程,建立了包括市场需求分析、产品族架构、功能指标确定、柔性与模糊性分析等的分析模型和数学模型,探讨了大规模定制下的定制参数、平台参数、产品平台、产品族等的规划设计方法。
第三,研究了模型的解析型算法,分别针对具有模糊目标与模糊约束的模糊双层规划以及具有模糊系数的模糊双层规划模型构建了求解方法,并给出产品族设计的数值算例验证了其可行性。
第四,研究了模型的智能型算法,分别建立了基于遗传算法和粒子群算法的模糊双层规划求解方法,给出了数值算例。
第五,将所研究的模型和方法应用于具有模糊参数的机械产品族优化设计,建立了产品族协同优化设计的模糊双层规划模型。
最后对全文工作做了总结,并对今后的进一步研究做了展望。
Product family design is the critical problem of mass customization. In previous literatures, methods of product family design for main function parameters and correlative subordinate function parameters are adopted respectively, so that the leader-follower relationship between them and the research on cooperative design with function parameters are neglected, especially with fuzzy parameters. It is a hotspot that how to solve the fuzzy multilevel optimization problems, because of its comprehensive realistic application, however, it has been focus on the academic meaning because of the difficulty to seek solution. Aiming at the realistic background, systemic research on fuzzy bilevel optimization models and methods faced to hierarchy optimization design of product family are made. The main work of this paper is as the followings:
Firstly, the deficiencies in the study based on summarizing the current research on product family design are pointed out, and the cooperative optimization design problems of product family with principal-subordinate structure are divided into two species: the global-local cooperative optimization and the pivotal-subordinative cooperative optimization.
Secondly, aiming at two problems of the global-local and the pivotal- subordinative cooperative optimization, the process of up building their notional models and mathematic models are researched, analysis models and mathematic models are set up, including analyzing market demand, constructing product family, ascertaining function index, analyzing flexibility and fuzziness and so on. Moreover, the programming design methods about customization parameters, flat parameters, product flat, product family in mass customization are discussed.
Thirdly, analytical solution to the models are researched and the method of resolving problems are constructed, aiming at fuzzy bilevel optimization models with fuzzy objects and fuzzy bilevel programming and fuzzy bilevel optimization models with fuzzy parameters, respectively. Numeral example of product family design is put forward to prove it feasible.
Fourthly, intelligent algorithms of the models are researched, the solution to fuzzy bi-level programming based on genetic algorithm and Particle Swarm Optimization are constructed, respectively, and then numeral example are put forward.
Fifthly, the models and methods studied in this paper are applied to mechanical product family optimization design with fuzzy parameters, furthermore, fuzzy bi-level optimization models of product family cooperative optimization design are set up.
Finally, the total work of the paper is summarized and the vista of further research is made.
第一,基于对目前产品族参数设计的研究综述,分析并指出了研究中的不足;提出了基于主从关联结构的产品族协同优化设计的理念,将具有主从结构的产品族协同优化设计问题分为两类:全局-局部协同优化和关键-从属协同优化。
第二,对于全局-局部协同优化和关键-从属协同优化两类问题,研究了其概念模型和数学模型建立的全过程,建立了包括市场需求分析、产品族架构、功能指标确定、柔性与模糊性分析等的分析模型和数学模型,探讨了大规模定制下的定制参数、平台参数、产品平台、产品族等的规划设计方法。
第三,研究了模型的解析型算法,分别针对具有模糊目标与模糊约束的模糊双层规划以及具有模糊系数的模糊双层规划模型构建了求解方法,并给出产品族设计的数值算例验证了其可行性。
第四,研究了模型的智能型算法,分别建立了基于遗传算法和粒子群算法的模糊双层规划求解方法,给出了数值算例。
第五,将所研究的模型和方法应用于具有模糊参数的机械产品族优化设计,建立了产品族协同优化设计的模糊双层规划模型。
最后对全文工作做了总结,并对今后的进一步研究做了展望。
Product family design is the critical problem of mass customization. In previous literatures, methods of product family design for main function parameters and correlative subordinate function parameters are adopted respectively, so that the leader-follower relationship between them and the research on cooperative design with function parameters are neglected, especially with fuzzy parameters. It is a hotspot that how to solve the fuzzy multilevel optimization problems, because of its comprehensive realistic application, however, it has been focus on the academic meaning because of the difficulty to seek solution. Aiming at the realistic background, systemic research on fuzzy bilevel optimization models and methods faced to hierarchy optimization design of product family are made. The main work of this paper is as the followings:
Firstly, the deficiencies in the study based on summarizing the current research on product family design are pointed out, and the cooperative optimization design problems of product family with principal-subordinate structure are divided into two species: the global-local cooperative optimization and the pivotal-subordinative cooperative optimization.
Secondly, aiming at two problems of the global-local and the pivotal- subordinative cooperative optimization, the process of up building their notional models and mathematic models are researched, analysis models and mathematic models are set up, including analyzing market demand, constructing product family, ascertaining function index, analyzing flexibility and fuzziness and so on. Moreover, the programming design methods about customization parameters, flat parameters, product flat, product family in mass customization are discussed.
Thirdly, analytical solution to the models are researched and the method of resolving problems are constructed, aiming at fuzzy bilevel optimization models with fuzzy objects and fuzzy bilevel programming and fuzzy bilevel optimization models with fuzzy parameters, respectively. Numeral example of product family design is put forward to prove it feasible.
Fourthly, intelligent algorithms of the models are researched, the solution to fuzzy bi-level programming based on genetic algorithm and Particle Swarm Optimization are constructed, respectively, and then numeral example are put forward.
Fifthly, the models and methods studied in this paper are applied to mechanical product family optimization design with fuzzy parameters, furthermore, fuzzy bi-level optimization models of product family cooperative optimization design are set up.
Finally, the total work of the paper is summarized and the vista of further research is made.
引文
[1] 祁国宁,顾建新等 大批量定制技术及其应用[M].机械工业出版社,2003
[2] Kevin N. Otto, Kristin L. Wood 等著.齐春萍,宫小东,张帆 等译. 产品设计[M]. 电子工业出版社,2005
[3] 冯培恩,邱清盈,潘双夏等 机械产品的广义优化设计进程研究[J].中国科学(E 辑),1999,29(4):338～346
[4] 邱清盈.机械广义优化设计的若干关键技术问题研究[D].杭州:浙江大学机械与能源工程学院,2000
[5] Jean-Francois B. Multidisciplinary Design Optimization Definition [EB/OL]. http://mdob.larc.nasa.gov, 2002-9-13/2003-3-20
[6] Anthony A G Frequently Asked Questions [EB/OL]. http://www.aero.ufl.edu/~issmo/, 2002k-10-17/2003-3-20
[7] Kodiyalam S. Evaluation of Methods for Multidisciplinary Design Optimization (MDO)-Phase I[R]. NASA CR208716, Virgjia:NASA 1998
[8] Srinivas, Kodiyalam, Charles Yuan. Evaluation of Methods for Multidisciplinary Design Optimization (MDO)-Part Ⅱ[R], NASA/CR——210313, Virgjia:NASA 2000
[9] Livne E year-in-review, Multidisciplinary Design Optimization [EB/OL]. http://www.rpi.edu/~messac/Publications/article98.htm.
[10] 周廷美,蓝悦明 机械设计零件与系统优化设计建模及应用[M] 北京:化学工业出版社,2004
[11] Ichiro Nishizaki, Masatosh Sakawa, Fuzzy cooperative game arising from linear production programming problem with fuzzy parameters[J], Fuzzy Sets and Systems, 2000(114),11-21
[12] Clodeinir Ronei Peres at, Fuzzy model and hierarchical fuzzy control integration: an approach for milling process optimization[J], Computers in Industry, 1999(39),199-207
[13] Baoding Liu, Studies in Fuzziness and Soft Computing[M], Physica-Verlag Heidelberg, 2002
[14] Davis S M. Future Perfect [M]. Reading:Addison-Wesley Publishing, 1987
[15] Pine B J Ⅱ.Mass Customization:The new Frontier in Business Competition[M]. Boston:Harvard Business School Press, 1993
[16] Womack J P. A book review of mass customization. Sloan Management Review, 1993, 34(3):121～122
[17] Beaty R T. Mass customization manufacturing Engineer, 1996, 75(5):217～220
[18] Eastwood, Margaret A. Implementing mass customization. Computers in industry, 1996, 30(3):171～174
[19] Rebecca D, Peter T W, Glenn W, et. Cl. Approaches to mass customization:configurations and empirical validation. Journal of Operations Management, 2000, 18:605～625
[20] 苏宝华 面向大量定制生产的建模理论、方法以及其应用研究:[博士学位论文].杭州:浙江大学,1998
[21] 李仁旺 大批量定制的若干理论与方法问题研究:[博士学位论文].杭州:浙江大学,1999
[22] 李仁旺,祁国宁,顾建新,彭卫平,吴昭同 大批量生产及其实施方法初探.中国机械工程,2001, 12(4):405～408
[23] 孙伟,刘晓冰,徐中 大规模客户化生产模式的实施策略及产品设计技术研究.大连理工大学学报,2000,40(2):203～206
[24] 刘晓冰,董建华,孙伟 产品族建模技术研究.计算机辅助设计与图形学学报,2001,13(7):1～6
[25] 陈国权 大批量定制生产方式的基本概念与实施方法.系统工程理论与实践,2000,5:35～41,61
[26] 董建华,肖田元,乔桂秀,赵骥 面向大规模定制的制造系统关键技术.计算机集成制造系统——CIMS, 2002, 8(8):589～592
[27] 肖田元,乔桂秀,韩向利等 汽车制造业大批量定制实施策略及关键技术.计算机集成制造系统——CIMS, 2001, 7(9):1～7
[28] 郑华林,刘飞,王逢春等 面向大规模定制的产品需求建模方法研究.中国机械工程,2003, 14(6):471～474
[29] 吴锋,唐跃华 产品大批量定制哲理分析及应用案例研究.管理工程学报,2002, 16(4):95～97
[30] 邵晓峰,黄培清,季建华 大规模定制生产模式的研究.工业工程与管理,2001, 2:12～17
[31] Lau, Ronal S M. Mass customization: the next industrial revolution. Industrial Management, 1995, 37(5):18～19
[32] Gilmore J H. Pine B J Ⅱ. Markets of one: creating customer-unique value through mass customization. Harvard business review, July, 2000
[33] Qiang Tu, Mark A V, Ragu-Nathan T S. The impact of time-base manufacturing practices on mass customization and value to customer. Journal of OperationsManagement, 2001, 19:201～217
[34] Koufteros X A, Vonderembse M A, Doll W J. Developing measures of time-base manufacturing. Journal of Operations Management, 1998, 16(1):21～41
[35] Zipkin, Paul. The limits of mass customization. Sloan Management Review, 2001,42(3):81～87
[36] Ghiassi M, Spera C. Defining the Internet-based supply chain system for mass customized markets. Computer & industrial Engineering, 2003, 45:17～41
[37] Martin G H, Jiao J X. Research on E-product development(ePD) for mass customization. Technovation, 2002, 22:717～724
[38] Rachel C, Andrew B W. Requirements capture: theory and practice. Technovation 1998, 18(8/9):497～511
[39] Tseng M. Mitchell, Jiao Jianxin. Design by for mass customization. Annals of the CIRP, 1996, 45(1):153～156
[40] Barry Berman. Should your firm adopt a mass customization strategy. Business Horizins, 2002, July-august:51～60
[41] McAdams D A, Stone R B, Wood K L. Functional Interdependence and Product Similarity Based on Customer Needs. Research in engineering Design, 1999, 11:11～19
[42] Stone R B, Wood K L, Crawford R H. Using quantitative functional models to develop product architectures, Research in engineering Design, 2002, 21(3):239～260
