不确定条件下基于遗传算法的柔性作业车间调度问题研究
|
摘要
制造业是国民经济的重要组成部分。然而,实际生产中的制造加工时间、完工时间和产品交货期等无法用确定的参数进行描述和研究,生产过程的不确定性已成为现在调度理论应用于实际的瓶颈。人们迫切需要对不确定条件下的车间调度问题理论及其应用进行深入和广泛的研究,以更好地指导实际生产。本文正是在这样的背景下,结合实际生产调度问题所面临的多目标和多约束等问题,对具有不确定加工时间和交货期的柔性作业车间调度问题进行研究,并取得了一些有意义的研究成果。
本文首先对课题的来源,研究的目的、背景和意义进行介绍。概述调度问题和其主要研究方法,阐述调度问题的分类和主要特点,并针对不确定条件下的车间调度问题,对目前的主要研究方法和国内外研究现状进行系统地综述和深入的分析,指出所存在的问题。接着对不确定条件下的模糊调度问题相关理论进行介绍,给出模糊集合与模糊数概念,以及模糊数操作的法则。并在此基础上对不确定条件下的柔性作业车间模糊调度问题进行描述。
然后本文对柔性作业车间模糊调度算法进行了研究。先介绍了遗传算法的基本理论,并结合模糊集的相关理论应用改进遗传算法求解具有模糊加工时间和模糊交货期的单目标柔性作业车间调度问题,并通过对实例的测试,验证该算法在求解不确定条件下的柔性作业车间调度问题的有效性。之后介绍了多目标优化问题的基本概念,对多目标优化方法及其解决车间调度问题上的研究进行综述。结合遗传算法和模糊集理论,设计了改进NSGA-II算法求解具有模糊加工时间和模糊交货期的多目标柔性作业车间调度问题,给出算法的流程图,并通过对设计的实例进行测试,验证了该算法在求解不确定条件下的多目标柔性作业车间调度问题的有效性。
本文在算法研究的基础上开发出不确定条件下的柔性作业车间调度原型系统,并通过运行实例,对原型系统的功能和效果进行了描述,使理论研究能够应用于实际生产。
最后,对全文所做的工作进行总结,并对未来的研究方向进行展望。
Manufacturing is one of the most important parts of national economy. But the uncertainty of production becomes the bottleneck of the scheduling theory application in the real production, because the processing time, completion time, delivery time and so on can no longer be described as determined parameters as they are in the research. Combined with the complex multi-objective optimization problems in the real plant and production, the main research of this thesis is about flexible job shop scheduling problem under uncertainty with fuzzy processing time, fuzzy due date and multi-objective optimization. And some meaningful conclusions and results are pointed out from the research.
The fund of the subject, the purpose of the study, the background and the significance of the research are given at the beginning. After that, the thesis reviews the main research methods and analyses the current research of the scheduling problem under uncertainty. Then fuzzy set is introduced and flexible job shop problem under uncertainty is described.
The thesis introduces the basic knowledge of genetic algorithm, and proposes an improved genetic algorithm which can solve flexible job shop scheduling problem under uncertainty after that. The flow chart of the very algorithm is given, and enough complex examples are given as the evidence to prove and confirm the effectivity and availability of the algorithm. Then the thesis introduces the basic concept and methods of multi-objective optimization and reviewes their applications in solving scheduling problems. After that, an improved nondominated sorting genetic algorithm-II is designed and proposed to solve multi-objective flexible job shop scheduling problem under uncertainty with fuzzy processing time and fuzzy due date. The flow chart of the improved nondominated sorting genetic algorithm-II is drawn and enough complex examples are given to show its availability and effect of the algorithm.
The calculation and optimization prototype system for solving single/multi-objective flexible job shop scheduling problem under uncertainty is designed and programed based on two algorithms mentioned above. Some examples are given to introduce the function of the system and to show how to use the system. It proposes a way to extend the theory and algorithms which are researched in this paper into actual production and real plant application.
In the end of the thesis, the conclusion of the research is drawn and the future work and focus is pointed out.
