1250mm八辊五机架冷连轧机轧制规程优化研究
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摘要
轧制规程是冷连轧工艺研究的主要内容，合理的轧制规程是板带轧制精度与板型良好的根本保障，更是冷轧设备长期可靠稳定运行的重要保证。冷轧过程复杂，采用何种优化方法和轧制策略对轧制规程进行优化，都会对最终轧制规程的合理性产生影响。同时，传统方法的效果不佳，人工智能算法的不成熟，制约着轧制规程优化结果的最优性。本文从优化方法入手，分别从单目标与多目标的角度对轧制规程进行设计。
首先，从优化方法出发，分析各种优化方法特点，确定了将具有快速收敛性的粒子群算法作为轧制规程的优化方法，通过与混沌搜索结合，给出了协同优化算法，通过对测试函数进行仿真实验，协同优化算法利用混沌序列的均匀遍历性很好的克服了粒子群算法早熟收敛的缺点。
然后，根据1250mm八辊五机架冷连轧机的技术参数与设计特点，以等相对轧制功率分配作为目标对轧制规程进行优化设计，并采用协同优化算法作为优化方法，对轧制功率进行均衡分配。
最后，从实际生产中多方面要求考虑，通过对帕累托最优理论的研究，阐述了处理多目标问题的优化方法，进而给出了基于协同优化算法的多目标轧制规程优化设计。通过帕累托最优得到的轧制规程，更加符合实际生产的需求。
The rolling schedule is the main content of the cold rolling process, and reasonablerolling schedule is not only the fundamental guarantee of strip rolling accuracy and goodplate shape, but also the significant support of long-term reliable and stable operation ofcold rolling mill. In view of the complexity of the cold rolling process, the optimizationmethods and the rolling strategies chosen to optimize the rolling schedule will influencethe rationality of the final rolling schedule. At the same time, traditional methods ofrolling schedule optimization are ineffective, while the artificial intelligence algorithmsare immature. Both of them lead to a limited optimization of rolling schedule optimizationresults. In review of the optimization method, this paper designs the rolling schedule fromthe aspects of single objective and multi-objective respectively.
Firstly, starting from the optimization method, a variety of optimization methods wasanalyzed, and the particle swarm optimization with the rapid convergence is chosen as theoptimization method of rolling schedule. Then, the collaborative optimization algorithm isput forward through the combination of particle swarm optimization and chaotic search.Simulation results of the test functions prove that collaborative optimization algorithm canovercome the premature convergence of particle swarm optimization by the uniformergodicity of the chaotic sequence.
Then, considering the technical parameters and design features of the 1250mmeight-roller five-stand tandem cold rolling mill, a rolling schedule optimization is designedwith equal relative rolling power distribution as the target, using collaborativeoptimization algorithm as the optimization method. Experiment results show that therolling power achieves a balanced distribution after optimization.
Finally, taking the many requirements from the actual production and study of paretooptimality theory into account, the dissertation explains the optimization methods dealingwith multi-objective problem, and then puts forward a multi-objective rolling scheduleoptimization design based on collaborative optimization algorithm. The rolling scheduleobtained through pareto optimality is more in line with actual production requirements.
首先，从优化方法出发，分析各种优化方法特点，确定了将具有快速收敛性的粒子群算法作为轧制规程的优化方法，通过与混沌搜索结合，给出了协同优化算法，通过对测试函数进行仿真实验，协同优化算法利用混沌序列的均匀遍历性很好的克服了粒子群算法早熟收敛的缺点。
然后，根据1250mm八辊五机架冷连轧机的技术参数与设计特点，以等相对轧制功率分配作为目标对轧制规程进行优化设计，并采用协同优化算法作为优化方法，对轧制功率进行均衡分配。
最后，从实际生产中多方面要求考虑，通过对帕累托最优理论的研究，阐述了处理多目标问题的优化方法，进而给出了基于协同优化算法的多目标轧制规程优化设计。通过帕累托最优得到的轧制规程，更加符合实际生产的需求。
The rolling schedule is the main content of the cold rolling process, and reasonablerolling schedule is not only the fundamental guarantee of strip rolling accuracy and goodplate shape, but also the significant support of long-term reliable and stable operation ofcold rolling mill. In view of the complexity of the cold rolling process, the optimizationmethods and the rolling strategies chosen to optimize the rolling schedule will influencethe rationality of the final rolling schedule. At the same time, traditional methods ofrolling schedule optimization are ineffective, while the artificial intelligence algorithmsare immature. Both of them lead to a limited optimization of rolling schedule optimizationresults. In review of the optimization method, this paper designs the rolling schedule fromthe aspects of single objective and multi-objective respectively.