[43] Martin M V, Ishill K. Design for variety: developing standardized and modularized product platform architectures. Research in Engineering Design, 2002, 13:213～235
[44] Javier P Gonzalez-Zugasti, Kevin N Otto, John D Baker. Assessing value for product family design and selection [C]. ASME DETC, 99/DAC-8613
[45] 张曙 分散网络化制造[M].机械工业出版社,1999
[46] Joseph B II. Mass customization the new frontier in business competition[M]. Boston: Harvard Business School Press, 1993
[47] Mitchell M Tseng, Jianxin Jiao. A framework of virtual design for product customization [J] IEEE ,1997 (9):7～14
[48] Mitchell M Tseng, Jianxin Jiao. Case-based evolutionary design for mass customization[J] Computers and Industry Engineering, 1997,33 (1-2):319～323
[49] Jianxin Jiao, Mitchell M Tseng. Product family modeling design for mass customization[J] Computers and Industry Engineering , 1998 ,35 (3-4) :495～498
[50] Mitchell M Tseng, Jianxin Jiao. Design for mass customization[C] Annuals of the CIRP, 1996, 45 (1):153～156
[51] Bin S, Huang G Q, Mak KL. Web-based product platform development using graph theory [J] IEEE, 2002:107～112
[52] Javier P Gonz alez-Zugasti, Kevin N Otto. Platform-based spacecraft design: a formulat2ion and implementation procedure [J] IEEE, 2000:455～463
[53] Rebecca Duray, Peter T Ward. Approaches to mass customization: configuration and empirical validation [J] Operations Management, 2000,18:605～625
[54] Sehyun Mying, Soonhung Han. Knowledge-based parametric design of mechanical products based on configuration design method[J] Expert System with Applications, 2001 21:99～107
[55] Hernandez G, Allen J K, Simpson T W, et al. Robust design of families for products with production modeling and revaluation [J]. ASME Journal of Mechanical Design, 2001,6:183～190
[56] Jeffrey B Dahmus, Javier P Gonzalez-Zugasti, Kevin N Otto. Modular product architecture [C] ASME DETC, 2000/DTM-14565
[57] Mark V Martin, Kosuke Ishii. Design for variety:A methodology for developing product platform architectures[C] ASME DETC, 2000/DFM-14021
[58] Simpson T W, Chen W. Use of the robust concept exploration method to facilitate the design of a family of products[J] Simultaneous Engineering: Methodologies and Applications, 1999:247～278
[60] Messac A, Martinez M P , Simpson T W. Introduction of a product family penalty function using physical programming[J] ASME Journal of Mechanical Design, 2002 (2):164～172
[61] Nayak R U, Chen W, Simpson T W. A variation2based method for product family design [J] Engineering Optimization, 2002, 34 (1):65～81
[62] Messac A, Martinez M P, Simpson T W. A penalty function for product family design using physical programming [J] ASME Journal of Mechanical Design, 2002,124 (2):164～172
[63] Simpson T W, D’Souza B. A variable length genetic algorithm for product platform design[C] 9thAIAA/ ISSMO Symposium on Multidisciplinary Analysis and Optimization, Atlanta, GA, 2002, 9 (4-6):1～10
[64] D’Souza B, Simpson T W. A genetic algorithm based method for product family design optimization [J] ASME Design Engineering Technical Conferences -Design Automation Conference ( DAC) ,2002 ,9:1～10
[65] Hernandez G, Simpson T W, Allen J K. Robust design of product families for make-to-order systems[J] ASME Journal of Mechanical Design, 2001 , 23 (2):183～190
[66] Simpson T W, Chen W, Allen J K. Conceptual design of a family of products through the use of the robust concept exploration method[C] 6th AIAA/ USAF/NASA/ ISSMO Symposium on Multidisciplinary Analysis and Optimization, Bellevue, WA,1996, 9 (2):1535～1545
[67] Simpson T W, Mistree F. A concept exploration method for product family and product platform design [J] ASME Optimization in Industry II, 1999, 7:371～378
[68] Messac A , Martinez M P , Simpson T W. Effective product family design using physical programming and the product platform concept exploration method [J] Design ASME Automation Conference, 2000 (9):1～8
[69] Simpson T W, Maier J R A, Mistree F A. Product platform concept exploration method for product family design [D] ASME Design Theory and Methodology, 1999 (9):1～219
[70] Messac A, Martinez M P, Simpson T W. Effective product family design using physical program2ming [J] Engineering Optimization, 2002, 34 (3):245～261
[71] Daniel Sabin, Rainer Weigel. Product configuration framework-a survey[J] Intelligent Systems. IEEE, 1998:42～49
[72] Raviraj U Nayak, Wei Chen, Timothy W Simpson. A variation-based methodology for product family design[C] ASME DETC, 2000/DAC-14264
[73] Javier P Gonzalez-Zugasti, Kevin N Otto. Modular platform-based product family design[C] ASME DETC, 2000/DAC-14238
[74] 黄纯颖 设计方法学[M].机械工业出版社,1992
[75] 腾春贤,李智慧 二层规划的理论与应用,科学出版社,2002
[76] Bialas W F, Chew M N. On two-level optimization. IEEE transactions on automatic control, 1982,AC-26:211～214
[77] Bension H P. On the structure and properties of a linear multilevel programming problem Journal of Optimization Theory and Applications, 1989, 60:353～373
[78] Bard J F, Falk J E. An explicit solution to the multilevel programming problem. Computers and Operations Research, 1982, 9:77～100
[79] Kornal J, Liptak T. Two-level planning. Econometric, 1965, 33:141～169
[80] Freeland J, Baker N. Good partitioning in a hierarchical organization. Management Science, 1975, 3:673～678
[81] Cassidy R G, Kieby M J L, Raike W M. Efficient distribution of resource through three levels of government. Management Science, 1971, 17:462～473
[82] Baumol W J, Fabian T. Decomposition, pricing for decentralization and external economics. Management Science, 1964, 11:1～31
[83] Bracken J, McGill J. Mathematical programs with optimization problems in the constraints. Operations Research, 1973, 21:37～44
[84] Candler W, R Norton. Multilevel programming.1977, Technical Report 20, World Bank Development Research Center, Washington D. C
[85] Stackelberg H. The theory of the market economy. New York, Oxford:Oxford University Press. 1952
[86] Jeroslow R. The polynomial hierarchy and simple model for competitive analysis, Mathematical programming, 1985, 32:146～164
[87] Bard J. Some properties of the bilevel programming problem. Journal of Optimization Theory and Applications, 1991, 68:371～378
[88] Ben-Ayed O, Blair C. Computational difficulties of bilevel linear programming. Operations Research, 1990, 38:556～560
[89] Hansen P, Jaumard B, Savard G. New branch-and-bound rules for linear bilevel programming. SIAM Journal on Scientific and Statistical computing, 1992, 13:1194～1217
[90] Vicente L, Savard G, Judice J. Descent approaches for quadratic bilevel programming. Journal of Optimization Theory and Applications, 1994, 81:379～399
[91] Bard J. Optimality conditions for the bilevel programming problem. Naval Research Logistics Quarterly, 1984, 31:13～26
[92] Clarke P, Westerberg A. A note on the optimality conditions for the bilevel programming problem. Naval Research Logistics, 1988, 35:413～418
[93] Haurie A, Savard G, White D. A note on: an efficient point algorithm for a linear two-stage optimization problem. Operations Research, 1990, 38:553～555
[94] Bard J. An efficient algorithm for solving general bilevel programming problem. Mathematical Operations Research, 1983, 8:260～272
[95] Bard J. Convex two-level optimization. Mathematical Programming, 1988, 40:15～27
[96] Kostad C D, Lasdon L S. Derivative evaluation and computational experience with large bilevel mathematical programs. Journal of Optimization Theory and Applications. 1990, 65:485～499
[97] Ye J J, Ye X Y. Necessary optimality conditions for optimization problems with variational inequality constraints. Mathematical Operations Research, 1997, 22:977～997
[98] Chen Y, Florian M. The nonlinear bilevel programming problem: a general formulation and optimality condition. 1991, Technical Report CRT-974, Centre de Research sur les Transports
[99] Dempe S. A necessary and a sufficient optimality condition for bilevel programming problems. Optimization, 1992,25:341～354
[100] Dempe S. Optimality conditions for bilevel programming problem. In P. Kall, editor, System modeling and optimization. Berlin:Springer-Verlag, 1992:17～24
[101] Outrata J. Necessary optimality conditions for Strackelderg problems. Journal of Optimization Theory and Applications, 1993, 76:305～320
[102] Ye J, Zhu D. Optimality conditions for bilevel programming problems. Technical Report DMs-618-IR, University of Victoria, Department of Mathematics and Statistics, 1993
[103] Bi Z, Calamai P. Optimality conditions for a class of bilevel programming problems. Technical report # 191-O-191291, University of Waterloo, Department of systems Design Engineering, 1991
[104] Tanion T, Ogawa T. An algorithm for solving two-level convex optimization problems, Int. System Science, 1984, 15:163～174
[105] Shimizu K, Ishizuka Y. Optimality conditions and algorithms for parameter design problem with two-level structure. IEEE Transactions on Automatic Control, 1985, AC-30, 986～993
[106] Ishizuka, Y. Optimality conditions for quasi-differentiable programs with application to two-level optimization. SIAM Journal of Control Optimization, 1988, 26:1388～1398
[107] 王春峰,李光泉,郑丕谔 动态多人递阶决策问题——结构、非光滑及必要性条件.系统工程学报,1996,11(4):27～36
[108] Savard G, Gauvin J. The steepest descent direction for the nonlinear bilevel programming problem. Oprations Research Letters, 1994, 15:275～282
[109] Vicente L, Calamai P. Geometry and local optimality conditions for bilevel programs with quadratic strictly convex lower levels. In D.-Z. Du and P. M. Pardalos, editors, Minmax and applications. Dordrecht, The Netherlands:Kluwer Academic Publishers Group, 1995:141～151
[110] 王先甲,冯尚友 二层系统最优化理论[M].科学出版社,1995
[111] Shimizu K, Aiyoshi E. Hierarchical multi-objective decision systems for general resource allocation problem. Journal of Optimization Theory and Applications, 1981, 35:517～533
[112] Tarvainent K, Haimes Y Y. Coordination of hierarchical multi-objective systems. IEEE Transactions on systems. Man, and Cybernetics, 1982, SMC-12, 751～764
[113] Li D, Haimes Y Y. Hierarchical generating method for large scale multi-objective systems. Journal of Optimization Theory and Applications, 1987, 54:303～333
[114] 唐大宏 几类多目标决策问题的分析方法研究(博士论文).华中理工大学,1989
[115] 杨丰梅 双层多目标规划问题的 Pareto 有效解.北京化工大学学报,1994,21(3):79～85
[116] Zhen Ling, Wang Rishuang. Study on some problems of bilevel multi- objectivesystems. Beijing Huangkong Hangtian Xuebao, 1996, 22:623～628
[117] 王春峰,李光泉,郑丕谔 协商型从者多人递阶决策系统诱导策略的研究.系统工程理论与实践,1996,11:28～33
[118] 徐飞,王浣尘 两层多目标集值优化问题的最优性条件.上海交通大学学报,1999,11(10):1268～1271