本文首先对课题的来源,研究的目的、背景和意义进行介绍。概述调度问题和其主要研究方法,阐述调度问题的分类和主要特点,并针对不确定条件下的车间调度问题,对目前的主要研究方法和国内外研究现状进行系统地综述和深入的分析,指出所存在的问题。接着对不确定条件下的模糊调度问题相关理论进行介绍,给出模糊集合与模糊数概念,以及模糊数操作的法则。并在此基础上对不确定条件下的柔性作业车间模糊调度问题进行描述。
然后本文对柔性作业车间模糊调度算法进行了研究。先介绍了遗传算法的基本理论,并结合模糊集的相关理论应用改进遗传算法求解具有模糊加工时间和模糊交货期的单目标柔性作业车间调度问题,并通过对实例的测试,验证该算法在求解不确定条件下的柔性作业车间调度问题的有效性。之后介绍了多目标优化问题的基本概念,对多目标优化方法及其解决车间调度问题上的研究进行综述。结合遗传算法和模糊集理论,设计了改进NSGA-II算法求解具有模糊加工时间和模糊交货期的多目标柔性作业车间调度问题,给出算法的流程图,并通过对设计的实例进行测试,验证了该算法在求解不确定条件下的多目标柔性作业车间调度问题的有效性。
本文在算法研究的基础上开发出不确定条件下的柔性作业车间调度原型系统,并通过运行实例,对原型系统的功能和效果进行了描述,使理论研究能够应用于实际生产。
最后,对全文所做的工作进行总结,并对未来的研究方向进行展望。
Manufacturing is one of the most important parts of national economy. But the uncertainty of production becomes the bottleneck of the scheduling theory application in the real production, because the processing time, completion time, delivery time and so on can no longer be described as determined parameters as they are in the research. Combined with the complex multi-objective optimization problems in the real plant and production, the main research of this thesis is about flexible job shop scheduling problem under uncertainty with fuzzy processing time, fuzzy due date and multi-objective optimization. And some meaningful conclusions and results are pointed out from the research.
The fund of the subject, the purpose of the study, the background and the significance of the research are given at the beginning. After that, the thesis reviews the main research methods and analyses the current research of the scheduling problem under uncertainty. Then fuzzy set is introduced and flexible job shop problem under uncertainty is described.
The thesis introduces the basic knowledge of genetic algorithm, and proposes an improved genetic algorithm which can solve flexible job shop scheduling problem under uncertainty after that. The flow chart of the very algorithm is given, and enough complex examples are given as the evidence to prove and confirm the effectivity and availability of the algorithm. Then the thesis introduces the basic concept and methods of multi-objective optimization and reviewes their applications in solving scheduling problems. After that, an improved nondominated sorting genetic algorithm-II is designed and proposed to solve multi-objective flexible job shop scheduling problem under uncertainty with fuzzy processing time and fuzzy due date. The flow chart of the improved nondominated sorting genetic algorithm-II is drawn and enough complex examples are given to show its availability and effect of the algorithm.
The calculation and optimization prototype system for solving single/multi-objective flexible job shop scheduling problem under uncertainty is designed and programed based on two algorithms mentioned above. Some examples are given to introduce the function of the system and to show how to use the system. It proposes a way to extend the theory and algorithms which are researched in this paper into actual production and real plant application.
In the end of the thesis, the conclusion of the research is drawn and the future work and focus is pointed out.
引文
[1]王凌.车间调度及其遗传算法.北京:清华大学出版社,2003
[2]陈荣秋,马士华.生产与运作管理.北京:高等教育出版社,1999
[3] Baker K R. Introduction to Sequencing and Scheduling, New York: Wiley, 1974
[4]张超勇.基于自然启发式算法的作业车间调度问题理论与应用研究:[博士学位论文].武汉:华中科技大学机械科学与工程学院,2006
[5]朱剑英.现代制造系统模式、建模方法及关键技术的新发展.机械工程学报,2000,36(8):1～5
[6]何霆,刘飞,马玉林.车间生产调度问题研究.机械工程学报,2000,36(5):97～102