Firstly, starting from the optimization method, a variety of optimization methods wasanalyzed, and the particle swarm optimization with the rapid convergence is chosen as theoptimization method of rolling schedule. Then, the collaborative optimization algorithm isput forward through the combination of particle swarm optimization and chaotic search.Simulation results of the test functions prove that collaborative optimization algorithm canovercome the premature convergence of particle swarm optimization by the uniformergodicity of the chaotic sequence.
Then, considering the technical parameters and design features of the 1250mmeight-roller five-stand tandem cold rolling mill, a rolling schedule optimization is designedwith equal relative rolling power distribution as the target, using collaborativeoptimization algorithm as the optimization method. Experiment results show that therolling power achieves a balanced distribution after optimization.
Finally, taking the many requirements from the actual production and study of paretooptimality theory into account, the dissertation explains the optimization methods dealingwith multi-objective problem, and then puts forward a multi-objective rolling scheduleoptimization design based on collaborative optimization algorithm. The rolling scheduleobtained through pareto optimality is more in line with actual production requirements.
引文
[1]苏长青.冷连轧机液压压下控制系统中的几个关键问题的理论研究[D].沈阳:东北大学学位论文, 2005: 1-2.
[2] Hiroshi Kagechika. Production and Technology of Iron and Steel in Japan during 2006[J]. ISIJInternational, 2007, 47(6):773-794.
[3] Zhao Qilin, Liu Xianghua, Wang Guodong. On the direct contact between works roll surfacesoutside workpiece width during thin strip cold rolling[J]. Journal of Northeastern University,2008, 9(12):1715-1717, 1741.
[4] Sun Wenquan, Yang Quan, Shao Jian. Research on high precision profile control technique ofsilicon steel for UCM tandem cold rolling mill[C]. 2010 International Conference on MechanicAutomation and Control Engineering, 2010(6):5926-5929.
[5]奥金茸,齐小英.西安重型机械研究所结束我国高端汽车板依赖进口历史[EB/OL].(2011-06-23)[2012-2-3]. http://www.sxdaily.com.cn/data/kjkjdt/20110623_86376608_0.htm.
[6]郭立伟,杨荃,彭鹏,等.河北中钢公司全连续冷连轧机自动控制系统.冶金设备, 2006,2(1): 1-6.
[7]杨光辉,曹建国,张杰. SmanCrown冷连轧机板形控制新技术改进研究与应用[J].钢铁,2006,41(9):56-59.
[8] J. Pittner, M. A. Simaan. Control of a continuous tandem cold metal rolling process[J]. ControlEngineering Practice, 2008, 23 (3):1379-1390.
[9]华建新.全连续式冷连轧机过程控制[M].北京:冶金工业出版社, 2000: 1-15.
[10]张进之.板带轧制工艺控制理论概要[J].中国工程科学, 2001, 4(3): 46-55.
[11]曲克.轧钢工艺学[M].北京:冶金工业出版社, 1991: 454-455.
[12]镰田正诚.板带连续轧制-追求世界一流技术的记录[M].北京:冶金工业出版社, 2002:15-17.
[13]周宜淼,夏桂芳,周紫箭等.用KH计算法编制铝板带压下规程[J].轻合金加工技术, 2003,31(2): 23-46.
[14]张扬，余弛斌，韩双华．五机架冷连轧的轧制规程优化[J].甘肃冶金，2006，28(1): 1-3, 20.
[15]刘相华，徐俊，邱格君．冷连轧过程中间厚度在线优化设定技术[J].钢铁, 2007, 42(8): 49-51.
[16]张扬.冷连轧规程设计计算与优化系统开发[D],武汉:武汉科技大学工学硕士论文. 2006:58-61.
[17]白金兰,常安,王国栋,等.六辊轧机的负荷分配计算[J].重型机械, 2005(6)：49-52.
[18]刘晓星.冷连轧机轧制规程的多目标模糊优化设计[J].钢铁, 2000, 35(8): 34-36.