[119] Macal Charles M, (Argonne Nat1 Lab) Hurter Arthur P. Dependence of bilevel mathematical programs on irrelevant constraints. Computers and Operations Research, 1997, 24:1129～1140
[120] Candler W, Townsley R. A linear two-level programming problem. Computers and Operations Research, 1982, 9:59～76
[121] Bard J. An investigation of the lilnear three level programming problem. IEEE Transactions on System, Man, and Cybernetics, 1984, 14:711～717
[122] Bialas W, M Karwan. Two-level linear programming. Management Science, 1984, 30:1001～1020
[123] Wen U. The “Kth –Best” algorithm for multilevel programming. Technical Report, Department of Operations Research, State University of Mew York at Buffalo, 1981
[124] 刘红英,刘三阳,周永生 两层广义线性规划.系统工程学报,2000,15(2):131～135
[125] Papavassilopoulcs G. Algorithms for static Stracklberg games with linear costs and polyhedral constraints. In Proceedings of the 21st IEEE Conference on Decisions and Control, 1982, 647～652
[126] H. Tuy, A. Migdalas, and P. Varbrand. A global optimization approach for the linear two-level program. Journal of Global Optimization, 1993,3:1～23
[127] Chen Y. Florian M. On the geometry structure of linear bilevel programs: a dual approach. Technical Report, CRT-867, Centre de Researche sur les Transports, 1992
[128] Chen Y, Florian M, Wu S. A descent dual approach of linear bilevel programs. Technical Report, CRT-866, Centre de Researche sur les Transports, 1992
[129] Dempe S. A simple algorithm for the linear bilevel programming problem. Optimization, 1987, 18:373～385
[130] Fortuny-Amart J, McCarl B. A representation and economic interpretation of a two-level programming problem. Journal of the Optimization Research Science, 1981, 32:783～792
[131] Bard J, Moore J. A branch and bound algorithm for the bilevel programming problem. SIAM Journal on Scientific and Statistical Computing, 1990, 11:281～292
[132] AI-Khayyal F, Horst R, Pardalos P. Global optimization of concave functionsubject to quadratic constrains: an application in nonlinear bilevel programming. Annual of Operations Research, 1992, 34:125～147
[133] Edmunds T, Bard J. Algorithms for nonlinear bilevel mathematical programming. IEEE Transactions on Systems, Man, and Cybernetics, 1991, 21:83～89
[134] Hansen P, Jaumard B, Savard G. New branch-and –bound rules for linear bilevel programming.SIAM Journal on Scientific and Statistical Computing, 1992,13:1194～1217
[135] Bard J, Moore J. An algorithm for the discrete bilevel programming problem. Naval Research Logistics, 1992, 39:419～435
[136] Moore J, Bard J. The mixed integer linear bilevel programming problem. Operations Research, 1990, 38:911～921
[137] Wen U, Yang Y. Algorithm solving the mixed integer two-level linear programming problem. Computing and Operations Research, 1990, 17:133～142
[138] Wu S, Marotte P, Chen Y. A cutting plane method for linear bilevel programs. Systems Sciences and Mathematical Sciences, 1998, 2:125～133
[139] 倪明放,徐南荣,仲俊伟 混合整数两层线性规划的一个代理约束方法.东南大学学报,1994,24(1):77～82
[140] 沈厚才,徐南荣,仲俊伟 一类含有 0-1 变量的多目标两层决策方法研究. 东南大学学报,1995,25(6):125～130
[141] Bialas W, Karwan M, Shaw J. A parametric complementary pivot approach for two-level linear programming. Technical Report 80-2, State University of New York at Buffalo, Operations Research Program, 1980
[142] Judice J, Faustino A. The solution of the linear bilevel programming problem by using the linear complementary problem. Investigation Operational, 1988, 8:77～95
[143] Judice J, Faustino A. A sequential LCP method for bilevel linear programming. Annals of Operations Research, 1992, 34:89～106
[144] Judice J, Faustino A. The linear-quadratic bilevel programming problem. INFOR, 1994, 32:87～98
[145] Onal H. A modified simplex approach for solving bilevel linear programming problems. European Journal of Operational Research, 1993, 67:126～135
[146] Aiyoshi E, Shimizu K. Hierarchical decentralized systems and its new solution by a barrier method. IEEE Transactions on Systems, Man, and Cybernetics, 1981, 11:444～449
[147] Aiyoshi E, Shimizu K. A solution method for the static constrained Stackelbergproblem via penalty-method. IEEE Transactions on Automatic Control, 1984, 29:1111～1114
[148] Shimizu K, Aiyoshi E, A new computational method for Stackelberg and min-max problems by use of a penalty method. IEEE Transactions on Automatic Control, 1981, 26:460～466
[149] K. Shimizu. Two-level decision problems and their new solution methods by a penalty method, Control science and technology for the progress of society. IFAC, 1982, 2:1303～1308
[150] Bi Z, Calamai P, Conn A. An exact penalty function approach for the linear bilevel programming problem. Technical Report # 167-O-310789, University of Waterloo, Department of Systems Design Engineering, 1989
[151] Bi Z, Calamai P, Conn A. An exact penalty function approach for the nonlinear bilevel programming problem. Technical Report # 180-O-170591, University of Waterloo, Department of Systems Design Engineering, 1991
[152] Ishizuka Y, Aiyoshi E. Double penalty method for bilevel optimization problems. Annuals of Operations Research, 1992, 34:73～88
[153] Luo Z Q, Pang J S, Wu S. Exact penalty functions for mathematical programs and bilevel programs with analytic constraints. Technical Report, Department of Electrical and Computer Engineering McMaster University, 1993
[154] 盛昭翰,曹忻 具有主——从策略的多层规划课题的稳定性及优化算法.南京工学院学报,1987,17(4):74～85
[155] White D, Anandalingam G. A penalty function approach for solving bilevel linear programs. Journal of Global Optimization, 1993, 3:397～419
[156] 贾富臣 结合全局最优策略的双层规划线性算法.北京理工大学学报,1995,15(1): 6～12
[157] 周水生,刘三阳,刘红英 价格控制问题及其推广形式的罚函数法.系统工程学报,1999,14(2):156～161
[158] Marrotte P, Zhu D L. Exact and inexact penalty method for the generalized bilevel programming problem. Mathematical programming, 1996, Series A, 74(2):141～152
[159] 邓先礼,雷万明 用罚函数求解二层凸规划的方法.应用数学学报,2001,24(2):161～167
[160] 裴峥,黄天民 二层线性规划的模糊数学解法(Ⅱ).西南交通大学学报,2000,35(1):98～101
[161] 刘新旺,达庆利 一种多人递阶资源分配问题的模糊满意解.系统工程理论与实践,2000,1:51～56
[162] 腾春贤,李皓白 多人双层多目标决策问题的 L-Ufuzzy 目标规划算法.黑龙江大学自然科学学报,2000,17(3):36～38
[163] Wen U P, Huang A D. Simple tabu search method to solve the mixed-integer linear bilevel programming problem. European Journal of Operation Research, 1996, 88(3):563～571
[164] Gendreau M, Marcotte P, Savard G. Hybrid tabu-ascent algorithm for the linear bilevel programming problem. Journal of Global Optimization, 1996, 8(2):217～233
[165] 谈烨,仲俊伟,徐南荣 基于遗传算法的一类资源分配两层规划问题求解.东南大学学报,1999,29(4):12～16
[166] Yin Yafeng. Genetic-algorithm-based approach for the bilevel programming models. Journal of Transportation Engineering. ASCE 2000, 126(2):115～120
[167] 仲俊伟,徐南荣 两层决策的波尔兹曼机算法.系统工程学报,1995,10(1):7～13
[168] Wu CangPu. Hybrid technique for global optimization of hierarchical systems. Proceedings of the IEEE International Conference on Systems,Man and Cybernetics 1996, 3:14～17
[169] 李志刚,吴沧浦 兵力部署优化问题的混合算法.控制与决策,1997,12(5):602～605
[170] 杨若黎,顾基发 一类非线性两级规划问题的模拟退火求解.系统工程理论与实践,1997(7):52～58
[171] Sahin Kermal H, Ciric Amy R. Dual temperature simulated annealing approach for solving bilevel programming problems. Computers & Chemical Engineering, 1998, 23(1):11～25
[172] Bard J. A grid search algorithm for the linear bilevel programming problem. In proceedings of the 14th Annual Meeting of the American Institute for Decision Science, 1982, 256～258
[173] Tuy H, Migdalas A, Varbrand P. A quasi-concave minimization method for solving linear two-level programs. Journal of Global Optimization, 1994, (4):243～263
[174] Narula S, Nwosu A. A dynamic programming solution for the hierarchical linear programming problem. Technical Report 37-82, Rensselaer Polytechnic Institute, Department of Operations Research and Statistics, 1982
[175] 刘国山,韩继业,汪寿阳 双层优化问题的信赖域算法.科学通报,1998,43(4):383～387
[176] 徐飞,王浣尘 一主多从两层非光滑优化问题的集成算法.上海交通大学学报,1998,32(12):115～119
[177] Loridan P, Morgan J. New results on approximate solution in two-leveloptimization. Optimization, 1989,(20):819～836
[178] 万仲平 关于二层规划的逼近问题.系统科学与数学,2000,20(3):89～294
[179] 万仲平,姜明启,胡铁松 具有极小风险解的二层规划及其近似分解法.工程数学学报,2000,2:25～30
[180] Jan Rong-Hong, Chern Maw-Sheng. Nonlinear integer bilevel programming. Euripean Journal of Operational Research, 1994, 72(3):574～587
[181] 吕庆喆，盛昭翰，徐南荣 一类二层决策问题的 Frank-Wolfe 算法.东南大学学报,1996,26(1):75～80
[182] 夏洪盛,郜林春,贺建勋 一种交互式 Stackelberg 主从对策的两层决策方法.上海理工大学学报,1994,16(1):18～24
[183] 夏洪盛,郜林春,贺建勋 两层决策问题的全局优化方法.海南大学学报(自然科学版),1994,12(2):108～113
[184] 夏洪盛,任海英 具有递阶结构的多目标群决策方法. 海华侨大学学报(自然科学版),1994,,15(2):148～152
[185] 夏洪盛,王浣尘 一种多人有关联双层多目标交互式算法. 上海交通大学学报,1994,28(2):90～97
[186] 夏洪盛,贺建勋 基于主从策略的两层约束尺度决策方法.湖南大学学报,1994,21(5):19～24
[187] 向丽,顾培亮,王哲 两层多目标决策问题的模糊交互式决策方式.系统工程学报,1999,14(4):305～310
[188] 向丽,刘栋林 基于模糊集理论的一主多从目标优化方法.石油大学学报(自然科学版),2000,24(5):94～97
[189] 刘善存,邱菀华,魏存平 极大熵方法求解双层多目标决策问题.系统工程理论与时间,2000,3:99～103
[190] 盛昭翰,梁梁,徐南荣 基于 Stackelberg 对策的两层多目标决策.自动化学报,1993,19(6):691～698
[191] 赵蔚 两层多目标规划的罚函数.自动化报,1998,24(3):331～337
[192] 盛昭翰 主从递阶决策论——Stackelberg 问题.北京:科学出版社,1998
[193] LeBlanc L J, Boyce D E. A bilevel programming algorithm for exact solution of the network design problem with user-optimal flows. Transportation Research, 1998,22(3):259～265
[194] Ben-Ayed O,Boyce D E, Blaic C E. A general bilevel linear programming formulation of the network design problem. Transportation Research, 1988,22(B):311～318
[195] Bard J. Practical bilevel optimization: algorithm and applications. KluwerAcademic Publishers, 1999
[196] Tzeng Gwo-Hshiung, Tsaur Sheng-Hshiung. Application of hierarchical multistage multiobjective approach to network design: case of express road. IEEE International Engineering Management Conference, 1995, 28～30
[197] 单连龙,高自友 城市公交系统连续平衡网络设计的双层规划模型及求解算法.系统工程理论与实践,2000,7:85～93
[198] Marcotte P, Marquis G. Efficient implementation of heuristics for the continuous network design problem. Annals of Operations Research, 1992, (34):163～176
[199] Suh S, Kim T. Solving nonlinear bilevel programming models of the equilibrium network design problem: a comparative review. Annals of Operations Research, 1992, (34):203～218
[200] Marcotte P. Network design problem with congestion effects: a case of bilevel programming. Mathematical Programming, 1986, (34):142～162
[201] Migadalas A, Paradalos P M, Varbrand P. Eds. Multilevel Optimization Algorithms and Applications. Kluwer Academic Publishers, 1998
[202] Florian M, Chen Y. A bilevel programming approach to estimating O-D matrix by traffic counts. Technical Report CRT-750, Centre de Recherche sur les Transports, 1991