[7] Johnson S. Optimal two-and-three stage production schedules with setup times included. Naval Research Logistics Quarterly, 1954, 1: 61~68
[8] Nowicki E, Smutnicki C. A decision support system for the resource constrained project scheduling problem, European Journal of Operational Research, 1994, 79:183~195
[9] Foo S Y and Takefuji Y. Stochastic neural networks for solving job shop scheduling: Part 1. Problem Representation, in Kosko B (ed.), IEEE International Conference on Neural Networks, San Diego, USA, Jul 24-27, 1988, 2: 275~282
[10] Panwalker S, Iskander W. A survey of scheduling. Operations Research, 1977, 25(1): 45~61
[11]越民义,韩继业. n个零件在m台机床上加工顺序问题.中国科学,1975,5:462～470
[12] Aarts E H L, Van Laarhoven P J M, Lenstra J K, et al. A computational study of local search algorithms for job shop scheduling. ORSA Journal on Computing, 1994, 6(2): 118~125
[13] Peter J M, Emile H L and Jan K L. Job shop scheduling by simulated annealing. Operations Research, 1992, 40(1): 113~125
[14] Laguna M, Barnes J W and Glover F. Tabu search methods for a single machine scheduling problem. Journal of Intelligent Manufacturing, 1991, 2: 63~74
[15] Nakano R, Yamada T. Conventional genetic algorithm for job shop problems. Proceeding of the Fourth International Conference on Genetic Algorithms, San Diego, CA. July 13-16, 1991, 474~479
[16]高亮,高海兵,周驰.基于粒子群优化的开放式车间调度.机械工程学报,2006,42(2):129～134
[17] Paseal Van Hentenryek. Scheduling and Packing in the Constraint Language CC(FD). Intelligent Scheduling, Morgan Kaufmann, ed:Michael B.Morgan, 1994:137~168
[18] M.J.shaw, S.Park, N.Raman. Intelligent Scheduling with Machine Learning Capacities: The Induction of Scheduling Knowledge. IIE Transactions. 1992, 24(2):156~168
[19] R.W.Conway, W.L.Maxwell, L.W.Miller. Theory of Scheduling. Reading Mass: Addison-Wesley, 1967
[20] Shaw M J, Park S, Raman N. Intelligent scheduling with machine learning capacities: the induction of scheduling knowledge. IEEE Transaction. 1992, 24(2): 156~168
[21] Allahverdi A.C.T.N, Cheng T.C.E, Kovalyov M.Y. A survey of scheduling problems with setup times or costs. European Journal of Operational Research, 2006
[22]潘全科.智能制造系统多目标车间调度研究:[博士学位论文].南京:南京航空航天大学图书馆,2003
[23] Parunak H V D, Arbor A. Characterizing the manufacturing scheduling problem. Journal of Manufacturing Systems, 1991, 10(3): 241~259
[24] Holland J H. Adaptation in natural and artificial systems. Ann Arbor, The University of Michigan Press, 1975
[25] Koza J R. Genetic Programming: On the Programming of Computers by Means of Natural Selection. MIT Press, Cambridge, MA, 1992
[26] Beyer H G, Schwefel H P. Evolution strategies-a comprehensive introduction. Natural Computing, 2002, 1(1): 3~52
[27] Fogel L J, Owens A J, Walsh M J. Artificial intelligence through simulated evolution, New York: John Wiley and Sons, 1966
[28] Feng-Tse Lin, Constructing A job-shop Scheduling model based on imprecise data, the IEEE international conference on fuzzy system, 2003
[29] Tzung-pei Hong, Tzu-Tin Wang, Fuzzy flexible flow shops at two machine centers for continuous fuzzy domains. Information Seienee, 2000, 129: 227~237
[30] Paul M.Stanfield, Russell E.King, Jeff A.Joines, Scheduling arrivals to a production system in a fuzzy environment. European journal of Operational Research, 1996, 93: 75~87
[31] Feng-Tse Lin, Fuzzy job shop scheduling based on ranking level (λ,1) interval-valued fuzzy numbers, 2002IEEE
[32] Jing-shing Yao, Feng-Tse Lin, Constructing a fuzzy flow-shop sequencing model based on statistical data. International journal of Approximate reasoning, 2002, 29: 215~234