[19]郭立伟,杨荃.基于模糊聚类分析的冷连轧负荷分配修正[J].钢铁, 2006, 41(7): 57-60.
[20] J. S. Son, D. M. Lee, I. S. Kim, S. G. Choi. A Study on On-line Learning Neural Network forPrediction for Rolling Force in Hot-rolling Mill[J]. Journal of Materials Processing Technology,2005, 164: 1612-1617.
[21]孙晓光,常春,刘相华,等.精轧机组负荷分配的人工神经网络识别[J].钢铁, 1995, 30(11):25-29.
[22] D. M. Lee, S. G. Choi. Application of On-line Adaptable Neural Network for the Rolling ForceSet-up of a Plate Mill[J]. Engineering Applications of Artificial Intelligence, 2004, 17(5):557-565.
[23] N. Chakraborti, B. Siva Kumar, V. Satish Babu, etc. Optimizing Surface Profiles During HotRolling: A Genetic Algorithms Based Multi-Objective Optimization[J]. Computational MaterialsScience, 2006,37(12):159-165.
[24]王焱,刘景录,孙一康.免疫遗传算法对精轧机组负荷分配的优化[J].北京科技大学学报,2002, 24(3): 339-341.
[25] A. Tsangrassoulis, V. Bourdakis, V. Geros, et al. A Genetic Algorithm Solution to the Design ofSlat-type Shading System[J]. Renewable Energy, 2006, 31(14): 2321-2328.
[26]郭立伟,杨荃.冷连轧负荷分配优化方法[J].钢铁研究学报, 2007, 19(12): 31-34.
[27] J. C. Zhou, W. J. Li, J. B. Zhu. Particle swarm optimization computer simulation of Ni clusters.Trans[J]. Nonferrous Met. Soc, 2008,18: 410-415.
[28] A. H. Kashan, B. Karimi. A discrete particle swarm optimization algorithm for schedulingparallel machines[J]. Computers & Industrial Engineering, 2009, 56(1): 216-223.
[29]张延华,刘相华,王国栋.基于数据挖掘的中厚钢板轧制负荷分配方法的研究[J].钢铁,2005, 40(4): 44-45, 52.
[30]王焱,刘景录,孙一康.基于IGA-BP网络混合模型的冷连轧机组负荷分配优化法[J].钢铁研究学报, 2002, 14(3): 64-67.
[31]孙一康.冷热轧板带轧机的模型与控制[M].北京:冶金工业出版社, 2010.
[32]任勇,程晓茹.轧制规程数学模型[M].北京:冶金工业出版社, 2008.
[33]车海军,刘畅,孙晓娜,等.基于遗传粒子群算法的冷连轧轧制规程优化设计[J].轧钢,2009,1(26): 22-25.
[34]杨景明,徐雅洁,韩宗刚,等.神经网络预报在冷连轧规程设计中的应用[J].冶金设备,2006(1): 7-11.
[35]张大志.以板形板厚为目标的冷连轧机及其轧制参数智能化优化设计[D]．北京:北京科技大学工学博士论文. 1999：98-101.
[36] Kennedy J, Eberhart R. Particle swarm optimization[C]. Proc of IEEE Int Conf on Piscataway,1995:1942-1948.
[37] Eberhart R C, Shi Y. Particle swarm optimization[C]. Proc of Congress on EvolutionaryComputation. Seou, 2001: 81-88.
[38] Peram T, Veeramachaneni K. Fitness-Distance-Ratio based particle swarm optimization[J]. In:Proc. of the IEEE Swarm Intelligence Symp. Indianapolis: IEEE Inc., 2003:174 181.
[39] Naka S, Genji T, Yura T, and Fukuyama Y. Practical Distribution State Estimation using HybridParticle Swarm Optimization[C]. In IEEE Power Engineering Society Winter Meeting, 2001,1(2):815-820.
[40] Clerc M, Kennedy J. The Particle Swarm: explosion, stability, and convergence in a multi-dimensional complex space[C]. IEEE Transaction on Evolutionary Computation, 2002, 6: 58-73.
[41]阮旻智,李庆民,王红军,等.人工免疫粒子群算法在系统可靠性优化中的应用[J].控制理论与应用, 2010, 27(9): 1253-1258.
[42]周頔,孙俊,须文波.具有量子行为的协同粒子群优化算法[J].控制与决策,2011,26(4):582-586.
[43] Zhong Weimin, Li Shaojun, Qian Feng.θ-PSO: A new strategy of particle swarmoptimization[J]. Journal of Zhejiang University Science A, 2008, 9 (6): 786-790.
[44]孟红记,郑鹏,梅国晖,谢植.基于混沌序列的粒子群优化算法[J].控制与决策, 2006, 3:263-266.
[45]王华秋,曹长修.基于模拟退火的并行粒子群优化研究[J].控制与决策, 2005, 5: 500-504.
[46] Dong Sifang, Dong Zengchuan, Ma Junjian, Chen Kangning. Improved PSO algorithm based onchaos theory and its application to design flood hydrograph[J]. Water Science and Engineering,2010, 3(2): 156-165.
[47]朱海梅,吴永萍.一种高速收敛粒子群优化算法[J].控制与决策, 2010, 1: 20-24.
[48] Kennedy J. The Particle Swarm: Social Adaptation of Knowledge[C]. In Proceedings of the IEEEInternational Conference on Evolutionary Computation, 1997,4: 303-308.
[49]单梁,强浩,等.基于Tent映射的混沌优化算法[J].控制与决策, 2005, 2: 179-182.
[50]张学良,温淑花,李海楠,等.基于Tent映射的混沌粒子群优化算法及其应用[J].中国机械工程,2008,19(17) : 2108-2112.
[51] Pires C T A , Ferreira H C , Sales R M,et al. Set-up Optimization for Tandem Cold Mills : a CaseStudy[J ].Journal of Materials Processing Technology , 2006 , 173(3) : 368-375.
[52]李海军,徐建忠,龚殿尧,等.动量项技术在带钢热连轧负荷分配中的应用[J].钢铁, 2006,41 (2): 46-50.
[53]李勇,刘建昌,王昱.改进权重自适应GA及冷连轧轧制规程多目标优化[J].控制理论与应用, 2009, 26(6): 687-693.
[54]魏立新,李兴强,李莹,等.基于改进自适应遗传算法的冷连轧轧制规程优化设计[J].机械工程学报, 2010, 46(16): 136-141.
[55]杨景明,窦富萍,刘舒慧,等.基于遗传算法的冷连轧轧制规程优化设计[J].中国机械工程,2007,18(15):1868-1871.
[56]陈东宁,姜万录,王益群.基于粒子群算法的冷连轧机轧制负荷分配优化[J].中国机械工程,2007, 18 (11): 1303-1306.
[57] Li Y, Liu J.C, Wang Y. An Adaptive Weight PSO for Rolling Schedules Multi-objectiveOptimization of Tandem Cold Rolling[C]. Proceedings of the IEEE International Conference onAutomation and Logistics, 2009, 8: 895-899.
[58]刘华强,唐荻,杨荃,等.多目标遗传算法在八辊五机架全连续冷连轧机轧制策略优化中的应用[J].冶金自动化, 2006(4): 49-53.
[59] I. Das, J. Dennis. A Closer Look at Drawbacks of Minimizing Weightd Sums of Objects forPareto Set Generation in Multicriteria Optimization Problems[J]. Strutural Optimization, 1997,14(1): 63-69.
[60] Y. Jin, M. Olhofer, B.Sendhoff. Dynamic Weighted Aggregation for EvolutionaryMulti-Objective Optimization: Why does it Work and How?[C] In Proceedings of the GeneticAlgorithm and Evolutionary Computation Conference, 2001: 1042-1049.
[61] X. Hu, R. C. Eberhart. Multiobjective Optimization using Dynamic Neighborhood ParticleSwarm Optimization[C]. In Proceedings of the IEEE Congress on Evolutionary Computation,2002, 3(2): 1677-1681.
[62] Engelbrecht A.P.计算机群体智能基础[M].清华大学出版社, 2009, 10: 185-190.
[63] L. Zhang, C. Zhou, X. Liu, et al. Solving Multi Objective Optimization Problems Using ParticleSwarm Optimization[C]. In Proceedings of the IEEE Congress on Evolutionary Computation,2003(4): 2400-2405.
[64] T. bartz-Beielstein, P. Limbourg, J. Mehnen, et al. Particle Swarm Optimizers for ParetoOptimization with Enhanced Archiving Techniques[C]. In Proceedings of the IEEE Congress onEvolutionary Computation, 2003: 1780-1787.
[65] Engelbrecht A.P.计算机群体智能基础[M].清华大学出版社, 2009, 10: 190-193.
[66] J. E. Fieldsend. Novel Algorithms for Multi-Objective Search and their Application in Mult-Objective Evolutionary Neural Network Training[D]. University of California, 2003.
[67]刘衍民,赵庆祯,牛奔,等.基于ε占优的自适应多目标粒子群算法[J].控制与决策, 2011,26(1): 89-95.
[68]王丽萍,江波,邱飞岳.基于多目标进化算法的系统设计冲突消解方法[J].计算机集成制造系统, 2010, 16(9): 1836-1843.
[69]施展,陈庆伟.基于QPSO和拥挤距离排序的多目标量子粒子群优化算法[J].控制与决策,2011, 26(4): 540-547.
[2] Hiroshi Kagechika. Production and Technology of Iron and Steel in Japan during 2006[J]. ISIJInternational, 2007, 47(6):773-794.
[3] Zhao Qilin, Liu Xianghua, Wang Guodong. On the direct contact between works roll surfacesoutside workpiece width during thin strip cold rolling[J]. Journal of Northeastern University,2008, 9(12):1715-1717, 1741.
[4] Sun Wenquan, Yang Quan, Shao Jian. Research on high precision profile control technique ofsilicon steel for UCM tandem cold rolling mill[C]. 2010 International Conference on MechanicAutomation and Control Engineering, 2010(6):5926-5929.
[5]奥金茸,齐小英.西安重型机械研究所结束我国高端汽车板依赖进口历史[EB/OL].(2011-06-23)[2012-2-3]. http://www.sxdaily.com.cn/data/kjkjdt/20110623_86376608_0.htm.
[6]郭立伟,杨荃,彭鹏,等.河北中钢公司全连续冷连轧机自动控制系统.冶金设备, 2006,2(1): 1-6.
[7]杨光辉,曹建国,张杰. SmanCrown冷连轧机板形控制新技术改进研究与应用[J].钢铁,2006,41(9):56-59.
[8] J. Pittner, M. A. Simaan. Control of a continuous tandem cold metal rolling process[J]. ControlEngineering Practice, 2008, 23 (3):1379-1390.
[9]华建新.全连续式冷连轧机过程控制[M].北京:冶金工业出版社, 2000: 1-15.
[10]张进之.板带轧制工艺控制理论概要[J].中国工程科学, 2001, 4(3): 46-55.
[11]曲克.轧钢工艺学[M].北京:冶金工业出版社, 1991: 454-455.
[12]镰田正诚.板带连续轧制-追求世界一流技术的记录[M].北京:冶金工业出版社, 2002:15-17.
[13]周宜淼,夏桂芳,周紫箭等.用KH计算法编制铝板带压下规程[J].轻合金加工技术, 2003,31(2): 23-46.
[14]张扬，余弛斌，韩双华．五机架冷连轧的轧制规程优化[J].甘肃冶金，2006，28(1): 1-3, 20.
[15]刘相华，徐俊，邱格君．冷连轧过程中间厚度在线优化设定技术[J].钢铁, 2007, 42(8): 49-51.
[16]张扬.冷连轧规程设计计算与优化系统开发[D],武汉:武汉科技大学工学硕士论文. 2006:58-61.
[17]白金兰,常安,王国栋,等.六辊轧机的负荷分配计算[J].重型机械, 2005(6)：49-52.
[18]刘晓星.冷连轧机轧制规程的多目标模糊优化设计[J].钢铁, 2000, 35(8): 34-36.
[19]郭立伟,杨荃.基于模糊聚类分析的冷连轧负荷分配修正[J].钢铁, 2006, 41(7): 57-60.
[20] J. S. Son, D. M. Lee, I. S. Kim, S. G. Choi. A Study on On-line Learning Neural Network forPrediction for Rolling Force in Hot-rolling Mill[J]. Journal of Materials Processing Technology,2005, 164: 1612-1617.
[21]孙晓光,常春,刘相华,等.精轧机组负荷分配的人工神经网络识别[J].钢铁, 1995, 30(11):25-29.
[22] D. M. Lee, S. G. Choi. Application of On-line Adaptable Neural Network for the Rolling ForceSet-up of a Plate Mill[J]. Engineering Applications of Artificial Intelligence, 2004, 17(5):557-565.
[23] N. Chakraborti, B. Siva Kumar, V. Satish Babu, etc. Optimizing Surface Profiles During HotRolling: A Genetic Algorithms Based Multi-Objective Optimization[J]. Computational MaterialsScience, 2006,37(12):159-165.
[24]王焱,刘景录,孙一康.免疫遗传算法对精轧机组负荷分配的优化[J].北京科技大学学报,2002, 24(3): 339-341.
[25] A. Tsangrassoulis, V. Bourdakis, V. Geros, et al. A Genetic Algorithm Solution to the Design ofSlat-type Shading System[J]. Renewable Energy, 2006, 31(14): 2321-2328.
[26]郭立伟,杨荃.冷连轧负荷分配优化方法[J].钢铁研究学报, 2007, 19(12): 31-34.
[27] J. C. Zhou, W. J. Li, J. B. Zhu. Particle swarm optimization computer simulation of Ni clusters.Trans[J]. Nonferrous Met. Soc, 2008,18: 410-415.
[28] A. H. Kashan, B. Karimi. A discrete particle swarm optimization algorithm for schedulingparallel machines[J]. Computers & Industrial Engineering, 2009, 56(1): 216-223.
[29]张延华,刘相华,王国栋.基于数据挖掘的中厚钢板轧制负荷分配方法的研究[J].钢铁,2005, 40(4): 44-45, 52.
[30]王焱,刘景录,孙一康.基于IGA-BP网络混合模型的冷连轧机组负荷分配优化法[J].钢铁研究学报, 2002, 14(3): 64-67.
[31]孙一康.冷热轧板带轧机的模型与控制[M].北京:冶金工业出版社, 2010.
[32]任勇,程晓茹.轧制规程数学模型[M].北京:冶金工业出版社, 2008.
[33]车海军,刘畅,孙晓娜,等.基于遗传粒子群算法的冷连轧轧制规程优化设计[J].轧钢,2009,1(26): 22-25.
[34]杨景明,徐雅洁,韩宗刚,等.神经网络预报在冷连轧规程设计中的应用[J].冶金设备,2006(1): 7-11.
[35]张大志.以板形板厚为目标的冷连轧机及其轧制参数智能化优化设计[D]．北京:北京科技大学工学博士论文. 1999：98-101.
[36] Kennedy J, Eberhart R. Particle swarm optimization[C]. Proc of IEEE Int Conf on Piscataway,1995:1942-1948.
[37] Eberhart R C, Shi Y. Particle swarm optimization[C]. Proc of Congress on EvolutionaryComputation. Seou, 2001: 81-88.
[38] Peram T, Veeramachaneni K. Fitness-Distance-Ratio based particle swarm optimization[J]. In:Proc. of the IEEE Swarm Intelligence Symp. Indianapolis: IEEE Inc., 2003:174 181.
[39] Naka S, Genji T, Yura T, and Fukuyama Y. Practical Distribution State Estimation using HybridParticle Swarm Optimization[C]. In IEEE Power Engineering Society Winter Meeting, 2001,1(2):815-820.
[40] Clerc M, Kennedy J. The Particle Swarm: explosion, stability, and convergence in a multi-dimensional complex space[C]. IEEE Transaction on Evolutionary Computation, 2002, 6: 58-73.
[41]阮旻智,李庆民,王红军,等.人工免疫粒子群算法在系统可靠性优化中的应用[J].控制理论与应用, 2010, 27(9): 1253-1258.
[42]周頔,孙俊,须文波.具有量子行为的协同粒子群优化算法[J].控制与决策,2011,26(4):582-586.
[43] Zhong Weimin, Li Shaojun, Qian Feng.θ-PSO: A new strategy of particle swarmoptimization[J]. Journal of Zhejiang University Science A, 2008, 9 (6): 786-790.
[44]孟红记,郑鹏,梅国晖,谢植.基于混沌序列的粒子群优化算法[J].控制与决策, 2006, 3:263-266.
[45]王华秋,曹长修.基于模拟退火的并行粒子群优化研究[J].控制与决策, 2005, 5: 500-504.
[46] Dong Sifang, Dong Zengchuan, Ma Junjian, Chen Kangning. Improved PSO algorithm based onchaos theory and its application to design flood hydrograph[J]. Water Science and Engineering,2010, 3(2): 156-165.
[47]朱海梅,吴永萍.一种高速收敛粒子群优化算法[J].控制与决策, 2010, 1: 20-24.
[48] Kennedy J. The Particle Swarm: Social Adaptation of Knowledge[C]. In Proceedings of the IEEEInternational Conference on Evolutionary Computation, 1997,4: 303-308.
[49]单梁,强浩,等.基于Tent映射的混沌优化算法[J].控制与决策, 2005, 2: 179-182.
[50]张学良,温淑花,李海楠,等.基于Tent映射的混沌粒子群优化算法及其应用[J].中国机械工程,2008,19(17) : 2108-2112.
[51] Pires C T A , Ferreira H C , Sales R M,et al. Set-up Optimization for Tandem Cold Mills : a CaseStudy[J ].Journal of Materials Processing Technology , 2006 , 173(3) : 368-375.
[52]李海军,徐建忠,龚殿尧,等.动量项技术在带钢热连轧负荷分配中的应用[J].钢铁, 2006,41 (2): 46-50.
[53]李勇,刘建昌,王昱.改进权重自适应GA及冷连轧轧制规程多目标优化[J].控制理论与应用, 2009, 26(6): 687-693.
[54]魏立新,李兴强,李莹,等.基于改进自适应遗传算法的冷连轧轧制规程优化设计[J].机械工程学报, 2010, 46(16): 136-141.
[55]杨景明,窦富萍,刘舒慧,等.基于遗传算法的冷连轧轧制规程优化设计[J].中国机械工程,2007,18(15):1868-1871.
[56]陈东宁,姜万录,王益群.基于粒子群算法的冷连轧机轧制负荷分配优化[J].中国机械工程,2007, 18 (11): 1303-1306.
[57] Li Y, Liu J.C, Wang Y. An Adaptive Weight PSO for Rolling Schedules Multi-objectiveOptimization of Tandem Cold Rolling[C]. Proceedings of the IEEE International Conference onAutomation and Logistics, 2009, 8: 895-899.
[58]刘华强,唐荻,杨荃,等.多目标遗传算法在八辊五机架全连续冷连轧机轧制策略优化中的应用[J].冶金自动化, 2006(4): 49-53.
[59] I. Das, J. Dennis. A Closer Look at Drawbacks of Minimizing Weightd Sums of Objects forPareto Set Generation in Multicriteria Optimization Problems[J]. Strutural Optimization, 1997,14(1): 63-69.
[60] Y. Jin, M. Olhofer, B.Sendhoff. Dynamic Weighted Aggregation for EvolutionaryMulti-Objective Optimization: Why does it Work and How?[C] In Proceedings of the GeneticAlgorithm and Evolutionary Computation Conference, 2001: 1042-1049.
[61] X. Hu, R. C. Eberhart. Multiobjective Optimization using Dynamic Neighborhood ParticleSwarm Optimization[C]. In Proceedings of the IEEE Congress on Evolutionary Computation,2002, 3(2): 1677-1681.
[62] Engelbrecht A.P.计算机群体智能基础[M].清华大学出版社, 2009, 10: 185-190.
[63] L. Zhang, C. Zhou, X. Liu, et al. Solving Multi Objective Optimization Problems Using ParticleSwarm Optimization[C]. In Proceedings of the IEEE Congress on Evolutionary Computation,2003(4): 2400-2405.
[64] T. bartz-Beielstein, P. Limbourg, J. Mehnen, et al. Particle Swarm Optimizers for ParetoOptimization with Enhanced Archiving Techniques[C]. In Proceedings of the IEEE Congress onEvolutionary Computation, 2003: 1780-1787.
[65] Engelbrecht A.P.计算机群体智能基础[M].清华大学出版社, 2009, 10: 190-193.
[66] J. E. Fieldsend. Novel Algorithms for Multi-Objective Search and their Application in Mult-Objective Evolutionary Neural Network Training[D]. University of California, 2003.
[67]刘衍民,赵庆祯,牛奔,等.基于ε占优的自适应多目标粒子群算法[J].控制与决策, 2011,26(1): 89-95.
[68]王丽萍,江波,邱飞岳.基于多目标进化算法的系统设计冲突消解方法[J].计算机集成制造系统, 2010, 16(9): 1836-1843.
[69]施展,陈庆伟.基于QPSO和拥挤距离排序的多目标量子粒子群优化算法[J].控制与决策,2011, 26(4): 540-547.