[203] Florian M, Chen Y. A coordinate descent method for bilevel O-D matrix estimation problems. Technical Report CRT-807, Centre de Recherche sur les Transports, 1993
[204] Maher Micheal J, Zhang Xiaoyan. Bi-level programming approach for trip matrix estimation and traffic control problems with stochastic user equilibtium link flows. Transportation Research, Part B: Methodological, 2001, 35(1):23～40
[205] 安梅,高自友,杨璐 O-D 需求估计的双层规划模型及基于灵敏度分析的求解算法.中国管理科学,2000,8(3):13～19
[206] Yang Hai, Yagar SAM. Traffic assignment and traffic control in general free way-arterial corridor systems. Transportation Research, Part B: Methodological, 1994, 28(6):463～486
[207] Yang Hai, Yagar SAM. Traffic assignment and traffic control in saturated road networks. Transportation Research, Part A: Policy and Practice, 1995, 29(2):125～139
[208] Migdalas, Athanasios. Bilevel programming in traffic planning: Models, methods and challenge. Journal of Global Optimization, 1995, 7(4):381～405
[209] Yang Hai. Equilibrium network traffic signal setting under conditions of queuing and congestion. Proceeding of the International Conference on Applications of Advanced Technologies in Transportation Engineering, 1995,578～582
[210] Yin Yafeng, Lu Huapu. Dynamic network traffic signal setting model. Gonglu Jiaotong Keji, 1997,14(3):11～16
[211] Chiou Suh-Wen. Optimization of area traffic control for equilibrium network flows. Transportation Science,1999, 33(3):279～289
[212] Bard J, Plummer J. Bilevel programming approach to determining Tax credits for biofuel production. European Journal of Operational Research, 2000, 120(1):30～46
[213] 谈烨,仲俊伟,徐荣南 多种资源在多项目间分配的两层决策方法.系统工程学报,1999,14(3):290～295
[214] Hobbs B, Nelson S. A nonlinear bilevel model for analysis of electric utility demand-side planning issues. Annals of Operation Research, 1992, (34):255～274
[215] Iyer R R, Grossmann I E. Synthesis and operational planning of utility systems for multiperiod operation. Computers & Chemical Engineering, 1998, 22(7～8):979～993
[216] 王先甲,关洪林 灌溉系统最优规划的二层动态规划模型.水电能源科学,1995,13(1):1～10
[217] Amouzegar Mahyar A, Moshirvaziri Khosrow. Determining optimal pollution control policies: an application of bilevel programming. European Journal of Operational Research, 1999, 119(1):100～120
[218] Goel, Preety Haghani, and Ali. Model for determining airline fares for meeting or convention demand. Journal of Transportation Engineering, 2000, 126(2):107~114
[219] Lam W H K, Zhou J. Optimal fare structure for transit networks with elastic demand. Transportation Research Record, 2000, (1733):8～14
[220] Haurie A, Loulou R, Savard G. A two-level systems analysis model of power cogeneration under asymmetric pricing. In Proceeding of IEEE Automatic Control Conference, San Diego, 1990
[221] Yokoyama, Ryohei, Tto, Koichi. Analysis of cooperation between central power utility and dispersed cogeneration systems through time-of-use pricing. American Society of Mechanical Engineers (Paper) n GT 1998
[222] 杨华,王庆 钢铁企业价格与产品结构综合决策问题研究.运筹与管理,1998,7(3):51～56
[223] 陈安,刘鲁,李刚,陈宁 虚拟企业协作博弈中的双优策略.系统工程理论与实践,2000,8:12～17
[224] 黄小原,卢震 一种交互式进化规划及其在供应链问题中的应用.东北大学学报(自然科学版),2000,21(5):569～572
[225] Nicholls Miles G. Aluminum production modeling-a nonlinear bilevel programming approach. Operations Research, 1995, 43(2):208～218
[226] Nicholls Miles G. Developing an integrated model of an aluminum smelter incorporating sub-models with different time bases and levels of aggregation. European Journal of Operational Research, 1997, 99(2):477～490
[227] Nicholls Miles G. Application of a nonlinear bilevel programming algorithm for the optimization of an aluminum smelter’s operations on a monthly and multiperiod basis. Proceeding-Annual Meeting of the Decision Sciences Institute, 1996, (2):969～971
[228] Karlof John K, Wang Wei. Bilevel programming applied to the flow shop-scheduling problem. Computers & Operations Research, 1996, 23(5):443～451
[229] 王锡禄,姚伟力,冯恩民 Job-Shop 调度问题的优化模型及算法.系统工程理论与实践,2000,11:84～93
[230] 李志刚,吴沧浦兵力部署优化问题的两层规划模型.北京理工大学学报,1997,17(3):268～272
[231] Miller T, Fiesz T, Tobin R. Heruistic algorithms for delivered price spatially competitive network facility location problems. Annals of Operations Research, 1993, (34):177～202
[232] Tobin R, Fiesz T, Spatial competition facility location models: definition, formulation and solution approach. Annals of Operations Research, 1986, (6):49～74
[233] Boyce David, Matsson Lar-Goran. Modeling residential location choice in relation to housing location and road tolls on congested urban highway networks. Transportation Research, Part B: Methodological, 1999, 33(8):581～591
[234] Candler W, Fortuny-Amat J, McCarl B. The potential role of multilevel programming in agricultural economics. American Journal of Agricultural Economics, 1981, (63):521～531
[235] Candler W, Norton R. Multilevel programming and development policy. Technical Report 258, World Bank Development Research Center, Washigton D. C. , 1977
[236] Onal, Hayri Darmawan, Delima H. Multilevel analysis of Agriculture credit distribution in East Java, Indonesia. Computers & Operations Research, 1995, 22(2):227～236
[237] Cellis M, Dennis J, Tapia R. A trust region strategy for nonlinear equality constrained optimization. In P. Boggs, R. Byrd, and R. Schnabel, editors, Numerrical Optimization 1984, 71～82. Philadelphia: SIAM Publ. , 1985
[238] Marcotte P, Savard G. Novel approaches to the discrimination problem. ZOR-Methods and Models of Optimizations Research, 1992, (36):517～545
[239] Lignola M, Morgan J. Topology and existence and stability for stackelberg problems. Journal of Optimizations of Theory and Applications, 1995, (84):145～169
[240] Kocvara M. Topology optimization with displacement constraints: A bilevel programming approach. Structural Optimization, 1997, 14(4):256～263
[241] Inuiguchi M, Higashitani H. On computation methods of the minimax regret solution for linear programming problems with uncertain objective function coefficients. Proceedings of the IEEE International Conference on Systems, Man and Cybernetics, 1999, 3(15):979～984
[242] Zadeh L. A., Fuzzy Sets, Information and Control, 1965, 8.338～353
[243] Bellman R. E., Zadeh L A. Decision~making in Fuzzy Environment[J], Mgt.Sci.1970, 17(2):141～164
[244] Verdegay J L, Using parametric programming in fuzzy linear programming [J], Fuzzy Sets and Systems, 1998, 11(3).243～251
[245] Werners B., An interactive fuzzy programming system [J]. Fuzzy Sets and Systems, 1998, 23(1):131～147
[246] 高培旺 模糊线性规划问题的一种新的单纯形法算法.模糊系统与数学,2002,16(3):64～68
[247] Zimmermann H J. Description and optimization of fuzzy system [J] Int. J. of General System, 1976, 2(3):209～216
[248] K. David Jamison, Weldon A. Lodwick, Fuzzy linear programming using a penalty method, Fuzzy Sets and Systems, 2001, 119.97～110
[249] 张曾科 模糊数学在自动化技术中的应用,北京:清华大学出版社,1997
[250] Rongjun Li and E. Stanly Lee, Fuzzy multiple objective programming and compromise programming with Pareto optimum, Fuzzy Sets and Systems, 1993, 53.275～288
[251] Trappey J. F. C., et al, Fuzzy non~linear programming: theory and application in manufacturing [J], Int. J. of Production Research, 1998, 26 (5):957～985
[252] 李荣钧 模糊多准则决策理论与应用,北京:科学出版社,2002
[253] H.R. Maleki, M. Tata, M. Mashinchi, Linear programming with fuzzy variables, Fuzzy Sets and Systems, 2000, 109.21～33
[254] Buckley J. Possibilistic linear programming with triangular fuzzy parameters (short communication) [J] Fuzzy Sets and Systems, 1988, 23.135～138
[255] 刘新旺,达庆利 一种基于约束满意度的模糊线性规划解法,系统工程学报,1998,13(3):35～40
[256] 彭祖赠 孙韫玉编著 模糊(Fuzzy)数学及其应用,武汉:武汉大学出版社,2003
[257] Xinwang Liu., Measuring the satisfaction of constraints in fuzzy linear programming, Fuzzy Sets and Systems, 2001, 122.263～275
[258] L. Lushu, S. Zhaohan, A new approach to fuzzy multiple objective programming [J], Fuzzy Math, 1996, 4(2):255～361
[259] Hsiao-Fan Wang, Yi-Chun Liao, Fuzzy non-linear integer programming by parametric programming approach, Fuzzy Sets and Systems, 2001,122.245～251
[260] 宋业新,姜礼平,陈绵云 一类模糊线性规划模型的模糊最优区间解,模糊系统与数学,2002,16(2):86～91
[261] M.K. Luhandiyla, Multiple objective programming problems with Possibilistic coefficients, Fuzzy Sets and Systems, 1987, 21.135～145
[262] 唐加福,汪定伟 模糊非线性规划对称模型基于遗传算法的模糊最优解,控制理论与应用,1998,15(4):525～530
[263] 曾庆宁 模糊系数规划,模糊系统与数学,2000,14(3):99～105
[264] M. Sakawa and H. Yano, Feasibility and Pareto optimality for multiobjective nonlinear programming problems with fuzzy parameters, Fuzzy Sets and Systems, 1991,43.1～15
[265] M. Sakawa and H. Yano, Interactive decision making for multiobjective nonlinear programming problems with fuzzy parameters, Fuzzy Sets and Systems, 1989, 29.315～326
[266] E. I. Ammar, Interactive stability of multiobjective NLP problems with fuzzy parameters in the objective functions and constrains, Fuzzy Sets and Systems, 2000,109.83～90
[267] 刘宝碇,赵瑞清 随机规划与模糊规划.北京:清华大学出版社,1998
[268] Liu B, Iwamura K. Fuzzy programming with fuzzy decisions and fuzzy simulation based evolutionary algorithm. Technical Report, 1997
[269] 秦红斌,肖人彬,钟毅芳 面向大批量定制的公共产品平台研究.中国机械工程,2004(2),221～225
[270] Robertson D, Ulrich K (1998), Planning for product platform, Sloan Management Review 39:19～31
[271] Achille Messas, Michael P. Martinez and Timothy W. Simpson, Effective Product Family Design Using Physical Programming, Engineering Optimization, 2002, Vol. 34, pp.245～261
[272] Raviraj U. Nayak, Wei Chen and Timothy W. Simpson, A Variation-Based Method for Product Family Design, Engineering Optimization, 2002, Vol. 34(1).65～81
[273] Timothy W. Simpson, Jonathan R. A. Maier, Farrokin Mistree, Product platform design: method and application, Research in Engineer Design, 13 (2001) 2～22
[274] Simpson, T. W. (1998), A concept exploration method for product family design, Ph.D. Dissertation, G. W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA
[275] 曹永强,曲晓飞 一种新的模糊线性规划方法,系统工程学报,1995,10(1):21～31
[276] 《运筹学》教材编写组,运筹学(修订版).北京:清华大学出版社,1990
[277] 吴育华、杜纲,管理科学基础.天津:天津大学出版社,2001
[278] H. Sh. Shih., Y. J. Lai., E. S. Lee., Fuzzy approach for multi-level programming problems, Computer & Operations Research, 1996,23(1).73～91
[279] 陈贻源 模糊数学.武汉:华中工学院出版社,1984
[280] 李全新 区间分析在管理方法中的应用:[硕士学位论文],天津:天津大学,1994
[281] 彭锦,刘宝碇,不确定规划的研究现状及其发展前景,运筹与管理,2002,11(2):1～10
[282] Meyer M. H. and Lehnerd A. P. (1997), The power of product: building value and cost leadership. Free Press, New York
[283] Eberhart R C ,Kennedy J. A new optimizer using particle swarm theory. In: Proceedings Sixth Symposiumon Micro Machine and Human Science, Piscataway, NJ, IEEE Service Center, 1995. 39243.