[33] Juite Wang, A fuzzy robust scheduling approach for product development projects. European journal of operational research, 2004, 152: 180~194
[34] Tsujimura Y, Cen M, Kuboa E. Solving job-shop scheduling problems with fuzzyprocessing time using genetic algorithms. Journal of Japan society for fuzzy theory and systems, 1995, 7(2): 1073~1083
[35] Ish iiH, TadaM, M asuda T. Two scheduling problems with fuzzy due dates. Fuzzy Sets and Systems, 1992: 46(3): 339~347
[36] Hisao Ishibuchi, Naohisa Yamamoto, Shinta Misaki and Hideo Tanaka. Local search algorithms for flow shop scheduling with fuzzy due-dates. International Journal of Production Economics, 1994, 33(1-3): 53~66
[37] Han S, Ishii H, Fujii S. One machine scheduling problem with fuzzy due dates. European J. Operational Research, 1994, 79: 1~12
[38] Adampoulos G L, Papois C P. A neighborhood-based hybrid method for scheduling with fuzzy due dates. International transactions in operational research, 1998, 5(3):147~153
[39] Sakawa M, Mori T. A efficient genetic algorithm for job-shop scheduling problems with fuzzy processing time and fuzzy due date. Computers & Industrial Engineering, 1999, 36(2): 325~341
[40] Itoh T, Ishi H. Fuzzy due date scheduling problem with fuzzy processing time. International Transactions in Operational Research, 1999, 6(6): 639~647
[41] Chanas S, Kasperski A. Minimizing maximum lateness in a single machine scheduling problem with fuzzy processing times and fuzzy dudates. Engineering Applications of Artificial Intelligence, 2001, 14(3): 377~386
[42] S.S.lam, X.cai. Single machine scheduling with nonlinear lateness cost functions and fuzzy due dates. Nonlinear Analysis: real world Applications, 2002, 3:307~316
[43] Yuan Kun, Zhu Jianying, Sun Zhijun. Flexible job-shop scheduling with fuzzy goal through IOCDGA. Transactions of Nanjing University of Aeronautics and Astronautics, 2006, 23(2): 144~148
[44] Lei De-Ming, Guo Xiu-Ping. Solving fuzzy flexible job shop scheduling problems using genetic algorithm. Proceedings of the 7th International Conference on Machine Learning and Cybernetics, ICMLC, 2008, 1014~1019
[45]吴会江.一种具有模糊交货期的单机调度问题.科学技术与工程. 2005,5(9):592～593
[46]李富明,朱云龙,尹朝万,宋晓宇.基于模糊遗传算法的模糊调度研究.信息与控制,2004,33(6):703～708
[47]潘全科,朱剑英.多工艺路线的作业车间模糊调度优化.中国机械工程,2004,15(24):2199～2202
[48]谢源,谢剑英,邓小龙.模糊加工时间和/或模糊交货期下的单机调度问题.上海交通大学学报,2005(8):159～162
[49]谢源,谢剑英,邓小龙.混合优先约束下带模糊交货期的单机调度问题的研究.信息与控制,2005,34(3):369～372
[50]耿兆强.模糊决策与模糊调度问题的研究及应用:[博士学位论文].沈阳:中国科学院自动化研究所图书馆,2002
[51]耿兆强,邹益仁.基于遗传算法的作业车间模糊调度问题的研究.计算机集成制造系统-CIMS,2002,8 (8):616～620
[52]卢冰原,陈华平,古春生,谷峰.基于模糊逻辑的偏柔性工作车间调度模型.中国管理科学,2004,12(6):52～55
[53]谷峰,陈华平,卢冰原.基于遗传算法的模糊柔性工作车间调度优化,系统工程与电子技术,2006,28(7):1017～1038
[54] Omar A.ghrayeb,A bi-criteria optimization: Minimizing the integral value and spread of the fuzzy makespan of job shop scheduling problems. Applied soft computing, 2003, 2/3F: 197~210
[55] Tadahiko Murata, Hisao Ishibuchi, Mtsuo Gen, Multi-Objective Fuzzy Scheduling with the OWA Operator for Handling Different Scheduling Criteria and Different Job Importance. IEEE International Fuzzy systems conference Proceedings, August 22-25, 1999, Seoul, Korea
[56] Masatoshi sakawa, Ryo Kubota. Fuzzy programming for multi-objective job shop scheduling with fuzzy processing time and fuzzy duedate through genetic algorithm. European Journal of Operational Research, 2000, 120(2): 393~407