[284] Kennedy J,Eberhart R. Particle swarmoptimization[C]. IEEE International Conference on Neural Networks (Perth, Australia), IEEE Service Center, Piscataway, NJ, 1995, IV: 1942～1948.
[285] Shi Y, Eberhart R. A modified particle swarm optimizer [C]. IEEE International Conference on Evolutionary Computation, Anchorage, Alaska, May429,1998.
[286] Liu B, Y2K Liu. Expected value of fuzzy variable and fuzzy expected value models [J]. IEEE T ransations on Fuzzy Systems, 2002, 10 (4): 445- 450.
[287] Liu B. Theo ry and P ract ice of U ncertain P rogramm ing[M], Physica-V erlag,Heidelberg, 2002.
[2] Kevin N. Otto, Kristin L. Wood 等著.齐春萍,宫小东,张帆 等译. 产品设计[M]. 电子工业出版社,2005
[3] 冯培恩,邱清盈,潘双夏等 机械产品的广义优化设计进程研究[J].中国科学(E 辑),1999,29(4):338～346
[4] 邱清盈.机械广义优化设计的若干关键技术问题研究[D].杭州:浙江大学机械与能源工程学院,2000
[5] Jean-Francois B. Multidisciplinary Design Optimization Definition [EB/OL]. http://mdob.larc.nasa.gov, 2002-9-13/2003-3-20
[6] Anthony A G Frequently Asked Questions [EB/OL]. http://www.aero.ufl.edu/~issmo/, 2002k-10-17/2003-3-20
[7] Kodiyalam S. Evaluation of Methods for Multidisciplinary Design Optimization (MDO)-Phase I[R]. NASA CR208716, Virgjia:NASA 1998
[8] Srinivas, Kodiyalam, Charles Yuan. Evaluation of Methods for Multidisciplinary Design Optimization (MDO)-Part Ⅱ[R], NASA/CR——210313, Virgjia:NASA 2000
[9] Livne E year-in-review, Multidisciplinary Design Optimization [EB/OL]. http://www.rpi.edu/~messac/Publications/article98.htm.
[10] 周廷美,蓝悦明 机械设计零件与系统优化设计建模及应用[M] 北京:化学工业出版社,2004
[11] Ichiro Nishizaki, Masatosh Sakawa, Fuzzy cooperative game arising from linear production programming problem with fuzzy parameters[J], Fuzzy Sets and Systems, 2000(114),11-21
[12] Clodeinir Ronei Peres at, Fuzzy model and hierarchical fuzzy control integration: an approach for milling process optimization[J], Computers in Industry, 1999(39),199-207
[13] Baoding Liu, Studies in Fuzziness and Soft Computing[M], Physica-Verlag Heidelberg, 2002
[14] Davis S M. Future Perfect [M]. Reading:Addison-Wesley Publishing, 1987
[15] Pine B J Ⅱ.Mass Customization:The new Frontier in Business Competition[M]. Boston:Harvard Business School Press, 1993
[16] Womack J P. A book review of mass customization. Sloan Management Review, 1993, 34(3):121～122
[17] Beaty R T. Mass customization manufacturing Engineer, 1996, 75(5):217～220
[18] Eastwood, Margaret A. Implementing mass customization. Computers in industry, 1996, 30(3):171～174
[19] Rebecca D, Peter T W, Glenn W, et. Cl. Approaches to mass customization:configurations and empirical validation. Journal of Operations Management, 2000, 18:605～625
[20] 苏宝华 面向大量定制生产的建模理论、方法以及其应用研究:[博士学位论文].杭州:浙江大学,1998
[21] 李仁旺 大批量定制的若干理论与方法问题研究:[博士学位论文].杭州:浙江大学,1999
[22] 李仁旺,祁国宁,顾建新,彭卫平,吴昭同 大批量生产及其实施方法初探.中国机械工程,2001, 12(4):405～408
[23] 孙伟,刘晓冰,徐中 大规模客户化生产模式的实施策略及产品设计技术研究.大连理工大学学报,2000,40(2):203～206
[24] 刘晓冰,董建华,孙伟 产品族建模技术研究.计算机辅助设计与图形学学报,2001,13(7):1～6
[25] 陈国权 大批量定制生产方式的基本概念与实施方法.系统工程理论与实践,2000,5:35～41,61
[26] 董建华,肖田元,乔桂秀,赵骥 面向大规模定制的制造系统关键技术.计算机集成制造系统——CIMS, 2002, 8(8):589～592
[27] 肖田元,乔桂秀,韩向利等 汽车制造业大批量定制实施策略及关键技术.计算机集成制造系统——CIMS, 2001, 7(9):1～7
[28] 郑华林,刘飞,王逢春等 面向大规模定制的产品需求建模方法研究.中国机械工程,2003, 14(6):471～474
[29] 吴锋,唐跃华 产品大批量定制哲理分析及应用案例研究.管理工程学报,2002, 16(4):95～97
[30] 邵晓峰,黄培清,季建华 大规模定制生产模式的研究.工业工程与管理,2001, 2:12～17
[31] Lau, Ronal S M. Mass customization: the next industrial revolution. Industrial Management, 1995, 37(5):18～19
[32] Gilmore J H. Pine B J Ⅱ. Markets of one: creating customer-unique value through mass customization. Harvard business review, July, 2000
[33] Qiang Tu, Mark A V, Ragu-Nathan T S. The impact of time-base manufacturing practices on mass customization and value to customer. Journal of OperationsManagement, 2001, 19:201～217
[34] Koufteros X A, Vonderembse M A, Doll W J. Developing measures of time-base manufacturing. Journal of Operations Management, 1998, 16(1):21～41
[35] Zipkin, Paul. The limits of mass customization. Sloan Management Review, 2001,42(3):81～87
[36] Ghiassi M, Spera C. Defining the Internet-based supply chain system for mass customized markets. Computer & industrial Engineering, 2003, 45:17～41
[37] Martin G H, Jiao J X. Research on E-product development(ePD) for mass customization. Technovation, 2002, 22:717～724
[38] Rachel C, Andrew B W. Requirements capture: theory and practice. Technovation 1998, 18(8/9):497～511
[39] Tseng M. Mitchell, Jiao Jianxin. Design by for mass customization. Annals of the CIRP, 1996, 45(1):153～156
[40] Barry Berman. Should your firm adopt a mass customization strategy. Business Horizins, 2002, July-august:51～60
[41] McAdams D A, Stone R B, Wood K L. Functional Interdependence and Product Similarity Based on Customer Needs. Research in engineering Design, 1999, 11:11～19
[42] Stone R B, Wood K L, Crawford R H. Using quantitative functional models to develop product architectures, Research in engineering Design, 2002, 21(3):239～260
[43] Martin M V, Ishill K. Design for variety: developing standardized and modularized product platform architectures. Research in Engineering Design, 2002, 13:213～235
[44] Javier P Gonzalez-Zugasti, Kevin N Otto, John D Baker. Assessing value for product family design and selection [C]. ASME DETC, 99/DAC-8613
[45] 张曙 分散网络化制造[M].机械工业出版社,1999
[46] Joseph B II. Mass customization the new frontier in business competition[M]. Boston: Harvard Business School Press, 1993
[47] Mitchell M Tseng, Jianxin Jiao. A framework of virtual design for product customization [J] IEEE ,1997 (9):7～14
[48] Mitchell M Tseng, Jianxin Jiao. Case-based evolutionary design for mass customization[J] Computers and Industry Engineering, 1997,33 (1-2):319～323
[49] Jianxin Jiao, Mitchell M Tseng. Product family modeling design for mass customization[J] Computers and Industry Engineering , 1998 ,35 (3-4) :495～498
[50] Mitchell M Tseng, Jianxin Jiao. Design for mass customization[C] Annuals of the CIRP, 1996, 45 (1):153～156
[51] Bin S, Huang G Q, Mak KL. Web-based product platform development using graph theory [J] IEEE, 2002:107～112
[52] Javier P Gonz alez-Zugasti, Kevin N Otto. Platform-based spacecraft design: a formulat2ion and implementation procedure [J] IEEE, 2000:455～463
[53] Rebecca Duray, Peter T Ward. Approaches to mass customization: configuration and empirical validation [J] Operations Management, 2000,18:605～625
[54] Sehyun Mying, Soonhung Han. Knowledge-based parametric design of mechanical products based on configuration design method[J] Expert System with Applications, 2001 21:99～107
[55] Hernandez G, Allen J K, Simpson T W, et al. Robust design of families for products with production modeling and revaluation [J]. ASME Journal of Mechanical Design, 2001,6:183～190
[56] Jeffrey B Dahmus, Javier P Gonzalez-Zugasti, Kevin N Otto. Modular product architecture [C] ASME DETC, 2000/DTM-14565
[57] Mark V Martin, Kosuke Ishii. Design for variety:A methodology for developing product platform architectures[C] ASME DETC, 2000/DFM-14021
[58] Simpson T W, Chen W. Use of the robust concept exploration method to facilitate the design of a family of products[J] Simultaneous Engineering: Methodologies and Applications, 1999:247～278
[60] Messac A, Martinez M P , Simpson T W. Introduction of a product family penalty function using physical programming[J] ASME Journal of Mechanical Design, 2002 (2):164～172
[61] Nayak R U, Chen W, Simpson T W. A variation2based method for product family design [J] Engineering Optimization, 2002, 34 (1):65～81
[62] Messac A, Martinez M P, Simpson T W. A penalty function for product family design using physical programming [J] ASME Journal of Mechanical Design, 2002,124 (2):164～172
[63] Simpson T W, D’Souza B. A variable length genetic algorithm for product platform design[C] 9thAIAA/ ISSMO Symposium on Multidisciplinary Analysis and Optimization, Atlanta, GA, 2002, 9 (4-6):1～10
[64] D’Souza B, Simpson T W. A genetic algorithm based method for product family design optimization [J] ASME Design Engineering Technical Conferences -Design Automation Conference ( DAC) ,2002 ,9:1～10
[65] Hernandez G, Simpson T W, Allen J K. Robust design of product families for make-to-order systems[J] ASME Journal of Mechanical Design, 2001 , 23 (2):183～190
[66] Simpson T W, Chen W, Allen J K. Conceptual design of a family of products through the use of the robust concept exploration method[C] 6th AIAA/ USAF/NASA/ ISSMO Symposium on Multidisciplinary Analysis and Optimization, Bellevue, WA,1996, 9 (2):1535～1545
[67] Simpson T W, Mistree F. A concept exploration method for product family and product platform design [J] ASME Optimization in Industry II, 1999, 7:371～378
[68] Messac A , Martinez M P , Simpson T W. Effective product family design using physical programming and the product platform concept exploration method [J] Design ASME Automation Conference, 2000 (9):1～8
[69] Simpson T W, Maier J R A, Mistree F A. Product platform concept exploration method for product family design [D] ASME Design Theory and Methodology, 1999 (9):1～219
[70] Messac A, Martinez M P, Simpson T W. Effective product family design using physical program2ming [J] Engineering Optimization, 2002, 34 (3):245～261
[71] Daniel Sabin, Rainer Weigel. Product configuration framework-a survey[J] Intelligent Systems. IEEE, 1998:42～49
[72] Raviraj U Nayak, Wei Chen, Timothy W Simpson. A variation-based methodology for product family design[C] ASME DETC, 2000/DAC-14264
[73] Javier P Gonzalez-Zugasti, Kevin N Otto. Modular platform-based product family design[C] ASME DETC, 2000/DAC-14238
[74] 黄纯颖 设计方法学[M].机械工业出版社,1992
[75] 腾春贤,李智慧 二层规划的理论与应用,科学出版社,2002
[76] Bialas W F, Chew M N. On two-level optimization. IEEE transactions on automatic control, 1982,AC-26:211～214
[77] Bension H P. On the structure and properties of a linear multilevel programming problem Journal of Optimization Theory and Applications, 1989, 60:353～373
[78] Bard J F, Falk J E. An explicit solution to the multilevel programming problem. Computers and Operations Research, 1982, 9:77～100
[79] Kornal J, Liptak T. Two-level planning. Econometric, 1965, 33:141～169
[80] Freeland J, Baker N. Good partitioning in a hierarchical organization. Management Science, 1975, 3:673～678
[81] Cassidy R G, Kieby M J L, Raike W M. Efficient distribution of resource through three levels of government. Management Science, 1971, 17:462～473
[82] Baumol W J, Fabian T. Decomposition, pricing for decentralization and external economics. Management Science, 1964, 11:1～31
[83] Bracken J, McGill J. Mathematical programs with optimization problems in the constraints. Operations Research, 1973, 21:37～44
[84] Candler W, R Norton. Multilevel programming.1977, Technical Report 20, World Bank Development Research Center, Washington D. C
[85] Stackelberg H. The theory of the market economy. New York, Oxford:Oxford University Press. 1952
[86] Jeroslow R. The polynomial hierarchy and simple model for competitive analysis, Mathematical programming, 1985, 32:146～164
[87] Bard J. Some properties of the bilevel programming problem. Journal of Optimization Theory and Applications, 1991, 68:371～378
[88] Ben-Ayed O, Blair C. Computational difficulties of bilevel linear programming. Operations Research, 1990, 38:556～560
[89] Hansen P, Jaumard B, Savard G. New branch-and-bound rules for linear bilevel programming. SIAM Journal on Scientific and Statistical computing, 1992, 13:1194～1217
[90] Vicente L, Savard G, Judice J. Descent approaches for quadratic bilevel programming. Journal of Optimization Theory and Applications, 1994, 81:379～399
[91] Bard J. Optimality conditions for the bilevel programming problem. Naval Research Logistics Quarterly, 1984, 31:13～26
[92] Clarke P, Westerberg A. A note on the optimality conditions for the bilevel programming problem. Naval Research Logistics, 1988, 35:413～418
[93] Haurie A, Savard G, White D. A note on: an efficient point algorithm for a linear two-stage optimization problem. Operations Research, 1990, 38:553～555
[94] Bard J. An efficient algorithm for solving general bilevel programming problem. Mathematical Operations Research, 1983, 8:260～272
[95] Bard J. Convex two-level optimization. Mathematical Programming, 1988, 40:15～27
[96] Kostad C D, Lasdon L S. Derivative evaluation and computational experience with large bilevel mathematical programs. Journal of Optimization Theory and Applications. 1990, 65:485～499
[97] Ye J J, Ye X Y. Necessary optimality conditions for optimization problems with variational inequality constraints. Mathematical Operations Research, 1997, 22:977～997
[98] Chen Y, Florian M. The nonlinear bilevel programming problem: a general formulation and optimality condition. 1991, Technical Report CRT-974, Centre de Research sur les Transports
[99] Dempe S. A necessary and a sufficient optimality condition for bilevel programming problems. Optimization, 1992,25:341～354
[100] Dempe S. Optimality conditions for bilevel programming problem. In P. Kall, editor, System modeling and optimization. Berlin:Springer-Verlag, 1992:17～24
[101] Outrata J. Necessary optimality conditions for Strackelderg problems. Journal of Optimization Theory and Applications, 1993, 76:305～320
[102] Ye J, Zhu D. Optimality conditions for bilevel programming problems. Technical Report DMs-618-IR, University of Victoria, Department of Mathematics and Statistics, 1993
[103] Bi Z, Calamai P. Optimality conditions for a class of bilevel programming problems. Technical report # 191-O-191291, University of Waterloo, Department of systems Design Engineering, 1991
[104] Tanion T, Ogawa T. An algorithm for solving two-level convex optimization problems, Int. System Science, 1984, 15:163～174
[105] Shimizu K, Ishizuka Y. Optimality conditions and algorithms for parameter design problem with two-level structure. IEEE Transactions on Automatic Control, 1985, AC-30, 986～993
[106] Ishizuka, Y. Optimality conditions for quasi-differentiable programs with application to two-level optimization. SIAM Journal of Control Optimization, 1988, 26:1388～1398
[107] 王春峰,李光泉,郑丕谔 动态多人递阶决策问题——结构、非光滑及必要性条件.系统工程学报,1996,11(4):27～36
[108] Savard G, Gauvin J. The steepest descent direction for the nonlinear bilevel programming problem. Oprations Research Letters, 1994, 15:275～282
[109] Vicente L, Calamai P. Geometry and local optimality conditions for bilevel programs with quadratic strictly convex lower levels. In D.-Z. Du and P. M. Pardalos, editors, Minmax and applications. Dordrecht, The Netherlands:Kluwer Academic Publishers Group, 1995:141～151
[110] 王先甲,冯尚友 二层系统最优化理论[M].科学出版社,1995
[111] Shimizu K, Aiyoshi E. Hierarchical multi-objective decision systems for general resource allocation problem. Journal of Optimization Theory and Applications, 1981, 35:517～533
[112] Tarvainent K, Haimes Y Y. Coordination of hierarchical multi-objective systems. IEEE Transactions on systems. Man, and Cybernetics, 1982, SMC-12, 751～764
[113] Li D, Haimes Y Y. Hierarchical generating method for large scale multi-objective systems. Journal of Optimization Theory and Applications, 1987, 54:303～333
[114] 唐大宏 几类多目标决策问题的分析方法研究(博士论文).华中理工大学,1989
[115] 杨丰梅 双层多目标规划问题的 Pareto 有效解.北京化工大学学报,1994,21(3):79～85
[116] Zhen Ling, Wang Rishuang. Study on some problems of bilevel multi- objectivesystems. Beijing Huangkong Hangtian Xuebao, 1996, 22:623～628
[117] 王春峰,李光泉,郑丕谔 协商型从者多人递阶决策系统诱导策略的研究.系统工程理论与实践,1996,11:28～33
[118] 徐飞,王浣尘 两层多目标集值优化问题的最优性条件.上海交通大学学报,1999,11(10):1268～1271
[119] Macal Charles M, (Argonne Nat1 Lab) Hurter Arthur P. Dependence of bilevel mathematical programs on irrelevant constraints. Computers and Operations Research, 1997, 24:1129～1140
[120] Candler W, Townsley R. A linear two-level programming problem. Computers and Operations Research, 1982, 9:59～76
[121] Bard J. An investigation of the lilnear three level programming problem. IEEE Transactions on System, Man, and Cybernetics, 1984, 14:711～717
[122] Bialas W, M Karwan. Two-level linear programming. Management Science, 1984, 30:1001～1020
[123] Wen U. The “Kth –Best” algorithm for multilevel programming. Technical Report, Department of Operations Research, State University of Mew York at Buffalo, 1981
[124] 刘红英,刘三阳,周永生 两层广义线性规划.系统工程学报,2000,15(2):131～135
[125] Papavassilopoulcs G. Algorithms for static Stracklberg games with linear costs and polyhedral constraints. In Proceedings of the 21st IEEE Conference on Decisions and Control, 1982, 647～652
[126] H. Tuy, A. Migdalas, and P. Varbrand. A global optimization approach for the linear two-level program. Journal of Global Optimization, 1993,3:1～23
[127] Chen Y. Florian M. On the geometry structure of linear bilevel programs: a dual approach. Technical Report, CRT-867, Centre de Researche sur les Transports, 1992
[128] Chen Y, Florian M, Wu S. A descent dual approach of linear bilevel programs. Technical Report, CRT-866, Centre de Researche sur les Transports, 1992
[129] Dempe S. A simple algorithm for the linear bilevel programming problem. Optimization, 1987, 18:373～385
[130] Fortuny-Amart J, McCarl B. A representation and economic interpretation of a two-level programming problem. Journal of the Optimization Research Science, 1981, 32:783～792
[131] Bard J, Moore J. A branch and bound algorithm for the bilevel programming problem. SIAM Journal on Scientific and Statistical Computing, 1990, 11:281～292
[132] AI-Khayyal F, Horst R, Pardalos P. Global optimization of concave functionsubject to quadratic constrains: an application in nonlinear bilevel programming. Annual of Operations Research, 1992, 34:125～147
[133] Edmunds T, Bard J. Algorithms for nonlinear bilevel mathematical programming. IEEE Transactions on Systems, Man, and Cybernetics, 1991, 21:83～89
[134] Hansen P, Jaumard B, Savard G. New branch-and –bound rules for linear bilevel programming.SIAM Journal on Scientific and Statistical Computing, 1992,13:1194～1217
[135] Bard J, Moore J. An algorithm for the discrete bilevel programming problem. Naval Research Logistics, 1992, 39:419～435
[136] Moore J, Bard J. The mixed integer linear bilevel programming problem. Operations Research, 1990, 38:911～921
[137] Wen U, Yang Y. Algorithm solving the mixed integer two-level linear programming problem. Computing and Operations Research, 1990, 17:133～142
[138] Wu S, Marotte P, Chen Y. A cutting plane method for linear bilevel programs. Systems Sciences and Mathematical Sciences, 1998, 2:125～133
[139] 倪明放,徐南荣,仲俊伟 混合整数两层线性规划的一个代理约束方法.东南大学学报,1994,24(1):77～82
[140] 沈厚才,徐南荣,仲俊伟 一类含有 0-1 变量的多目标两层决策方法研究. 东南大学学报,1995,25(6):125～130