[57] Imed Kacem, Slim Hammadi and Pierre Borne. Pareto-optimality approach for flexible job-shop scheduling problems: hybridization of evolutionary algorithms and fuzzy logic. Mathematics and Computers in Simulation, 2002, 60(3-5): 245~276
[58] Dobrila Petrovic, Alejandra Duenas and Sanja Petrovic. Decision Support Systems, 2007, 43(4): 1527~1538
[59] Fu-ming Li, Yun-long Zhu, Chao-wan Yin et al. Fuzzy Programming for Multiobjective Fuzzy JobShop Scheduling with Alternative MachinesThrough Genetic Algorithms. L. Wang, K. Chen, and Y.S. 2005, pp: 992~1004
[60] Deming Lei. Pareto archive particle swarm optimization for multi-objective fuzzy job shop scheduling problems. International Journal of Advanced Manufacturing and Technology, 2008, 37: 157~165
[61]雷德明,吴智铭.多目标模糊作业车间调度问题研究.计算机集成制造系统,2006,12(2):174～179
[62] Zadeh L A. Fuzzy Sets. Information and Control, 1965, 8(3): 338~353
[63] Pawlak Z. Rough Sets. International Journal of Information and Computer Science.1982, 11: 341~356
[64]韩祯祥,张琦,文福拴.粗糙集理论及其应用综述.控制理论与应用,1999,16(2): 153～157
[65] Shefer G.A Mathematical Theory of Evidence. Princeton Univ. Press, 1976
[66]李凡.模糊信息处理系统.北京:北京大学出版社,1998
[67] D.E.Goldberg,Genetic Algorithms in Search, Optimization and Machine Learning. Reading, MA: Addison-Wesley, 1989
[68] Michalewicz Z. Genetic algorithm + data Structures = evolution programs. Springer, New York, 1994
[69]张超勇,饶运清,李培根.基于POX交叉的遗传算法求解Job-Shop调度问题.中国机械工程,2004,15(23):2149～2153
[70] Imed Kacem, Slim Hammadi, Pierre Borne. Approach by Localization and Multiobjective Evolutionary Optimization for Flexible Job-Shop Scheduling Problems. IEEE Transactions on systems, man, and cybernetics -Part C: Applications and reviews, 2002, 32(1)
[71] Hausdorff F. Set Theory, New York, NY: Chelsea, 1957
[72]郑金华.多目标进化算法及其应用.北京:科学出版社,2007
[73] Schaffer J D. Multiple objective optimization with vector evaluated genetic algorithms. In: Proceedings of the first International Conference on Genetic Algorithms. Lawrence Erlbaum Associates, Hillsdale, 1985, pp: 93~100
[74] Srinivas N, Deb K. Multi-objective optimization using non-dominated sorting in genetic algorithms. Evolutionary Computation, 1994, 2(3): 221~248
[75] Horn J, Nafpliotis N, Goldberg D E. A niched pareto genetic algorithm for multiobjective optimization. Proceedings of the first IEEE Conference on Evolutionary Computation, Piscataway USA, 1994, 82~87
[76] Zitzler E, Thiele L. Multiobjective evolutionary algorithms: a comparative case study and the strength pareto approach. IEEE Transactions on Evolutionary Computation, 1999, 3(4): 257~271
[77] Zitzler E, Laumanns M, Thiele L. SPEA2: improving the strength pareto evolutionary algorithm, TIK-Report 103, 2001
[78] Deb K, Pratap A, Agarwal S, Meyarivan T. A fast and elitist multiobjective genetic algorithm NSGA-II. IEEE Transaction on Evolutionary Computation, 2002, 6(2): 182~197
[79] Zeng Sanyou, Kang Lishan, Ding Lixin. An Orthogonal Multi-objective Evolutionary Algorithm for Multi-objective Optimization Problems with Constraints EvolutionaryComputation. MIT Press, 2004
[80]郭秀萍.多目标进化算法及其在制造系统中的应用研究:[博士学位论文].上海:上海交通大学图书馆,2007
[81] Xia W J, Wu Z M. An effective hybrid optimization approach for multi objective flexible job shop scheduling problems. Computers & Industrial Engineering, 2005, 48(2): 409~425
[82]吴秀丽.多目标柔性作业车间调度技术研究:[博士学位论文].西安:西北工业大学图书馆,2006
[83]余建军,孙树栋,郝京辉.免疫算法求解多目标柔性作业车间调度研究.计算机集成制造系统,2006,12(10):1643～1650
[2]陈荣秋,马士华.生产与运作管理.北京:高等教育出版社,1999
[3] Baker K R. Introduction to Sequencing and Scheduling, New York: Wiley, 1974
[4]张超勇.基于自然启发式算法的作业车间调度问题理论与应用研究:[博士学位论文].武汉:华中科技大学机械科学与工程学院,2006