[141] Bialas W, Karwan M, Shaw J. A parametric complementary pivot approach for two-level linear programming. Technical Report 80-2, State University of New York at Buffalo, Operations Research Program, 1980
[142] Judice J, Faustino A. The solution of the linear bilevel programming problem by using the linear complementary problem. Investigation Operational, 1988, 8:77～95
[143] Judice J, Faustino A. A sequential LCP method for bilevel linear programming. Annals of Operations Research, 1992, 34:89～106
[144] Judice J, Faustino A. The linear-quadratic bilevel programming problem. INFOR, 1994, 32:87～98
[145] Onal H. A modified simplex approach for solving bilevel linear programming problems. European Journal of Operational Research, 1993, 67:126～135
[146] Aiyoshi E, Shimizu K. Hierarchical decentralized systems and its new solution by a barrier method. IEEE Transactions on Systems, Man, and Cybernetics, 1981, 11:444～449
[147] Aiyoshi E, Shimizu K. A solution method for the static constrained Stackelbergproblem via penalty-method. IEEE Transactions on Automatic Control, 1984, 29:1111～1114
[148] Shimizu K, Aiyoshi E, A new computational method for Stackelberg and min-max problems by use of a penalty method. IEEE Transactions on Automatic Control, 1981, 26:460～466
[149] K. Shimizu. Two-level decision problems and their new solution methods by a penalty method, Control science and technology for the progress of society. IFAC, 1982, 2:1303～1308
[150] Bi Z, Calamai P, Conn A. An exact penalty function approach for the linear bilevel programming problem. Technical Report # 167-O-310789, University of Waterloo, Department of Systems Design Engineering, 1989
[151] Bi Z, Calamai P, Conn A. An exact penalty function approach for the nonlinear bilevel programming problem. Technical Report # 180-O-170591, University of Waterloo, Department of Systems Design Engineering, 1991
[152] Ishizuka Y, Aiyoshi E. Double penalty method for bilevel optimization problems. Annuals of Operations Research, 1992, 34:73～88
[153] Luo Z Q, Pang J S, Wu S. Exact penalty functions for mathematical programs and bilevel programs with analytic constraints. Technical Report, Department of Electrical and Computer Engineering McMaster University, 1993
[154] 盛昭翰,曹忻 具有主——从策略的多层规划课题的稳定性及优化算法.南京工学院学报,1987,17(4):74～85
[155] White D, Anandalingam G. A penalty function approach for solving bilevel linear programs. Journal of Global Optimization, 1993, 3:397～419
[156] 贾富臣 结合全局最优策略的双层规划线性算法.北京理工大学学报,1995,15(1): 6～12
[157] 周水生,刘三阳,刘红英 价格控制问题及其推广形式的罚函数法.系统工程学报,1999,14(2):156～161
[158] Marrotte P, Zhu D L. Exact and inexact penalty method for the generalized bilevel programming problem. Mathematical programming, 1996, Series A, 74(2):141～152
[159] 邓先礼,雷万明 用罚函数求解二层凸规划的方法.应用数学学报,2001,24(2):161～167
[160] 裴峥,黄天民 二层线性规划的模糊数学解法(Ⅱ).西南交通大学学报,2000,35(1):98～101
[161] 刘新旺,达庆利 一种多人递阶资源分配问题的模糊满意解.系统工程理论与实践,2000,1:51～56
[162] 腾春贤,李皓白 多人双层多目标决策问题的 L-Ufuzzy 目标规划算法.黑龙江大学自然科学学报,2000,17(3):36～38
[163] Wen U P, Huang A D. Simple tabu search method to solve the mixed-integer linear bilevel programming problem. European Journal of Operation Research, 1996, 88(3):563～571
[164] Gendreau M, Marcotte P, Savard G. Hybrid tabu-ascent algorithm for the linear bilevel programming problem. Journal of Global Optimization, 1996, 8(2):217～233
[165] 谈烨,仲俊伟,徐南荣 基于遗传算法的一类资源分配两层规划问题求解.东南大学学报,1999,29(4):12～16
[166] Yin Yafeng. Genetic-algorithm-based approach for the bilevel programming models. Journal of Transportation Engineering. ASCE 2000, 126(2):115～120
[167] 仲俊伟,徐南荣 两层决策的波尔兹曼机算法.系统工程学报,1995,10(1):7～13
[168] Wu CangPu. Hybrid technique for global optimization of hierarchical systems. Proceedings of the IEEE International Conference on Systems,Man and Cybernetics 1996, 3:14～17
[169] 李志刚,吴沧浦 兵力部署优化问题的混合算法.控制与决策,1997,12(5):602～605
[170] 杨若黎,顾基发 一类非线性两级规划问题的模拟退火求解.系统工程理论与实践,1997(7):52～58
[171] Sahin Kermal H, Ciric Amy R. Dual temperature simulated annealing approach for solving bilevel programming problems. Computers & Chemical Engineering, 1998, 23(1):11～25
[172] Bard J. A grid search algorithm for the linear bilevel programming problem. In proceedings of the 14th Annual Meeting of the American Institute for Decision Science, 1982, 256～258
[173] Tuy H, Migdalas A, Varbrand P. A quasi-concave minimization method for solving linear two-level programs. Journal of Global Optimization, 1994, (4):243～263
[174] Narula S, Nwosu A. A dynamic programming solution for the hierarchical linear programming problem. Technical Report 37-82, Rensselaer Polytechnic Institute, Department of Operations Research and Statistics, 1982
[175] 刘国山,韩继业,汪寿阳 双层优化问题的信赖域算法.科学通报,1998,43(4):383～387
[176] 徐飞,王浣尘 一主多从两层非光滑优化问题的集成算法.上海交通大学学报,1998,32(12):115～119
[177] Loridan P, Morgan J. New results on approximate solution in two-leveloptimization. Optimization, 1989,(20):819～836
[178] 万仲平 关于二层规划的逼近问题.系统科学与数学,2000,20(3):89～294
[179] 万仲平,姜明启,胡铁松 具有极小风险解的二层规划及其近似分解法.工程数学学报,2000,2:25～30
[180] Jan Rong-Hong, Chern Maw-Sheng. Nonlinear integer bilevel programming. Euripean Journal of Operational Research, 1994, 72(3):574～587
[181] 吕庆喆，盛昭翰，徐南荣 一类二层决策问题的 Frank-Wolfe 算法.东南大学学报,1996,26(1):75～80
[182] 夏洪盛,郜林春,贺建勋 一种交互式 Stackelberg 主从对策的两层决策方法.上海理工大学学报,1994,16(1):18～24
[183] 夏洪盛,郜林春,贺建勋 两层决策问题的全局优化方法.海南大学学报(自然科学版),1994,12(2):108～113
[184] 夏洪盛,任海英 具有递阶结构的多目标群决策方法. 海华侨大学学报(自然科学版),1994,,15(2):148～152
[185] 夏洪盛,王浣尘 一种多人有关联双层多目标交互式算法. 上海交通大学学报,1994,28(2):90～97
[186] 夏洪盛,贺建勋 基于主从策略的两层约束尺度决策方法.湖南大学学报,1994,21(5):19～24
[187] 向丽,顾培亮,王哲 两层多目标决策问题的模糊交互式决策方式.系统工程学报,1999,14(4):305～310
[188] 向丽,刘栋林 基于模糊集理论的一主多从目标优化方法.石油大学学报(自然科学版),2000,24(5):94～97
[189] 刘善存,邱菀华,魏存平 极大熵方法求解双层多目标决策问题.系统工程理论与时间,2000,3:99～103
[190] 盛昭翰,梁梁,徐南荣 基于 Stackelberg 对策的两层多目标决策.自动化学报,1993,19(6):691～698
[191] 赵蔚 两层多目标规划的罚函数.自动化报,1998,24(3):331～337
[192] 盛昭翰 主从递阶决策论——Stackelberg 问题.北京:科学出版社,1998
[193] LeBlanc L J, Boyce D E. A bilevel programming algorithm for exact solution of the network design problem with user-optimal flows. Transportation Research, 1998,22(3):259～265
[194] Ben-Ayed O,Boyce D E, Blaic C E. A general bilevel linear programming formulation of the network design problem. Transportation Research, 1988,22(B):311～318
[195] Bard J. Practical bilevel optimization: algorithm and applications. KluwerAcademic Publishers, 1999
[196] Tzeng Gwo-Hshiung, Tsaur Sheng-Hshiung. Application of hierarchical multistage multiobjective approach to network design: case of express road. IEEE International Engineering Management Conference, 1995, 28～30
[197] 单连龙,高自友 城市公交系统连续平衡网络设计的双层规划模型及求解算法.系统工程理论与实践,2000,7:85～93
[198] Marcotte P, Marquis G. Efficient implementation of heuristics for the continuous network design problem. Annals of Operations Research, 1992, (34):163～176
[199] Suh S, Kim T. Solving nonlinear bilevel programming models of the equilibrium network design problem: a comparative review. Annals of Operations Research, 1992, (34):203～218
[200] Marcotte P. Network design problem with congestion effects: a case of bilevel programming. Mathematical Programming, 1986, (34):142～162
[201] Migadalas A, Paradalos P M, Varbrand P. Eds. Multilevel Optimization Algorithms and Applications. Kluwer Academic Publishers, 1998
[202] Florian M, Chen Y. A bilevel programming approach to estimating O-D matrix by traffic counts. Technical Report CRT-750, Centre de Recherche sur les Transports, 1991
[203] Florian M, Chen Y. A coordinate descent method for bilevel O-D matrix estimation problems. Technical Report CRT-807, Centre de Recherche sur les Transports, 1993
[204] Maher Micheal J, Zhang Xiaoyan. Bi-level programming approach for trip matrix estimation and traffic control problems with stochastic user equilibtium link flows. Transportation Research, Part B: Methodological, 2001, 35(1):23～40
[205] 安梅,高自友,杨璐 O-D 需求估计的双层规划模型及基于灵敏度分析的求解算法.中国管理科学,2000,8(3):13～19
[206] Yang Hai, Yagar SAM. Traffic assignment and traffic control in general free way-arterial corridor systems. Transportation Research, Part B: Methodological, 1994, 28(6):463～486
[207] Yang Hai, Yagar SAM. Traffic assignment and traffic control in saturated road networks. Transportation Research, Part A: Policy and Practice, 1995, 29(2):125～139
[208] Migdalas, Athanasios. Bilevel programming in traffic planning: Models, methods and challenge. Journal of Global Optimization, 1995, 7(4):381～405
[209] Yang Hai. Equilibrium network traffic signal setting under conditions of queuing and congestion. Proceeding of the International Conference on Applications of Advanced Technologies in Transportation Engineering, 1995,578～582
[210] Yin Yafeng, Lu Huapu. Dynamic network traffic signal setting model. Gonglu Jiaotong Keji, 1997,14(3):11～16
[211] Chiou Suh-Wen. Optimization of area traffic control for equilibrium network flows. Transportation Science,1999, 33(3):279～289
[212] Bard J, Plummer J. Bilevel programming approach to determining Tax credits for biofuel production. European Journal of Operational Research, 2000, 120(1):30～46
[213] 谈烨,仲俊伟,徐荣南 多种资源在多项目间分配的两层决策方法.系统工程学报,1999,14(3):290～295
[214] Hobbs B, Nelson S. A nonlinear bilevel model for analysis of electric utility demand-side planning issues. Annals of Operation Research, 1992, (34):255～274