[5]朱剑英.现代制造系统模式、建模方法及关键技术的新发展.机械工程学报,2000,36(8):1～5
[6]何霆,刘飞,马玉林.车间生产调度问题研究.机械工程学报,2000,36(5):97～102
[7] Johnson S. Optimal two-and-three stage production schedules with setup times included. Naval Research Logistics Quarterly, 1954, 1: 61~68
[8] Nowicki E, Smutnicki C. A decision support system for the resource constrained project scheduling problem, European Journal of Operational Research, 1994, 79:183~195
[9] Foo S Y and Takefuji Y. Stochastic neural networks for solving job shop scheduling: Part 1. Problem Representation, in Kosko B (ed.), IEEE International Conference on Neural Networks, San Diego, USA, Jul 24-27, 1988, 2: 275~282
[10] Panwalker S, Iskander W. A survey of scheduling. Operations Research, 1977, 25(1): 45~61
[11]越民义,韩继业. n个零件在m台机床上加工顺序问题.中国科学,1975,5:462～470
[12] Aarts E H L, Van Laarhoven P J M, Lenstra J K, et al. A computational study of local search algorithms for job shop scheduling. ORSA Journal on Computing, 1994, 6(2): 118~125
[13] Peter J M, Emile H L and Jan K L. Job shop scheduling by simulated annealing. Operations Research, 1992, 40(1): 113~125
[14] Laguna M, Barnes J W and Glover F. Tabu search methods for a single machine scheduling problem. Journal of Intelligent Manufacturing, 1991, 2: 63~74
[15] Nakano R, Yamada T. Conventional genetic algorithm for job shop problems. Proceeding of the Fourth International Conference on Genetic Algorithms, San Diego, CA. July 13-16, 1991, 474~479
[16]高亮,高海兵,周驰.基于粒子群优化的开放式车间调度.机械工程学报,2006,42(2):129～134
[17] Paseal Van Hentenryek. Scheduling and Packing in the Constraint Language CC(FD). Intelligent Scheduling, Morgan Kaufmann, ed:Michael B.Morgan, 1994:137~168
[18] M.J.shaw, S.Park, N.Raman. Intelligent Scheduling with Machine Learning Capacities: The Induction of Scheduling Knowledge. IIE Transactions. 1992, 24(2):156~168
[19] R.W.Conway, W.L.Maxwell, L.W.Miller. Theory of Scheduling. Reading Mass: Addison-Wesley, 1967
[20] Shaw M J, Park S, Raman N. Intelligent scheduling with machine learning capacities: the induction of scheduling knowledge. IEEE Transaction. 1992, 24(2): 156~168
[21] Allahverdi A.C.T.N, Cheng T.C.E, Kovalyov M.Y. A survey of scheduling problems with setup times or costs. European Journal of Operational Research, 2006
[22]潘全科.智能制造系统多目标车间调度研究:[博士学位论文].南京:南京航空航天大学图书馆,2003
[23] Parunak H V D, Arbor A. Characterizing the manufacturing scheduling problem. Journal of Manufacturing Systems, 1991, 10(3): 241~259
[24] Holland J H. Adaptation in natural and artificial systems. Ann Arbor, The University of Michigan Press, 1975
[25] Koza J R. Genetic Programming: On the Programming of Computers by Means of Natural Selection. MIT Press, Cambridge, MA, 1992
[26] Beyer H G, Schwefel H P. Evolution strategies-a comprehensive introduction. Natural Computing, 2002, 1(1): 3~52
[27] Fogel L J, Owens A J, Walsh M J. Artificial intelligence through simulated evolution, New York: John Wiley and Sons, 1966
[28] Feng-Tse Lin, Constructing A job-shop Scheduling model based on imprecise data, the IEEE international conference on fuzzy system, 2003
[29] Tzung-pei Hong, Tzu-Tin Wang, Fuzzy flexible flow shops at two machine centers for continuous fuzzy domains. Information Seienee, 2000, 129: 227~237
[30] Paul M.Stanfield, Russell E.King, Jeff A.Joines, Scheduling arrivals to a production system in a fuzzy environment. European journal of Operational Research, 1996, 93: 75~87
[31] Feng-Tse Lin, Fuzzy job shop scheduling based on ranking level (λ,1) interval-valued fuzzy numbers, 2002IEEE
[32] Jing-shing Yao, Feng-Tse Lin, Constructing a fuzzy flow-shop sequencing model based on statistical data. International journal of Approximate reasoning, 2002, 29: 215~234
[33] Juite Wang, A fuzzy robust scheduling approach for product development projects. European journal of operational research, 2004, 152: 180~194
[34] Tsujimura Y, Cen M, Kuboa E. Solving job-shop scheduling problems with fuzzyprocessing time using genetic algorithms. Journal of Japan society for fuzzy theory and systems, 1995, 7(2): 1073~1083
[35] Ish iiH, TadaM, M asuda T. Two scheduling problems with fuzzy due dates. Fuzzy Sets and Systems, 1992: 46(3): 339~347
[36] Hisao Ishibuchi, Naohisa Yamamoto, Shinta Misaki and Hideo Tanaka. Local search algorithms for flow shop scheduling with fuzzy due-dates. International Journal of Production Economics, 1994, 33(1-3): 53~66
[37] Han S, Ishii H, Fujii S. One machine scheduling problem with fuzzy due dates. European J. Operational Research, 1994, 79: 1~12
[38] Adampoulos G L, Papois C P. A neighborhood-based hybrid method for scheduling with fuzzy due dates. International transactions in operational research, 1998, 5(3):147~153
[39] Sakawa M, Mori T. A efficient genetic algorithm for job-shop scheduling problems with fuzzy processing time and fuzzy due date. Computers & Industrial Engineering, 1999, 36(2): 325~341
[40] Itoh T, Ishi H. Fuzzy due date scheduling problem with fuzzy processing time. International Transactions in Operational Research, 1999, 6(6): 639~647
[41] Chanas S, Kasperski A. Minimizing maximum lateness in a single machine scheduling problem with fuzzy processing times and fuzzy dudates. Engineering Applications of Artificial Intelligence, 2001, 14(3): 377~386
[42] S.S.lam, X.cai. Single machine scheduling with nonlinear lateness cost functions and fuzzy due dates. Nonlinear Analysis: real world Applications, 2002, 3:307~316
[43] Yuan Kun, Zhu Jianying, Sun Zhijun. Flexible job-shop scheduling with fuzzy goal through IOCDGA. Transactions of Nanjing University of Aeronautics and Astronautics, 2006, 23(2): 144~148
[44] Lei De-Ming, Guo Xiu-Ping. Solving fuzzy flexible job shop scheduling problems using genetic algorithm. Proceedings of the 7th International Conference on Machine Learning and Cybernetics, ICMLC, 2008, 1014~1019
[45]吴会江.一种具有模糊交货期的单机调度问题.科学技术与工程. 2005,5(9):592～593
[46]李富明,朱云龙,尹朝万,宋晓宇.基于模糊遗传算法的模糊调度研究.信息与控制,2004,33(6):703～708
[47]潘全科,朱剑英.多工艺路线的作业车间模糊调度优化.中国机械工程,2004,15(24):2199～2202
[48]谢源,谢剑英,邓小龙.模糊加工时间和/或模糊交货期下的单机调度问题.上海交通大学学报,2005(8):159～162
[49]谢源,谢剑英,邓小龙.混合优先约束下带模糊交货期的单机调度问题的研究.信息与控制,2005,34(3):369～372
[50]耿兆强.模糊决策与模糊调度问题的研究及应用:[博士学位论文].沈阳:中国科学院自动化研究所图书馆,2002
[51]耿兆强,邹益仁.基于遗传算法的作业车间模糊调度问题的研究.计算机集成制造系统-CIMS,2002,8 (8):616～620
[52]卢冰原,陈华平,古春生,谷峰.基于模糊逻辑的偏柔性工作车间调度模型.中国管理科学,2004,12(6):52～55
[53]谷峰,陈华平,卢冰原.基于遗传算法的模糊柔性工作车间调度优化,系统工程与电子技术,2006,28(7):1017～1038
[54] Omar A.ghrayeb,A bi-criteria optimization: Minimizing the integral value and spread of the fuzzy makespan of job shop scheduling problems. Applied soft computing, 2003, 2/3F: 197~210
[55] Tadahiko Murata, Hisao Ishibuchi, Mtsuo Gen, Multi-Objective Fuzzy Scheduling with the OWA Operator for Handling Different Scheduling Criteria and Different Job Importance. IEEE International Fuzzy systems conference Proceedings, August 22-25, 1999, Seoul, Korea
[56] Masatoshi sakawa, Ryo Kubota. Fuzzy programming for multi-objective job shop scheduling with fuzzy processing time and fuzzy duedate through genetic algorithm. European Journal of Operational Research, 2000, 120(2): 393~407
[57] Imed Kacem, Slim Hammadi and Pierre Borne. Pareto-optimality approach for flexible job-shop scheduling problems: hybridization of evolutionary algorithms and fuzzy logic. Mathematics and Computers in Simulation, 2002, 60(3-5): 245~276
[58] Dobrila Petrovic, Alejandra Duenas and Sanja Petrovic. Decision Support Systems, 2007, 43(4): 1527~1538
[59] Fu-ming Li, Yun-long Zhu, Chao-wan Yin et al. Fuzzy Programming for Multiobjective Fuzzy JobShop Scheduling with Alternative MachinesThrough Genetic Algorithms. L. Wang, K. Chen, and Y.S. 2005, pp: 992~1004
[60] Deming Lei. Pareto archive particle swarm optimization for multi-objective fuzzy job shop scheduling problems. International Journal of Advanced Manufacturing and Technology, 2008, 37: 157~165
[61]雷德明,吴智铭.多目标模糊作业车间调度问题研究.计算机集成制造系统,2006,12(2):174～179
[62] Zadeh L A. Fuzzy Sets. Information and Control, 1965, 8(3): 338~353
[63] Pawlak Z. Rough Sets. International Journal of Information and Computer Science.1982, 11: 341~356
[64]韩祯祥,张琦,文福拴.粗糙集理论及其应用综述.控制理论与应用,1999,16(2): 153～157
[65] Shefer G.A Mathematical Theory of Evidence. Princeton Univ. Press, 1976
[66]李凡.模糊信息处理系统.北京:北京大学出版社,1998
[67] D.E.Goldberg,Genetic Algorithms in Search, Optimization and Machine Learning. Reading, MA: Addison-Wesley, 1989
[68] Michalewicz Z. Genetic algorithm + data Structures = evolution programs. Springer, New York, 1994
[69]张超勇,饶运清,李培根.基于POX交叉的遗传算法求解Job-Shop调度问题.中国机械工程,2004,15(23):2149～2153
[70] Imed Kacem, Slim Hammadi, Pierre Borne. Approach by Localization and Multiobjective Evolutionary Optimization for Flexible Job-Shop Scheduling Problems. IEEE Transactions on systems, man, and cybernetics -Part C: Applications and reviews, 2002, 32(1)
[71] Hausdorff F. Set Theory, New York, NY: Chelsea, 1957
[72]郑金华.多目标进化算法及其应用.北京:科学出版社,2007
[73] Schaffer J D. Multiple objective optimization with vector evaluated genetic algorithms. In: Proceedings of the first International Conference on Genetic Algorithms. Lawrence Erlbaum Associates, Hillsdale, 1985, pp: 93~100
[74] Srinivas N, Deb K. Multi-objective optimization using non-dominated sorting in genetic algorithms. Evolutionary Computation, 1994, 2(3): 221~248
[75] Horn J, Nafpliotis N, Goldberg D E. A niched pareto genetic algorithm for multiobjective optimization. Proceedings of the first IEEE Conference on Evolutionary Computation, Piscataway USA, 1994, 82~87
[76] Zitzler E, Thiele L. Multiobjective evolutionary algorithms: a comparative case study and the strength pareto approach. IEEE Transactions on Evolutionary Computation, 1999, 3(4): 257~271
[77] Zitzler E, Laumanns M, Thiele L. SPEA2: improving the strength pareto evolutionary algorithm, TIK-Report 103, 2001
[78] Deb K, Pratap A, Agarwal S, Meyarivan T. A fast and elitist multiobjective genetic algorithm NSGA-II. IEEE Transaction on Evolutionary Computation, 2002, 6(2): 182~197
[79] Zeng Sanyou, Kang Lishan, Ding Lixin. An Orthogonal Multi-objective Evolutionary Algorithm for Multi-objective Optimization Problems with Constraints EvolutionaryComputation. MIT Press, 2004
[80]郭秀萍.多目标进化算法及其在制造系统中的应用研究:[博士学位论文].上海:上海交通大学图书馆,2007
[81] Xia W J, Wu Z M. An effective hybrid optimization approach for multi objective flexible job shop scheduling problems. Computers & Industrial Engineering, 2005, 48(2): 409~425
[82]吴秀丽.多目标柔性作业车间调度技术研究:[博士学位论文].西安:西北工业大学图书馆,2006
[83]余建军,孙树栋,郝京辉.免疫算法求解多目标柔性作业车间调度研究.计算机集成制造系统,2006,12(10):1643～1650