[215] Iyer R R, Grossmann I E. Synthesis and operational planning of utility systems for multiperiod operation. Computers & Chemical Engineering, 1998, 22(7～8):979～993
[216] 王先甲,关洪林 灌溉系统最优规划的二层动态规划模型.水电能源科学,1995,13(1):1～10
[217] Amouzegar Mahyar A, Moshirvaziri Khosrow. Determining optimal pollution control policies: an application of bilevel programming. European Journal of Operational Research, 1999, 119(1):100～120
[218] Goel, Preety Haghani, and Ali. Model for determining airline fares for meeting or convention demand. Journal of Transportation Engineering, 2000, 126(2):107~114
[219] Lam W H K, Zhou J. Optimal fare structure for transit networks with elastic demand. Transportation Research Record, 2000, (1733):8～14
[220] Haurie A, Loulou R, Savard G. A two-level systems analysis model of power cogeneration under asymmetric pricing. In Proceeding of IEEE Automatic Control Conference, San Diego, 1990
[221] Yokoyama, Ryohei, Tto, Koichi. Analysis of cooperation between central power utility and dispersed cogeneration systems through time-of-use pricing. American Society of Mechanical Engineers (Paper) n GT 1998
[222] 杨华,王庆 钢铁企业价格与产品结构综合决策问题研究.运筹与管理,1998,7(3):51～56
[223] 陈安,刘鲁,李刚,陈宁 虚拟企业协作博弈中的双优策略.系统工程理论与实践,2000,8:12～17
[224] 黄小原,卢震 一种交互式进化规划及其在供应链问题中的应用.东北大学学报(自然科学版),2000,21(5):569～572
[225] Nicholls Miles G. Aluminum production modeling-a nonlinear bilevel programming approach. Operations Research, 1995, 43(2):208～218
[226] Nicholls Miles G. Developing an integrated model of an aluminum smelter incorporating sub-models with different time bases and levels of aggregation. European Journal of Operational Research, 1997, 99(2):477～490
[227] Nicholls Miles G. Application of a nonlinear bilevel programming algorithm for the optimization of an aluminum smelter’s operations on a monthly and multiperiod basis. Proceeding-Annual Meeting of the Decision Sciences Institute, 1996, (2):969～971
[228] Karlof John K, Wang Wei. Bilevel programming applied to the flow shop-scheduling problem. Computers & Operations Research, 1996, 23(5):443～451
[229] 王锡禄,姚伟力,冯恩民 Job-Shop 调度问题的优化模型及算法.系统工程理论与实践,2000,11:84～93
[230] 李志刚,吴沧浦兵力部署优化问题的两层规划模型.北京理工大学学报,1997,17(3):268～272
[231] Miller T, Fiesz T, Tobin R. Heruistic algorithms for delivered price spatially competitive network facility location problems. Annals of Operations Research, 1993, (34):177～202
[232] Tobin R, Fiesz T, Spatial competition facility location models: definition, formulation and solution approach. Annals of Operations Research, 1986, (6):49～74
[233] Boyce David, Matsson Lar-Goran. Modeling residential location choice in relation to housing location and road tolls on congested urban highway networks. Transportation Research, Part B: Methodological, 1999, 33(8):581～591
[234] Candler W, Fortuny-Amat J, McCarl B. The potential role of multilevel programming in agricultural economics. American Journal of Agricultural Economics, 1981, (63):521～531
[235] Candler W, Norton R. Multilevel programming and development policy. Technical Report 258, World Bank Development Research Center, Washigton D. C. , 1977
[236] Onal, Hayri Darmawan, Delima H. Multilevel analysis of Agriculture credit distribution in East Java, Indonesia. Computers & Operations Research, 1995, 22(2):227～236
[237] Cellis M, Dennis J, Tapia R. A trust region strategy for nonlinear equality constrained optimization. In P. Boggs, R. Byrd, and R. Schnabel, editors, Numerrical Optimization 1984, 71～82. Philadelphia: SIAM Publ. , 1985
[238] Marcotte P, Savard G. Novel approaches to the discrimination problem. ZOR-Methods and Models of Optimizations Research, 1992, (36):517～545
[239] Lignola M, Morgan J. Topology and existence and stability for stackelberg problems. Journal of Optimizations of Theory and Applications, 1995, (84):145～169
[240] Kocvara M. Topology optimization with displacement constraints: A bilevel programming approach. Structural Optimization, 1997, 14(4):256～263
[241] Inuiguchi M, Higashitani H. On computation methods of the minimax regret solution for linear programming problems with uncertain objective function coefficients. Proceedings of the IEEE International Conference on Systems, Man and Cybernetics, 1999, 3(15):979～984
[242] Zadeh L. A., Fuzzy Sets, Information and Control, 1965, 8.338～353
[243] Bellman R. E., Zadeh L A. Decision~making in Fuzzy Environment[J], Mgt.Sci.1970, 17(2):141～164
[244] Verdegay J L, Using parametric programming in fuzzy linear programming [J], Fuzzy Sets and Systems, 1998, 11(3).243～251
[245] Werners B., An interactive fuzzy programming system [J]. Fuzzy Sets and Systems, 1998, 23(1):131～147
[246] 高培旺 模糊线性规划问题的一种新的单纯形法算法.模糊系统与数学,2002,16(3):64～68
[247] Zimmermann H J. Description and optimization of fuzzy system [J] Int. J. of General System, 1976, 2(3):209～216
[248] K. David Jamison, Weldon A. Lodwick, Fuzzy linear programming using a penalty method, Fuzzy Sets and Systems, 2001, 119.97～110
[249] 张曾科 模糊数学在自动化技术中的应用,北京:清华大学出版社,1997
[250] Rongjun Li and E. Stanly Lee, Fuzzy multiple objective programming and compromise programming with Pareto optimum, Fuzzy Sets and Systems, 1993, 53.275～288
[251] Trappey J. F. C., et al, Fuzzy non~linear programming: theory and application in manufacturing [J], Int. J. of Production Research, 1998, 26 (5):957～985
[252] 李荣钧 模糊多准则决策理论与应用,北京:科学出版社,2002
[253] H.R. Maleki, M. Tata, M. Mashinchi, Linear programming with fuzzy variables, Fuzzy Sets and Systems, 2000, 109.21～33
[254] Buckley J. Possibilistic linear programming with triangular fuzzy parameters (short communication) [J] Fuzzy Sets and Systems, 1988, 23.135～138
[255] 刘新旺,达庆利 一种基于约束满意度的模糊线性规划解法,系统工程学报,1998,13(3):35～40
[256] 彭祖赠 孙韫玉编著 模糊(Fuzzy)数学及其应用,武汉:武汉大学出版社,2003
[257] Xinwang Liu., Measuring the satisfaction of constraints in fuzzy linear programming, Fuzzy Sets and Systems, 2001, 122.263～275
[258] L. Lushu, S. Zhaohan, A new approach to fuzzy multiple objective programming [J], Fuzzy Math, 1996, 4(2):255～361
[259] Hsiao-Fan Wang, Yi-Chun Liao, Fuzzy non-linear integer programming by parametric programming approach, Fuzzy Sets and Systems, 2001,122.245～251
[260] 宋业新,姜礼平,陈绵云 一类模糊线性规划模型的模糊最优区间解,模糊系统与数学,2002,16(2):86～91
[261] M.K. Luhandiyla, Multiple objective programming problems with Possibilistic coefficients, Fuzzy Sets and Systems, 1987, 21.135～145
[262] 唐加福,汪定伟 模糊非线性规划对称模型基于遗传算法的模糊最优解,控制理论与应用,1998,15(4):525～530
[263] 曾庆宁 模糊系数规划,模糊系统与数学,2000,14(3):99～105
[264] M. Sakawa and H. Yano, Feasibility and Pareto optimality for multiobjective nonlinear programming problems with fuzzy parameters, Fuzzy Sets and Systems, 1991,43.1～15
[265] M. Sakawa and H. Yano, Interactive decision making for multiobjective nonlinear programming problems with fuzzy parameters, Fuzzy Sets and Systems, 1989, 29.315～326
[266] E. I. Ammar, Interactive stability of multiobjective NLP problems with fuzzy parameters in the objective functions and constrains, Fuzzy Sets and Systems, 2000,109.83～90
[267] 刘宝碇,赵瑞清 随机规划与模糊规划.北京:清华大学出版社,1998
[268] Liu B, Iwamura K. Fuzzy programming with fuzzy decisions and fuzzy simulation based evolutionary algorithm. Technical Report, 1997
[269] 秦红斌,肖人彬,钟毅芳 面向大批量定制的公共产品平台研究.中国机械工程,2004(2),221～225
[270] Robertson D, Ulrich K (1998), Planning for product platform, Sloan Management Review 39:19～31
[271] Achille Messas, Michael P. Martinez and Timothy W. Simpson, Effective Product Family Design Using Physical Programming, Engineering Optimization, 2002, Vol. 34, pp.245～261
[272] Raviraj U. Nayak, Wei Chen and Timothy W. Simpson, A Variation-Based Method for Product Family Design, Engineering Optimization, 2002, Vol. 34(1).65～81
[273] Timothy W. Simpson, Jonathan R. A. Maier, Farrokin Mistree, Product platform design: method and application, Research in Engineer Design, 13 (2001) 2～22
[274] Simpson, T. W. (1998), A concept exploration method for product family design, Ph.D. Dissertation, G. W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA
[275] 曹永强,曲晓飞 一种新的模糊线性规划方法,系统工程学报,1995,10(1):21～31
[276] 《运筹学》教材编写组,运筹学(修订版).北京:清华大学出版社,1990
[277] 吴育华、杜纲,管理科学基础.天津:天津大学出版社,2001
[278] H. Sh. Shih., Y. J. Lai., E. S. Lee., Fuzzy approach for multi-level programming problems, Computer & Operations Research, 1996,23(1).73～91
[279] 陈贻源 模糊数学.武汉:华中工学院出版社,1984
[280] 李全新 区间分析在管理方法中的应用:[硕士学位论文],天津:天津大学,1994
[281] 彭锦,刘宝碇,不确定规划的研究现状及其发展前景,运筹与管理,2002,11(2):1～10
[282] Meyer M. H. and Lehnerd A. P. (1997), The power of product: building value and cost leadership. Free Press, New York
[283] Eberhart R C ,Kennedy J. A new optimizer using particle swarm theory. In: Proceedings Sixth Symposiumon Micro Machine and Human Science, Piscataway, NJ, IEEE Service Center, 1995. 39243.
[284] Kennedy J,Eberhart R. Particle swarmoptimization[C]. IEEE International Conference on Neural Networks (Perth, Australia), IEEE Service Center, Piscataway, NJ, 1995, IV: 1942～1948.
[285] Shi Y, Eberhart R. A modified particle swarm optimizer [C]. IEEE International Conference on Evolutionary Computation, Anchorage, Alaska, May429,1998.
[286] Liu B, Y2K Liu. Expected value of fuzzy variable and fuzzy expected value models [J]. IEEE T ransations on Fuzzy Systems, 2002, 10 (4): 445- 450.
[287] Liu B. Theo ry and P ract ice of U ncertain P rogramm ing[M], Physica-V erlag,Heidelberg, 2002.
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |