量子进化算法的改进研究及其在轧制规程优化中的实践
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摘要
冷轧带钢生产在我国国民经济中占有重要的地位。目前，虽然我国钢铁产量巨大，但是整体生产水平偏低，尤其是冷轧板带生产的核心技术多掌握在国外公司手中。因此，建造拥有自主知识产权的现代化冷连轧生产线，生产出高质量的冷轧带钢，增强产品在市场上的竞争力是国内科研人员的共同目标。轧制规程设定是冷连轧工艺的核心技术之一，建立更合理的轧制规程是提高冷轧带钢质量的有效途径之一，在这方面我国与国际先进水平尚有一定的差距，必须进行更全面、更深入的研究，才能赶超国际先进水平。本文结合某厂1450mm全连续五机架冷连轧机工艺优化计算机系统研发的工程实践，对冷连轧机工艺优化计算机系统进行了基于量子进化算法和支持向量机的轧制规程优化研究与实践。
轧制工艺数学模型是进行轧制规程优化的基础，针对不同的工艺优化目标可以建立不同的目标函数及约束条件。本文对量子旋转门角度更新策略进行了研究，通过改进量子旋转门角度更新查询表提升了量子进化算法的收敛性能；以能耗最低为目标，应用改进的量子进化算法对轧制规程进行优化，使轧制总功率降低3%以上。将其应用于某厂五机架冷连轧机组的规程计算中，自2011年3月投产以来，节约了大量的能源，创造了巨大的经济效益。
在传统量子进化算法中，应用查询表对量子旋转门角度进行更新时必须针对具体问题具体设计查询表，通用性较差。为了克服这一缺点，引入粒子群算法和微分进化算法，通过其在角度空间进行启发式搜索的方式进行量子旋转门角度更新，提出了两种混合量子进化算法。通过标准函数测试表明，混合量子进化算法增强了量子进化算法的全局收敛性能，提高了通用性，将其应用于轧制规程优化，结果表明，应用该方法达到了均衡轧制力和轧制功率的目的，在工程应用中具有很高的实用价值。
在轧制规程优化过程中，处理多个优化目标的常用办法是将多个目标加权聚合为单个目标进行优化。为了避免权重赋值的人为因素，对应用多目标进化算法实现轧制规程优化进行了探讨。为了提高算法的执行效率，将量子计算以及混沌与多目标进化算法融合，提出了量子混沌多目标进化算法。标准函数测试表明，量子混沌多目标进化算法的收敛速度比NSGA-II高将近30%，最后将之应用于轧制规程优化，获得了合理的结果，为其在冷连轧机轧制规程优化中的应用提供了理论依据，多目标进化算法是规程优化的未来发展方向。
现代化轧机中安装了数以百计的高精度传感器，工艺优化计算机系统的数据库中存储了海量的设备状态数据和轧制过程数据。对数据挖掘工具——支持向量机在轧制力预报中的应用进行了研究和实践。首先整理数据库中的海量数据，建立支持向量机进行轧制力偏差预报的样本库。然后利用样本库中样本对支持向量机进行训练并预报轧制力偏差。最后据此对模型计算所得的轧制力设定值进行修正,冷连轧机的轧制力预报精度提高到5%以内，是轧制规程优化的有效手段。
在某厂全连续五机架冷连轧机工艺优化计算机系统开发实践中，基于WinCC组态软件和Microsoft SQL Server2005数据库平台，运用WinCC组件和ANSI-C和VBScript脚本语言，完成了轧制规程计算与优化程序，开发了完善的人机界面监视系统，实现了轧制过程数据和设备状态数据的归档、查询等功能。
Cold-rolled sheets played an important role in the national economy. Nowadays,Chinese steel production is very huge, but the level of production is lower, especially thecore of cold rolled steel strip production technology almost completely in the hands offoreign companies. Hence, modern cold rolling production line with independentintellectual property rights is built, and the cold-rolled sheets of high of high quality areproduced so as to enhance the competitiveness in the world market, which is a commontarget of domestic researchers. Rolling schedule calculation is one of the core technologiesof tandem cold rolling process, and a reasonable rolling schedule is an effective way ofimproving the quality of the cold-rolled sheets. However, in this respect, there exist greatgaps between Chinese enterprises and advanced international levels; in order to catch upwith the advanced technology in the world, the Chinese reseachers need to make moreintensive study. In this study, relying on engineering practice of process optimizationcomputer system of five stand tandem cold rolling mills in a cold rolled-sheets plant, theoptimization study and practice of the rolling schedule based on quantum evolutionaryalgorithm (QEA) and support vector machine (SVM) is applied to process optimizationcomputer system.
The mathematical models of rolling process are foundation of rolling scheduleoptimization. Aiming at the different technology objectives, different objective functionsand constraints are chosen. The objective functions are optimized by the improvedquantum evolutionary algorithm. Firstly, the lookup table of the quantum rotation gate isanalyzed, which is the most important influence factor of performance of the quantumevolutionary algorithm. The performance is improved by modifying the lookup table.Then, based on the minimize energy consumption objective function, the rolling scheduleis optimized by the improved quantum evolutionary algorithm. The total power reducedmore than3%. This method has already stable operation for two years in a plant, a largenumber of energy is saved and a lot of economic benefits are created.
In the traditional quantum evolutionary algorithm, the rotation angle of quantum rotation gate is updated by the lookup table, but the lookup table needs to be designedaccording to the specific questions, therefore its commonality is poor. For overcoming thisshortage, the particle swarm optimization (PSO) and differential evolutionary algorithm(DEA) are introduced to update the rotation angle of the quantum rotation gate by themean of heuristic search in the angle space, and the hybrid quantum evolutionaryalgorithm (HQEA) is constructed. The test results of standard functions show that thehybrid quantum evolutionary algorithm can strengthen the global convergenceperformance of the quantum evolutionary algorithm and improve its commonality. TheHQEA is applied to optimize the rolling schedule and the rolling force and power arebalanced. Its practical value In the engineering application is proved.
In the process of schedule optimization, the common method of dealing with multipleobjectives optimization is that a weight is given to every objective, and then they areaggregated into one single objective function. For eliminating the human impact of theweight assignment, it is researched that rolling schedule is optimized with multi-objectiveevolutionary algorithm (MOEA). To improve the execution efficiency of multi-objectiveevolutionary algorithm, the quantum computation and chaos are introduced to the MOEA,and quantum chaotic multi-objective evolutionary algorithm (QCMOEA) is proposed.Some standard functions testing show that the efficiency of QCMOEA is30%higher thanNSGA-II. Finally, the QCMOEA is applied to schedule optimization of tandem coldrolling mill, and the reasonable schedules are obtained. There is a theoretical foundationfor MOEA applying to schedule optimization, which is future direction.
At present, hundreds of high accuracy sensors are installed on the modern rolling mill.Therefore, a mass data about equipment status and rolling process are stored in thedatabase of the process optimization computer system. Application of data mining in therolling schedule optimization is discussed and practiced, and support vector machine waschosen as data mining tool to predict the rolling force. Firstly, the mass data in thedatabase is preprocessed and a sample set for rolling force prediction based on supportvector machine is built. Secondly, the support vector machine is trained by the samplesand predicted the rolling force deviations between setting value and measured value.Finally, the result is applied to adjust the setting value of the rolling force, and the accuracy of the rolling force prediction is improved to less than5%. It is an effectivemethod for schedule optimization.
The development of process optimization computer system of tandem cold rollingmill in a sheet plant is practiced based on the WinCC configuration tool and MicrosoftSQL Server2005database tool. The WinCC and programming languages such as ANSI-Cand VBScript are used for building human machine interface (HMI) monitoring system,accomplishing rolling schedule calculation and optimization, realizing the function offiling and query rolling process data and equipment status data, and improving the millmanagement function.
轧制工艺数学模型是进行轧制规程优化的基础，针对不同的工艺优化目标可以建立不同的目标函数及约束条件。本文对量子旋转门角度更新策略进行了研究，通过改进量子旋转门角度更新查询表提升了量子进化算法的收敛性能；以能耗最低为目标，应用改进的量子进化算法对轧制规程进行优化，使轧制总功率降低3%以上。将其应用于某厂五机架冷连轧机组的规程计算中，自2011年3月投产以来，节约了大量的能源，创造了巨大的经济效益。
在传统量子进化算法中，应用查询表对量子旋转门角度进行更新时必须针对具体问题具体设计查询表，通用性较差。为了克服这一缺点，引入粒子群算法和微分进化算法，通过其在角度空间进行启发式搜索的方式进行量子旋转门角度更新，提出了两种混合量子进化算法。通过标准函数测试表明，混合量子进化算法增强了量子进化算法的全局收敛性能，提高了通用性，将其应用于轧制规程优化，结果表明，应用该方法达到了均衡轧制力和轧制功率的目的，在工程应用中具有很高的实用价值。
在轧制规程优化过程中，处理多个优化目标的常用办法是将多个目标加权聚合为单个目标进行优化。为了避免权重赋值的人为因素，对应用多目标进化算法实现轧制规程优化进行了探讨。为了提高算法的执行效率，将量子计算以及混沌与多目标进化算法融合，提出了量子混沌多目标进化算法。标准函数测试表明，量子混沌多目标进化算法的收敛速度比NSGA-II高将近30%，最后将之应用于轧制规程优化，获得了合理的结果，为其在冷连轧机轧制规程优化中的应用提供了理论依据，多目标进化算法是规程优化的未来发展方向。
现代化轧机中安装了数以百计的高精度传感器，工艺优化计算机系统的数据库中存储了海量的设备状态数据和轧制过程数据。对数据挖掘工具——支持向量机在轧制力预报中的应用进行了研究和实践。首先整理数据库中的海量数据，建立支持向量机进行轧制力偏差预报的样本库。然后利用样本库中样本对支持向量机进行训练并预报轧制力偏差。最后据此对模型计算所得的轧制力设定值进行修正,冷连轧机的轧制力预报精度提高到5%以内，是轧制规程优化的有效手段。
在某厂全连续五机架冷连轧机工艺优化计算机系统开发实践中，基于WinCC组态软件和Microsoft SQL Server2005数据库平台，运用WinCC组件和ANSI-C和VBScript脚本语言，完成了轧制规程计算与优化程序，开发了完善的人机界面监视系统，实现了轧制过程数据和设备状态数据的归档、查询等功能。
Cold-rolled sheets played an important role in the national economy. Nowadays,Chinese steel production is very huge, but the level of production is lower, especially thecore of cold rolled steel strip production technology almost completely in the hands offoreign companies. Hence, modern cold rolling production line with independentintellectual property rights is built, and the cold-rolled sheets of high of high quality areproduced so as to enhance the competitiveness in the world market, which is a commontarget of domestic researchers. Rolling schedule calculation is one of the core technologiesof tandem cold rolling process, and a reasonable rolling schedule is an effective way ofimproving the quality of the cold-rolled sheets. However, in this respect, there exist greatgaps between Chinese enterprises and advanced international levels; in order to catch upwith the advanced technology in the world, the Chinese reseachers need to make moreintensive study. In this study, relying on engineering practice of process optimizationcomputer system of five stand tandem cold rolling mills in a cold rolled-sheets plant, theoptimization study and practice of the rolling schedule based on quantum evolutionaryalgorithm (QEA) and support vector machine (SVM) is applied to process optimizationcomputer system.
The mathematical models of rolling process are foundation of rolling scheduleoptimization. Aiming at the different technology objectives, different objective functionsand constraints are chosen. The objective functions are optimized by the improvedquantum evolutionary algorithm. Firstly, the lookup table of the quantum rotation gate isanalyzed, which is the most important influence factor of performance of the quantumevolutionary algorithm. The performance is improved by modifying the lookup table.Then, based on the minimize energy consumption objective function, the rolling scheduleis optimized by the improved quantum evolutionary algorithm. The total power reducedmore than3%. This method has already stable operation for two years in a plant, a largenumber of energy is saved and a lot of economic benefits are created.
In the traditional quantum evolutionary algorithm, the rotation angle of quantum rotation gate is updated by the lookup table, but the lookup table needs to be designedaccording to the specific questions, therefore its commonality is poor. For overcoming thisshortage, the particle swarm optimization (PSO) and differential evolutionary algorithm(DEA) are introduced to update the rotation angle of the quantum rotation gate by themean of heuristic search in the angle space, and the hybrid quantum evolutionaryalgorithm (HQEA) is constructed. The test results of standard functions show that thehybrid quantum evolutionary algorithm can strengthen the global convergenceperformance of the quantum evolutionary algorithm and improve its commonality. TheHQEA is applied to optimize the rolling schedule and the rolling force and power arebalanced. Its practical value In the engineering application is proved.
In the process of schedule optimization, the common method of dealing with multipleobjectives optimization is that a weight is given to every objective, and then they areaggregated into one single objective function. For eliminating the human impact of theweight assignment, it is researched that rolling schedule is optimized with multi-objectiveevolutionary algorithm (MOEA). To improve the execution efficiency of multi-objectiveevolutionary algorithm, the quantum computation and chaos are introduced to the MOEA,and quantum chaotic multi-objective evolutionary algorithm (QCMOEA) is proposed.Some standard functions testing show that the efficiency of QCMOEA is30%higher thanNSGA-II. Finally, the QCMOEA is applied to schedule optimization of tandem coldrolling mill, and the reasonable schedules are obtained. There is a theoretical foundationfor MOEA applying to schedule optimization, which is future direction.
At present, hundreds of high accuracy sensors are installed on the modern rolling mill.Therefore, a mass data about equipment status and rolling process are stored in thedatabase of the process optimization computer system. Application of data mining in therolling schedule optimization is discussed and practiced, and support vector machine waschosen as data mining tool to predict the rolling force. Firstly, the mass data in thedatabase is preprocessed and a sample set for rolling force prediction based on supportvector machine is built. Secondly, the support vector machine is trained by the samplesand predicted the rolling force deviations between setting value and measured value.Finally, the result is applied to adjust the setting value of the rolling force, and the accuracy of the rolling force prediction is improved to less than5%. It is an effectivemethod for schedule optimization.
The development of process optimization computer system of tandem cold rollingmill in a sheet plant is practiced based on the WinCC configuration tool and MicrosoftSQL Server2005database tool. The WinCC and programming languages such as ANSI-Cand VBScript are used for building human machine interface (HMI) monitoring system,accomplishing rolling schedule calculation and optimization, realizing the function offiling and query rolling process data and equipment status data, and improving the millmanagement function.
引文
[1]陈新良.钢铁产能过剩分析[J].中国经济报告,2013(04):66-69.
[2]黄文.国际薄板市场短期展望[J].冶金管理,2012(10):16-20.
[3]刘志兴,迟京东.我国冷连轧机工艺技术装备及生产水平浅析[J].中国钢铁业,2009(10):15-19.
[4]谢东钢,高林林.我国冷轧板带材生产技术现状及发展方向[J].重型机械,2011(4):2-6.
[5]我国首套自主化大型冷连轧机组投产[J].重型机械,2011(02):51.
[6]廖砚林.中国冷轧技术的自主创新能力[J].上海金属,2007,29(5):10-13.
[7]王国栋,刘相华.金属轧制过程人工智能优化[M].北京:冶金工业出版社,1999:1-8.
[8]徐金梧.中国冶金装备技术现状及发展对策思考[J].中国冶金,2009,19(11):1-4.
[9]许健勇.关于带钢冷轧机选型的探讨[J].钢铁,2008,43(5):1-6.
[10]何安瑞,张清东,杨荃,等.现代化冷连轧机的最佳机型配置[J].钢铁,2004,39(5):43-46.
[11]魏玉鹏.浅谈现代冷轧带钢技术的发展现状及趋势[J].中国新技术新产品,2012(13):124.
[12] Okamoto T, Kawasoko Y, Fujii S, et al. Fukuyama's Fully Continuous Tandem Cold Mill[J].Iron and Steel Engineer,1972,49(5):79-83.
[13]高宏适.近三十年新日铁轧制技术发展[N]．世界金属导报，2012-10-16(B04).
[14]华建新,王贞祥.全连续式冷连轧机过程控制[M].北京:冶金工业出版社,2000:6-10.
[15]刘战英.冷轧窄带钢节能压下规程的优化设计[J].钢铁研究,1997(1):15-18.
[16] Bryant G F. Automation of Tandem Mills[M]. London: Iron and Steel Institute,1973:13-16
[17]镰田正诚.板带连续轧制——追求世界一流技术的记录[M].李伏桃,陈岿,康永林,译.北京:冶金工业出版社,2002:3-15.
[18] Sekiguchi K, Seki Y, Okitani N, et al. The Advanced Set-Up and Control System for Dofasco'sTandem Cold Mill [J]. Industry Applications, IEEE Transactions on,1996,32(3):608-616.
[19] Li H, Xu J, Wang G, et al. Improvement on Conventional Load Distribution Algorithm in HotTandem Mills[J]. Journal of Iron and Steel Research, International,2007,14(2):36-41.
[20]矫志杰,赵启林,王军生,等.冷连轧机过程控制在线负荷分配方法[J].钢铁,2005(03):44-47.
[21]徐俊,周莲莲,胡海东,等.冷连轧机在线负荷设定技术的研究[J].中国冶金,2007(07):16-18.
[22]孙一康.带钢冷连轧计算机控制[M].北京：冶金工业出版社,2002:92-97.
[23]张进之.热连轧机负荷分配方法的分析和综述[J].宽厚板,2004(03):14-21.
[24]武贺,吕立华.板带轧机负荷分配方法的综述[J].控制工程,2009(S2):6-10.
[25]梁国平.关于轧机的最佳负荷分配问题[J].钢铁,1980(01):42-48.
[26]张大志,尹凤福,李谋渭,等.基于遗传算法的冷连轧参数优化设计系统[J].上海金属,2000(06):25-30.
[27]白振华,连家创,王骏飞.冷连轧机以预防打滑为目标的压下规程优化研究[J].钢铁,2003(10):35-38.
[28]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(11):1303-1306.
[29]车海军,刘畅,孙晓娜,等.基于粒子群算法的冷连轧轧制规程优化设计[J].钢铁研究,2009(03):20-23.
[30]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(01):22-25.
[31] Yang J, Che H, Dou F, et al. Genetic Algorithm-Based Optimization Used in Rolling Schedule[J].Journal of Iron and Steel Research, International,2008,15(2):18-22.
[32]王焱,孙一康.基于板厚板形综合目标函数的冷连轧机轧制参数智能优化新方法[J].冶金自动化,2002(03):11-14.
[33]王焱,孙一康.基于免疫遗传算法的冷连轧机轧制参数优化方法[J].信息与控制,2002(02):189-192.
[34] Wang D D, Tieu A K, D'Alessio G. Computational Intelligence-Based Process Optimization forTandem Cold Rolling[J]. Materials and Manufacturing processes,2005,20(3):479-496.
[35] Wang D D, Tieu A K, de Boer F G, et al. Toward a Heuristic Optimum Design of RollingSchedules for Tandem Cold Rolling Mills[J]. Engineering Applications of Artificial Intelligence,2000,13(4):397-406.
[36]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(15):1868-1871.
[37]杨景明,韩欣艳,车海军,等.基于改进自适应遗传算法的轧制规程优化设计[J].轧钢,2011(01):24-28.
[38] Li Y, Liu J, Wang Y. An Adaptive Weight PSO for Rolling Schedules Multi-ObjectiveOptimization of Tandem Cold Rolling[C]//Automation and Logistics,2009. ICAL'09. IEEEInternational Conference on, Shenyang, China,2009:895-899.
[39]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(06):687-693.
[40] Yang J, Zhang Q, Che H, et al. Multi-Objective Optimization for Tandem Cold Rolling Schedule[J]. Journal of Iron and Steel Research, International,2010,17(11):34-39.
[41] Chakraborti N, Siva Kumar B, Satish Babu V, et al. A New Multi-Objective Genetic AlgorithmApplied to Hot-Rolling Process [J]. Applied Mathematical Modelling,2008,32(9):1781-1789.
[42]李勇.多目标进化算法及其在轧制规程优化中的应用研究[D].沈阳：东北大学博士学位论文,2010:145.
[43] Poursina M, Dehkordi N T, Fattahi A, et al. Application of Genetic Algorithms to Optimizationof Rolling Schedules Based On Damage Mechanics[J]. Simulation Modelling Practice andTheory,2012,22:61-73.
[44] Kim Y K, Kwak W J, Shin T J, et al. A New Model for the Prediction of Roll Force and TensionProfiles in Flat Rolling [J]. ISIJ International,2010,50(11):1644-1652.
[45] Jiang Z Y, Xiong S W, Tieu A K, et al. Modelling of the Effect of Friction On Cold StripRolling[J]. Journal of Materials Processing Technology,2008,201(1–3):85-90.
[46] Tieu A K, Liu Y J. Friction Variation in the Cold-Rolling Process [J]. Tribology International,2004,37(2):177-183.
[47] Auzinger D, Pfaffermayr M, Pichler R, et al. Advanced Process Models for Today's Hot StripMill [J]. Metallurgical Plant and Technology International,1995,18(6):58-64.
[48] Larkiola J, Myllykoski P, Nylander J, et al. Prediction of Rolling Force in Cold Rolling by UsingPhysical Models and Neural Computing[J]. Journal of Materials Processing Technology,1996,60(1-4):381-386.
[49]干解民,单旭沂,胡贤磊,等.基于数据集市的轧制力预报BP网络的数据挖掘[C].中国金属学会2002年全国轧钢生产技术会议暨第七届轧钢年会.北京,2002.
[50]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):43-45,52.
[51]祝孔林,单旭沂.精轧负荷分配自动实现技术及应用[J].钢铁,2007,42(1):45-49.
[52] Dos Santos Filho A L, Javier Ramirez-Fernandez F. A Neural Network-Based Preset GenerationTool for a Steel Tandem Cold Mill[J]. Engineering Applications of Artificial Intelligence,2010,23(2):169-176.
[53] Shor P W. Algorithms for Quantum Computation: Discrete Logarithms and Factoring,1994:124-134.
[54] Cao G, Li H, Tu T, et al. Ultrafast Universal Quantum Control of a Quantum-Dot Charge QubitUsing Landau–Zener–Stückelberg Interference[J]. Nature communications,2013,4:1-6.
[55] Narayanan A, Moore M. Quantum-Inspired Genetic Algorithms[C]//Evolutionary Computation,1996., Proceedings of IEEE International Conference on, Nagoya,20-22May1996:61-66.
[56] Han K H, Kim J H. Genetic Quantum Algorithm and its Application to CombinatorialOptimization Problem[J]. Proceedings of The2000Congress on Evolutionary Computation, Vols1And2,2000:1354-1360.
[57] Han K, Kim J. Quantum-Inspired Evolutionary Algorithm for a Class of CombinatorialOptimization[J]. Evolutionary Computation, IEEE Transactions on,2002,6(6):580-593.
[58] Alba E, Dorronsoro B. The Exploration/Exploitation Tradeoff in Dynamic Cellular GeneticAlgorithms[J]. Evolutionary Computation, IEEE Transactions on,2005,9(2):126-142.
[59] Mikki S M, Kishk A A. Quantum Particle Swarm Optimization for Electromagnetics[J].Antennas and Propagation, IEEE Transactions on,2006,54(10):2764-2775.
[60] Nodehi S, Tayarani M, Mahmoudi F. A Novel Functional Sized Population QuantumEvolutionary Algorithm for Fractal Image Compression[C]//Computer Conference,2009. CSICC2009.14th International CSI, Tehran,2009,20-21Oct:564-569.
[61] Zhang G, Jin W, Hu L. A Novel Parallel Quantum Genetic Algorithm[C]//Parallel andDistributed Computing, Applications and Technologies,2003. PDCAT'2003. Proceedings of theFourth International Conference on,2003,27-29Aug.:693-697.
[62]杨俊安,庄镇泉,史亮.多宇宙并行量子遗传算法[J].电子学报,2004,32(6):923-928.
[63] Sun J, Xu W B, Feng B. A Global Search Strategy of Quantum-Behaved Particle SwarmOptimization[C]//Cybernetics and Intelligent Systems,2004IEEE Conference on,2004,1-3Dec:111-116.
[64]王凌,吴昊,唐芳,等.混合量子遗传算法及其性能分析[J].控制与决策,2005,20(2):156-160.
[65]李士勇,李盼池.基于实数编码和目标函数梯度的量子遗传算法[J].哈尔滨工业大学学报,2006,38(8):1216-1218,1223.
[66]李阳阳,焦李成.求解SAT问题的量子免疫克隆算法[J].计算机学报,2007,30(2):176-183.
[67] Li P C, Li S Y. Quantum-Inspired Evolutionary Algorithm for Continuous Space OptimizationBased On Bloch Coordinates of Qubits[J]. Neurocomputing,2008,72(1-3):581-591.
[68]高颖慧,沈振康.角度编码染色体量子遗传算法[J].计算机工程与科学,2009,31(3):75-79.
[69]周殊,潘炜,罗斌,等.一种基于粒子群优化方法的改进量子遗传算法及应用[J].电子学报,2006,34(5):897-901.
[70]李盼池,李士勇.求解连续空间优化问题的混沌量子免疫算法[J].模式识别与人工智能,2007,20(5):654-660.
[71] Zhao S, Xu G, Tao T, et al. Real-Coded Chaotic Quantum-Inspired Genetic Algorithm forTraining of Fuzzy Neural Networks[J]. Computers&Mathematics with Applications,2009,57(11–12):2009-2015.
[72] Xiao J, Xu J, Chen Z, et al. A Hybrid Quantum Chaotic Swarm Evolutionary Algorithm for DNAEncoding[J]. Computers&Mathematics with Applications,2009,57(11–12):1949-1958.
[73] Cai Y, Zhang M, Cai H. A Hybrid Chaotic Quantum Evolutionary Algorithm[C]//IntelligentComputing and Intelligent Systems (ICIS),2010IEEE International Conference on, Xiamen,2010,29-31Oct:771-776.
[74] Wang L, Li L. An Effective Hybrid Quantum-Inspired Evolutionary Algorithm for ParameterEstimation of Chaotic Systems[J]. Expert Systems with Applications,2010,37(2):1279-1285.
[75] Zhang G, Gheorghe M, Wu C. A Quantum-Inspired Evolutionary Algorithm Based On PSystems for Knapsack Problem[J]. Fundamenta informaticae,2008,87(1):93-116.
[76] Konak A, Coit D W, Smith A E. Multi-Objective Optimization Using Genetic Algorithms: ATutorial[J]. Reliability Engineering&System Safety,2006,91(9):992-1007.
[77]马小姝,李宇龙,严浪.传统多目标优化方法和多目标遗传算法的比较综述[J].电气传动自动化,2010,32(3):48-50,53.
[78]公茂果,焦李成,杨咚咚,等.进化多目标优化算法研究[J].软件学报,2009,20(2):271-289.
[79] Fonseca C M, Fleming P J. Genetic Algorithms for Multiobjective Optimization: Formulation,Discussion and Generalization.[C]//Proceedings of the Fifth International Conference onGenetic Algorithms, San Mateo,1993. Morgan Kauffman Publishers:416-423.
[80] Srinivas N, Deb K. Multiobjective Optimization Using Nondominated Sorting in GeneticAlgorithms[J].1994,2(03):221-248.
[81] Horn J, Nafpliotis N, Goldberg D E. A Niched Pareto Genetic Algorithm for MultiobjectiveOptimization[C]//Evolutionary Computation,1994. IEEE World Congress on ComputationalIntelligence., Proceedings of the First IEEE Conference on, Orlando, FL,1994,27-29Jun:82-87.
[82] Coello Coello C A. Evolutionary Multiobjective Optimization: Current and Future Challenges[J].Advances in Soft Computing-Engineering, Design and Manufacturing, Springer, Berlin,2003:243-256.
[83] Coello Coello C A. Evolutionary Multi-Objective Optimization: A Historical View of theField[J]. Computational Intelligence Magazine, IEEE,2006,1(1):28-36.
[84] Zitzler E, Laumanns M, Thiele L, et al. SPEA2: Improving the Strength Pareto EvolutionaryAlgorithm[R].Computer Engineering and Networks Laboratory, Department of ElectricalEngineering, Swiss Federal Institute of Technology (ETH), Zurich,2001.
[85] Knowles J D, Corne D W. Approximating the Non-Dominated Front Using the Pareto ArchivedEvolution Strategy[J]. Evolutionary Computation,2000,8(2):149-172.
[86] Corne D W, Knowles J D, Oates M J. The Pareto Envelope-Based Selection Algorithm forMulti-Objective Optimization[J]. Proc of Parallel Problem Solving for Nature-PPSN IV,2000,1917:839-848.
[87] Corne D W, Jerram N R, Knowles J D, et al. PESA-II:Region-Based Selection in EvolutionaryMulti-Objective Optimization[C]//Proceedings of the Genetic and Evolutionary ComputationConference (GECCO'2001), San Francisco,2001, July7-11:283-290.
[88] Deb K, Pratap A, Agarwal S, et al. A Fast and Elitist Multiobjective Genetic Algorithm:NSGA-II[J]. Evolutionary Computation, IEEE Transactions on,2002,6(2):182-197.
[89] Coello Coello C A, Pulido G T, Lechuga M S. Handling Multiple Objectives with ParticleSwarm Optimization[J]. Evolutionary Computation, IEEE Transactions on,2004,8(3):256-279.
[90] Gong M, Jiao L, Du H, et al. Multiobjective Immune Algorithm with NondominatedNeighbor-Based Selection[J]. Evol Comput,2008,16(2):225-255.
[91] Tan K C, Yang Y J, Goh C K. A Distributed Cooperative Coevolutionary Algorithm forMultiobjective Optimization[J]. Evolutionary Computation, IEEE Transactions on,2006,10(5):527-549.
[92] Laumanns M, Ocenasek J. Bayesian Optimization Algorithms for Multi-ObjectiveOptimization[M]//GUERVóS J J M, ADAMIDIS P, BEYER H, et al. Parallel Problem Solving fromNature—PPSN VII. Granada, Spain: Springer Berlin Heidelberg,2002:298-307.
[93] Robic T, Filipic B. DEMO: Differential Evolution for Multiobjective Optimization[M]//COELLOCOELLO C A, AGUIRRE A H, ZITZLER E. Evolutionary Multi-Criterion Optimization. SpringerBerlin Heidelberg,2005:520-533.
[94] Meshoul S, Mahdi K, Batouche M. A Quantum Inspired Evolutionary Framework forMulti-Objective Optimization[M]//BENTO C, CARDOSO A, DIAS G L. Progress in ArtificialIntelligence. Springer Berlin Heidelberg,2005:190-201.
[95] Kim Y, Kim J, Han K. Quantum-Inspired Multiobjective Evolutionary Algorithm forMultiobjective0/1Knapsack Problems[C]//Evolutionary Computation,2006. CEC2006. IEEECongress on, Vancouver, BC,2006:2601-2606.
[96]邹谊,魏文龙,李斌,等.多目标量子编码遗传算法[J].电子与信息学报,2007,29(11):2688-2692.
[97]唐欢容,蒋浩,郑金华.量子多目标进化算法研究[J].计算机工程与应用,2007,43(13):45-48,60.
[98] Li Z, Li Z, Rudolph G. On the Convergence Properties of Quantum-Inspired Multi-ObjectiveEvolutionary Algorithms[M]//HUANG D, HEUTTE L, LOOG M. Advanced Intelligent ComputingTheories and Applications. With Aspects of Contemporary Intelligent Computing Techniques.Springer Berlin Heidelberg,2007:245-255.
[99]李阳阳,焦李成.量子免疫克隆多目标优化算法[J].电子与信息学报,2008,30(6):1367-1371.
[100]Gao J, Wang J. A Hybrid Quantum-Inspired Immune Algorithm for MultiobjectiveOptimization[J]. Applied Mathematics and Computation,2011,217(9):4754-4770.
[101]范胜辉,石玉,刘楠楠.多目标优化量子进化算法及其在PID控制器中的应用[J].佳木斯大学学报（自然科学版）,2010,28(2):165-168,171.
[102]Ahmad N H, Rahman T K A, Aminuddin N. Multi-Objective Quantum-Inspired ArtificialImmune System Approach for Optimal Network Reconfiguration in DistributionSystem[C]//Power Engineering and Optimization Conference (PEDCO) Melaka, Malaysia,2012Ieee International, Melaka,2012,6-7June:384-388.
[103]Kumari A C, Srinivas K, Gupta M P. Software Requirements Selection Using Quantum-inspiredElitist Multi-objective Evolutionary Algorithm[C]//Advances in Engineering, Science andManagement (ICAESM),2012International Conference on, Nagapattinam, Tamil Nadu,2012,30-31March:782-787.
[104]王立伟.数据挖掘研究现状综述[J].图书与情报,2008(5):41-46.
[105]郭崇慧,陆玉昌.预测型数据挖掘中的优化方法[J].工程数学学报,2005,22(1):25-29.
[106]张学工.关于统计学习理论与支持向量机[J].自动化学报,2000(01):36-46.
[107]Evgeniou T, Pontil M, Poggio T. Regularization Networks and Support Vector Machines[J].Advances in Computational Mathematics,2000,13(1):1-50.
[108]Suykens J A K, Lukas L, Vandewalle J. Sparse Approximation Using Least Squares SupportVector Machines[C]//Circuits and Systems,2000. Proceedings. ISCAS2000Geneva. The2000IEEE International Symposium on, Geneva,2000:757-760.
[109]Espinoza M, Suykens J A K, De Moor B. Load Forecasting Using Fixed-Size Least SquaresSupport Vector Machines[C]//8th International Workshop on Artificial Neural Networks,IWANN2005: Computational Intelligence and Bioinspired Systems, June8,2005-June10,2005, Vilanova i la Geltru, Spain,2005. Springer Verlag:1018-1026.
[110]Vapnik V, Vashist A. A New Learning Paradigm: Learning Using Privileged Information[J].Neural Networks,2009,22(5–6):544-557.
[111]Suárez Sánchez A, García Nieto P J, Riesgo Fernández P, et al. Application of an SVM-basedRegression Model to the Air Quality Study at Local Scale in the Avilés Urban Area (Spain)[J].Mathematical and Computer Modelling,2011,54(5–6):1453-1466.
[112]叶美盈,汪晓东,张浩然.基于在线最小二乘支持向量机回归的混沌时间序列预测[J].物理学报,2005(06):2568-2573.
[113]杨滨,杨晓伟,黄岚,等.自适应迭代最小二乘支持向量机回归算法[J].电子学报,2010(07):1621-1625.
[114]Anguita D, Ridella S, Rivieccio F, et al. Quantum Optimization for Training Support VectorMachines.[J]. Neural Networks,2003,16(5/6):763-770.
[115]Pan G, Xia K, Dong Y, et al. An Improved LS-SVM Based on Quantum PSO Algorithm and itsApplication[C]//Natural Computation,2007. ICNC2007. Third International Conference on,Haikou,2007,24-27Aug:606-610.
[116]陈治明,罗飞,黄晓红,等.基于混沌优化支持向量机的轧制力预测[J].控制与决策,2009,24(6):808-812.
[117]刘俊,杨荃,何安瑞,等.贝叶斯框架下的LS-SVM在热连轧机轧制力预报中的应用[J].钢铁研究学报,2011,23(6):5-8,53.
[118]吴东升,王大志,杨青,等.基于ACPSO优化SVR的棒材连轧轧制力预测研究[J].仪器仪表学报,2012,33(11):2579-2585.
[119]王军生,白金兰,刘相华.带钢冷连轧原理与过程控制[M].北京:科学出版社,2009:166-167.
[120]黄力明,徐莹,于瑞琴.改进的量子遗传算法及应用[J].计算机工程与设计,2009,30(8):1987-1990.
[121]张葛祥,李娜.一种新量子遗传算法及其应用[J].电子学报,2004,32(3):476-479.
[122]Gu J, Gu X, Gu M. A Novel Parallel Quantum Genetic Algorithm for Stochastic Job ShopScheduling[J]. Journal of Mathematical Analysis and Applications,2009,355(1):63-81.
[123]Kennedy J, Eberhart R. Particle Swarm Optimization[C]//Neural Networks,1995. Proceedings.IEEE International Conference on,1995:1942-1948.
[124]Shi Y, Eberhart R. A Modified Particle Swarm Optimizer[C]//Evolutionary ComputationProceedings,1998. IEEE World Congress on Computational Intelligence, The1998IEEEInternational Conference on, Anchorage, AK,1998,4-9May:69-73.
[125]Storn R, Price K. Differential Evolution–A Simple and Efficient Heuristic for GlobalOptimization over Continuous Spaces[J]. Journal of Global Optimization,1997(11):341-359.
[126]刘波,王凌,金以慧.差分进化算法研究进展[J].控制与决策,2007(07):721-729.
[127]崔逊学,林闯.多目标进化算法的研究与进展[J].模式识别与人工智能,2003(03):306-314.
[128]Coello Coello C A, Lamont G B. Applications of Multi-objective Evolutionary Algorithms.2004[M]. World Scientific, Singapore,2004.
[129]Schaffer J D. Multiple Objective Optimization with Vector Evaluated Genetic Algorithms[C]//Proceedings of the Third International Conference on Genetic Algorithms, Pittsburgh,1985:93-100.
[130]Whitley D, Rana S, Dzubera J, et al. Evaluating Evolutionary Algorithms[J]. Artificialintelligence,1996,85(1):245-276.
[131]Deb K. Multi-Objective Genetic Algorithms: Problem Difficulties and Construction of TestProblems[J]. Evolutionary computation,1999,7(3):205-230.
[132]Van Veldhuizen D A, Lamont G B. Evolutionary Computation and Convergence to a Pareto Front,1998:221-228.
[133]Chan T, Man K, Tang K, et al. A Jumping Gene Paradigm for Evolutionary MultiobjectiveOptimization[J]. Evolutionary Computation, IEEE Transactions on,2008,12(2):143-159.
[134]刘立衡.多目标进化算法的研究及其在负荷分配中的应用[D].北京：华北电力大学（北京）博士学位论文,2010:48-49.
[135]董洪波,康永林.有限元模拟技术在板带钢轧制中的应用[J].轧钢,2004(02):44-47.
[136]杨志民,刘广利.不确定性支持向量机——原理及应用[M].科学出版社,2012:54-55.
[137]Vapnik V N, Chervonenkis A Y. On the Uniform Convergence of Relative Frequencies of Eventsto their Probabilities[J]. Theory of Probability&Its Applications,1971,16(2):264-280.
[138]Boser B E, Guyon I M, Vapnik V N. A Training Algorithm for Optimal Margin Classifiers,1992:144-152.
[139]Smola A J, Lkopf B S. A Tutorial On Support Vector Regression[J]. Statistics and Computing,2004,14(3):199-222.
[140]闫国华,朱永生.支持向量机回归的参数选择方法[J].计算机工程,2009,35(14):218-220.
[141]刘胜,李妍妍.自适应GA-SVM参数选择算法研究[J].哈尔滨工程大学学报,2007(04):398-402.
[142]Zhou L C, Yang H Z, Liu C B. QPSO-Based Hyper-Parameters Selection for LS-SVMRegression[C]//Natural Computation,2008. ICNC '08. Fourth International Conference on, Jinan,2008,18-20Oct.:130-133.
[143]Shi Y, Li X, Qi X. Parameter Optimization of Support Vector Machine Based on CombinedAlgorithm of QPSO and SA[C]//Pervasive Computing Signal Processing and Applications(PCSPA),2010First International Conference on, Harbin,2010,17-19Sept.:483-486.
[144]甄立东.西门子WinCC V7基础与应用[M].北京:机械工业出版社,2011:1-9.
[145]何华.深入浅出西门子WinCC V6[M].北京:北京航空航天大学出版社,2004:112-150.
[146]谢维成,苏长明. SQL Server2005实例精讲[M].北京:清华大学出版社,2008:150-154.
[2]黄文.国际薄板市场短期展望[J].冶金管理,2012(10):16-20.
[3]刘志兴,迟京东.我国冷连轧机工艺技术装备及生产水平浅析[J].中国钢铁业,2009(10):15-19.
[4]谢东钢,高林林.我国冷轧板带材生产技术现状及发展方向[J].重型机械,2011(4):2-6.
[5]我国首套自主化大型冷连轧机组投产[J].重型机械,2011(02):51.
[6]廖砚林.中国冷轧技术的自主创新能力[J].上海金属,2007,29(5):10-13.
[7]王国栋,刘相华.金属轧制过程人工智能优化[M].北京:冶金工业出版社,1999:1-8.
[8]徐金梧.中国冶金装备技术现状及发展对策思考[J].中国冶金,2009,19(11):1-4.
[9]许健勇.关于带钢冷轧机选型的探讨[J].钢铁,2008,43(5):1-6.
[10]何安瑞,张清东,杨荃,等.现代化冷连轧机的最佳机型配置[J].钢铁,2004,39(5):43-46.
[11]魏玉鹏.浅谈现代冷轧带钢技术的发展现状及趋势[J].中国新技术新产品,2012(13):124.
[12] Okamoto T, Kawasoko Y, Fujii S, et al. Fukuyama's Fully Continuous Tandem Cold Mill[J].Iron and Steel Engineer,1972,49(5):79-83.
[13]高宏适.近三十年新日铁轧制技术发展[N]．世界金属导报，2012-10-16(B04).
[14]华建新,王贞祥.全连续式冷连轧机过程控制[M].北京:冶金工业出版社,2000:6-10.
[15]刘战英.冷轧窄带钢节能压下规程的优化设计[J].钢铁研究,1997(1):15-18.
[16] Bryant G F. Automation of Tandem Mills[M]. London: Iron and Steel Institute,1973:13-16
[17]镰田正诚.板带连续轧制——追求世界一流技术的记录[M].李伏桃,陈岿,康永林,译.北京:冶金工业出版社,2002:3-15.
[18] Sekiguchi K, Seki Y, Okitani N, et al. The Advanced Set-Up and Control System for Dofasco'sTandem Cold Mill [J]. Industry Applications, IEEE Transactions on,1996,32(3):608-616.
[19] Li H, Xu J, Wang G, et al. Improvement on Conventional Load Distribution Algorithm in HotTandem Mills[J]. Journal of Iron and Steel Research, International,2007,14(2):36-41.
[20]矫志杰,赵启林,王军生,等.冷连轧机过程控制在线负荷分配方法[J].钢铁,2005(03):44-47.
[21]徐俊,周莲莲,胡海东,等.冷连轧机在线负荷设定技术的研究[J].中国冶金,2007(07):16-18.
[22]孙一康.带钢冷连轧计算机控制[M].北京：冶金工业出版社,2002:92-97.
[23]张进之.热连轧机负荷分配方法的分析和综述[J].宽厚板,2004(03):14-21.
[24]武贺,吕立华.板带轧机负荷分配方法的综述[J].控制工程,2009(S2):6-10.
[25]梁国平.关于轧机的最佳负荷分配问题[J].钢铁,1980(01):42-48.
[26]张大志,尹凤福,李谋渭,等.基于遗传算法的冷连轧参数优化设计系统[J].上海金属,2000(06):25-30.
[27]白振华,连家创,王骏飞.冷连轧机以预防打滑为目标的压下规程优化研究[J].钢铁,2003(10):35-38.
[28]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(11):1303-1306.
[29]车海军,刘畅,孙晓娜,等.基于粒子群算法的冷连轧轧制规程优化设计[J].钢铁研究,2009(03):20-23.
[30]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(01):22-25.
[31] Yang J, Che H, Dou F, et al. Genetic Algorithm-Based Optimization Used in Rolling Schedule[J].Journal of Iron and Steel Research, International,2008,15(2):18-22.
[32]王焱,孙一康.基于板厚板形综合目标函数的冷连轧机轧制参数智能优化新方法[J].冶金自动化,2002(03):11-14.
[33]王焱,孙一康.基于免疫遗传算法的冷连轧机轧制参数优化方法[J].信息与控制,2002(02):189-192.
[34] Wang D D, Tieu A K, D'Alessio G. Computational Intelligence-Based Process Optimization forTandem Cold Rolling[J]. Materials and Manufacturing processes,2005,20(3):479-496.
[35] Wang D D, Tieu A K, de Boer F G, et al. Toward a Heuristic Optimum Design of RollingSchedules for Tandem Cold Rolling Mills[J]. Engineering Applications of Artificial Intelligence,2000,13(4):397-406.
[36]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(15):1868-1871.
[37]杨景明,韩欣艳,车海军,等.基于改进自适应遗传算法的轧制规程优化设计[J].轧钢,2011(01):24-28.
[38] Li Y, Liu J, Wang Y. An Adaptive Weight PSO for Rolling Schedules Multi-ObjectiveOptimization of Tandem Cold Rolling[C]//Automation and Logistics,2009. ICAL'09. IEEEInternational Conference on, Shenyang, China,2009:895-899.
[39]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(06):687-693.
[40] Yang J, Zhang Q, Che H, et al. Multi-Objective Optimization for Tandem Cold Rolling Schedule[J]. Journal of Iron and Steel Research, International,2010,17(11):34-39.
[41] Chakraborti N, Siva Kumar B, Satish Babu V, et al. A New Multi-Objective Genetic AlgorithmApplied to Hot-Rolling Process [J]. Applied Mathematical Modelling,2008,32(9):1781-1789.
[42]李勇.多目标进化算法及其在轧制规程优化中的应用研究[D].沈阳：东北大学博士学位论文,2010:145.
[43] Poursina M, Dehkordi N T, Fattahi A, et al. Application of Genetic Algorithms to Optimizationof Rolling Schedules Based On Damage Mechanics[J]. Simulation Modelling Practice andTheory,2012,22:61-73.
[44] Kim Y K, Kwak W J, Shin T J, et al. A New Model for the Prediction of Roll Force and TensionProfiles in Flat Rolling [J]. ISIJ International,2010,50(11):1644-1652.
[45] Jiang Z Y, Xiong S W, Tieu A K, et al. Modelling of the Effect of Friction On Cold StripRolling[J]. Journal of Materials Processing Technology,2008,201(1–3):85-90.
[46] Tieu A K, Liu Y J. Friction Variation in the Cold-Rolling Process [J]. Tribology International,2004,37(2):177-183.
[47] Auzinger D, Pfaffermayr M, Pichler R, et al. Advanced Process Models for Today's Hot StripMill [J]. Metallurgical Plant and Technology International,1995,18(6):58-64.
[48] Larkiola J, Myllykoski P, Nylander J, et al. Prediction of Rolling Force in Cold Rolling by UsingPhysical Models and Neural Computing[J]. Journal of Materials Processing Technology,1996,60(1-4):381-386.
[49]干解民,单旭沂,胡贤磊,等.基于数据集市的轧制力预报BP网络的数据挖掘[C].中国金属学会2002年全国轧钢生产技术会议暨第七届轧钢年会.北京,2002.
[50]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):43-45,52.
[51]祝孔林,单旭沂.精轧负荷分配自动实现技术及应用[J].钢铁,2007,42(1):45-49.
[52] Dos Santos Filho A L, Javier Ramirez-Fernandez F. A Neural Network-Based Preset GenerationTool for a Steel Tandem Cold Mill[J]. Engineering Applications of Artificial Intelligence,2010,23(2):169-176.
[53] Shor P W. Algorithms for Quantum Computation: Discrete Logarithms and Factoring,1994:124-134.
[54] Cao G, Li H, Tu T, et al. Ultrafast Universal Quantum Control of a Quantum-Dot Charge QubitUsing Landau–Zener–Stückelberg Interference[J]. Nature communications,2013,4:1-6.
[55] Narayanan A, Moore M. Quantum-Inspired Genetic Algorithms[C]//Evolutionary Computation,1996., Proceedings of IEEE International Conference on, Nagoya,20-22May1996:61-66.
[56] Han K H, Kim J H. Genetic Quantum Algorithm and its Application to CombinatorialOptimization Problem[J]. Proceedings of The2000Congress on Evolutionary Computation, Vols1And2,2000:1354-1360.
[57] Han K, Kim J. Quantum-Inspired Evolutionary Algorithm for a Class of CombinatorialOptimization[J]. Evolutionary Computation, IEEE Transactions on,2002,6(6):580-593.
[58] Alba E, Dorronsoro B. The Exploration/Exploitation Tradeoff in Dynamic Cellular GeneticAlgorithms[J]. Evolutionary Computation, IEEE Transactions on,2005,9(2):126-142.
[59] Mikki S M, Kishk A A. Quantum Particle Swarm Optimization for Electromagnetics[J].Antennas and Propagation, IEEE Transactions on,2006,54(10):2764-2775.
[60] Nodehi S, Tayarani M, Mahmoudi F. A Novel Functional Sized Population QuantumEvolutionary Algorithm for Fractal Image Compression[C]//Computer Conference,2009. CSICC2009.14th International CSI, Tehran,2009,20-21Oct:564-569.
[61] Zhang G, Jin W, Hu L. A Novel Parallel Quantum Genetic Algorithm[C]//Parallel andDistributed Computing, Applications and Technologies,2003. PDCAT'2003. Proceedings of theFourth International Conference on,2003,27-29Aug.:693-697.
[62]杨俊安,庄镇泉,史亮.多宇宙并行量子遗传算法[J].电子学报,2004,32(6):923-928.
[63] Sun J, Xu W B, Feng B. A Global Search Strategy of Quantum-Behaved Particle SwarmOptimization[C]//Cybernetics and Intelligent Systems,2004IEEE Conference on,2004,1-3Dec:111-116.
[64]王凌,吴昊,唐芳,等.混合量子遗传算法及其性能分析[J].控制与决策,2005,20(2):156-160.
[65]李士勇,李盼池.基于实数编码和目标函数梯度的量子遗传算法[J].哈尔滨工业大学学报,2006,38(8):1216-1218,1223.
[66]李阳阳,焦李成.求解SAT问题的量子免疫克隆算法[J].计算机学报,2007,30(2):176-183.
[67] Li P C, Li S Y. Quantum-Inspired Evolutionary Algorithm for Continuous Space OptimizationBased On Bloch Coordinates of Qubits[J]. Neurocomputing,2008,72(1-3):581-591.
[68]高颖慧,沈振康.角度编码染色体量子遗传算法[J].计算机工程与科学,2009,31(3):75-79.
[69]周殊,潘炜,罗斌,等.一种基于粒子群优化方法的改进量子遗传算法及应用[J].电子学报,2006,34(5):897-901.
[70]李盼池,李士勇.求解连续空间优化问题的混沌量子免疫算法[J].模式识别与人工智能,2007,20(5):654-660.
[71] Zhao S, Xu G, Tao T, et al. Real-Coded Chaotic Quantum-Inspired Genetic Algorithm forTraining of Fuzzy Neural Networks[J]. Computers&Mathematics with Applications,2009,57(11–12):2009-2015.
[72] Xiao J, Xu J, Chen Z, et al. A Hybrid Quantum Chaotic Swarm Evolutionary Algorithm for DNAEncoding[J]. Computers&Mathematics with Applications,2009,57(11–12):1949-1958.
[73] Cai Y, Zhang M, Cai H. A Hybrid Chaotic Quantum Evolutionary Algorithm[C]//IntelligentComputing and Intelligent Systems (ICIS),2010IEEE International Conference on, Xiamen,2010,29-31Oct:771-776.
[74] Wang L, Li L. An Effective Hybrid Quantum-Inspired Evolutionary Algorithm for ParameterEstimation of Chaotic Systems[J]. Expert Systems with Applications,2010,37(2):1279-1285.
[75] Zhang G, Gheorghe M, Wu C. A Quantum-Inspired Evolutionary Algorithm Based On PSystems for Knapsack Problem[J]. Fundamenta informaticae,2008,87(1):93-116.
[76] Konak A, Coit D W, Smith A E. Multi-Objective Optimization Using Genetic Algorithms: ATutorial[J]. Reliability Engineering&System Safety,2006,91(9):992-1007.
[77]马小姝,李宇龙,严浪.传统多目标优化方法和多目标遗传算法的比较综述[J].电气传动自动化,2010,32(3):48-50,53.
[78]公茂果,焦李成,杨咚咚,等.进化多目标优化算法研究[J].软件学报,2009,20(2):271-289.
[79] Fonseca C M, Fleming P J. Genetic Algorithms for Multiobjective Optimization: Formulation,Discussion and Generalization.[C]//Proceedings of the Fifth International Conference onGenetic Algorithms, San Mateo,1993. Morgan Kauffman Publishers:416-423.
[80] Srinivas N, Deb K. Multiobjective Optimization Using Nondominated Sorting in GeneticAlgorithms[J].1994,2(03):221-248.
[81] Horn J, Nafpliotis N, Goldberg D E. A Niched Pareto Genetic Algorithm for MultiobjectiveOptimization[C]//Evolutionary Computation,1994. IEEE World Congress on ComputationalIntelligence., Proceedings of the First IEEE Conference on, Orlando, FL,1994,27-29Jun:82-87.
[82] Coello Coello C A. Evolutionary Multiobjective Optimization: Current and Future Challenges[J].Advances in Soft Computing-Engineering, Design and Manufacturing, Springer, Berlin,2003:243-256.
[83] Coello Coello C A. Evolutionary Multi-Objective Optimization: A Historical View of theField[J]. Computational Intelligence Magazine, IEEE,2006,1(1):28-36.
[84] Zitzler E, Laumanns M, Thiele L, et al. SPEA2: Improving the Strength Pareto EvolutionaryAlgorithm[R].Computer Engineering and Networks Laboratory, Department of ElectricalEngineering, Swiss Federal Institute of Technology (ETH), Zurich,2001.
[85] Knowles J D, Corne D W. Approximating the Non-Dominated Front Using the Pareto ArchivedEvolution Strategy[J]. Evolutionary Computation,2000,8(2):149-172.
[86] Corne D W, Knowles J D, Oates M J. The Pareto Envelope-Based Selection Algorithm forMulti-Objective Optimization[J]. Proc of Parallel Problem Solving for Nature-PPSN IV,2000,1917:839-848.
[87] Corne D W, Jerram N R, Knowles J D, et al. PESA-II:Region-Based Selection in EvolutionaryMulti-Objective Optimization[C]//Proceedings of the Genetic and Evolutionary ComputationConference (GECCO'2001), San Francisco,2001, July7-11:283-290.
[88] Deb K, Pratap A, Agarwal S, et al. A Fast and Elitist Multiobjective Genetic Algorithm:NSGA-II[J]. Evolutionary Computation, IEEE Transactions on,2002,6(2):182-197.
[89] Coello Coello C A, Pulido G T, Lechuga M S. Handling Multiple Objectives with ParticleSwarm Optimization[J]. Evolutionary Computation, IEEE Transactions on,2004,8(3):256-279.
[90] Gong M, Jiao L, Du H, et al. Multiobjective Immune Algorithm with NondominatedNeighbor-Based Selection[J]. Evol Comput,2008,16(2):225-255.
[91] Tan K C, Yang Y J, Goh C K. A Distributed Cooperative Coevolutionary Algorithm forMultiobjective Optimization[J]. Evolutionary Computation, IEEE Transactions on,2006,10(5):527-549.
[92] Laumanns M, Ocenasek J. Bayesian Optimization Algorithms for Multi-ObjectiveOptimization[M]//GUERVóS J J M, ADAMIDIS P, BEYER H, et al. Parallel Problem Solving fromNature—PPSN VII. Granada, Spain: Springer Berlin Heidelberg,2002:298-307.
[93] Robic T, Filipic B. DEMO: Differential Evolution for Multiobjective Optimization[M]//COELLOCOELLO C A, AGUIRRE A H, ZITZLER E. Evolutionary Multi-Criterion Optimization. SpringerBerlin Heidelberg,2005:520-533.
[94] Meshoul S, Mahdi K, Batouche M. A Quantum Inspired Evolutionary Framework forMulti-Objective Optimization[M]//BENTO C, CARDOSO A, DIAS G L. Progress in ArtificialIntelligence. Springer Berlin Heidelberg,2005:190-201.
[95] Kim Y, Kim J, Han K. Quantum-Inspired Multiobjective Evolutionary Algorithm forMultiobjective0/1Knapsack Problems[C]//Evolutionary Computation,2006. CEC2006. IEEECongress on, Vancouver, BC,2006:2601-2606.
[96]邹谊,魏文龙,李斌,等.多目标量子编码遗传算法[J].电子与信息学报,2007,29(11):2688-2692.
[97]唐欢容,蒋浩,郑金华.量子多目标进化算法研究[J].计算机工程与应用,2007,43(13):45-48,60.
[98] Li Z, Li Z, Rudolph G. On the Convergence Properties of Quantum-Inspired Multi-ObjectiveEvolutionary Algorithms[M]//HUANG D, HEUTTE L, LOOG M. Advanced Intelligent ComputingTheories and Applications. With Aspects of Contemporary Intelligent Computing Techniques.Springer Berlin Heidelberg,2007:245-255.
[99]李阳阳,焦李成.量子免疫克隆多目标优化算法[J].电子与信息学报,2008,30(6):1367-1371.
[100]Gao J, Wang J. A Hybrid Quantum-Inspired Immune Algorithm for MultiobjectiveOptimization[J]. Applied Mathematics and Computation,2011,217(9):4754-4770.
[101]范胜辉,石玉,刘楠楠.多目标优化量子进化算法及其在PID控制器中的应用[J].佳木斯大学学报（自然科学版）,2010,28(2):165-168,171.
[102]Ahmad N H, Rahman T K A, Aminuddin N. Multi-Objective Quantum-Inspired ArtificialImmune System Approach for Optimal Network Reconfiguration in DistributionSystem[C]//Power Engineering and Optimization Conference (PEDCO) Melaka, Malaysia,2012Ieee International, Melaka,2012,6-7June:384-388.
[103]Kumari A C, Srinivas K, Gupta M P. Software Requirements Selection Using Quantum-inspiredElitist Multi-objective Evolutionary Algorithm[C]//Advances in Engineering, Science andManagement (ICAESM),2012International Conference on, Nagapattinam, Tamil Nadu,2012,30-31March:782-787.
[104]王立伟.数据挖掘研究现状综述[J].图书与情报,2008(5):41-46.
[105]郭崇慧,陆玉昌.预测型数据挖掘中的优化方法[J].工程数学学报,2005,22(1):25-29.
[106]张学工.关于统计学习理论与支持向量机[J].自动化学报,2000(01):36-46.
[107]Evgeniou T, Pontil M, Poggio T. Regularization Networks and Support Vector Machines[J].Advances in Computational Mathematics,2000,13(1):1-50.
[108]Suykens J A K, Lukas L, Vandewalle J. Sparse Approximation Using Least Squares SupportVector Machines[C]//Circuits and Systems,2000. Proceedings. ISCAS2000Geneva. The2000IEEE International Symposium on, Geneva,2000:757-760.
[109]Espinoza M, Suykens J A K, De Moor B. Load Forecasting Using Fixed-Size Least SquaresSupport Vector Machines[C]//8th International Workshop on Artificial Neural Networks,IWANN2005: Computational Intelligence and Bioinspired Systems, June8,2005-June10,2005, Vilanova i la Geltru, Spain,2005. Springer Verlag:1018-1026.
[110]Vapnik V, Vashist A. A New Learning Paradigm: Learning Using Privileged Information[J].Neural Networks,2009,22(5–6):544-557.
[111]Suárez Sánchez A, García Nieto P J, Riesgo Fernández P, et al. Application of an SVM-basedRegression Model to the Air Quality Study at Local Scale in the Avilés Urban Area (Spain)[J].Mathematical and Computer Modelling,2011,54(5–6):1453-1466.
[112]叶美盈,汪晓东,张浩然.基于在线最小二乘支持向量机回归的混沌时间序列预测[J].物理学报,2005(06):2568-2573.
[113]杨滨,杨晓伟,黄岚,等.自适应迭代最小二乘支持向量机回归算法[J].电子学报,2010(07):1621-1625.
[114]Anguita D, Ridella S, Rivieccio F, et al. Quantum Optimization for Training Support VectorMachines.[J]. Neural Networks,2003,16(5/6):763-770.
[115]Pan G, Xia K, Dong Y, et al. An Improved LS-SVM Based on Quantum PSO Algorithm and itsApplication[C]//Natural Computation,2007. ICNC2007. Third International Conference on,Haikou,2007,24-27Aug:606-610.
[116]陈治明,罗飞,黄晓红,等.基于混沌优化支持向量机的轧制力预测[J].控制与决策,2009,24(6):808-812.
[117]刘俊,杨荃,何安瑞,等.贝叶斯框架下的LS-SVM在热连轧机轧制力预报中的应用[J].钢铁研究学报,2011,23(6):5-8,53.
[118]吴东升,王大志,杨青,等.基于ACPSO优化SVR的棒材连轧轧制力预测研究[J].仪器仪表学报,2012,33(11):2579-2585.
[119]王军生,白金兰,刘相华.带钢冷连轧原理与过程控制[M].北京:科学出版社,2009:166-167.
[120]黄力明,徐莹,于瑞琴.改进的量子遗传算法及应用[J].计算机工程与设计,2009,30(8):1987-1990.
[121]张葛祥,李娜.一种新量子遗传算法及其应用[J].电子学报,2004,32(3):476-479.
[122]Gu J, Gu X, Gu M. A Novel Parallel Quantum Genetic Algorithm for Stochastic Job ShopScheduling[J]. Journal of Mathematical Analysis and Applications,2009,355(1):63-81.
[123]Kennedy J, Eberhart R. Particle Swarm Optimization[C]//Neural Networks,1995. Proceedings.IEEE International Conference on,1995:1942-1948.
[124]Shi Y, Eberhart R. A Modified Particle Swarm Optimizer[C]//Evolutionary ComputationProceedings,1998. IEEE World Congress on Computational Intelligence, The1998IEEEInternational Conference on, Anchorage, AK,1998,4-9May:69-73.
[125]Storn R, Price K. Differential Evolution–A Simple and Efficient Heuristic for GlobalOptimization over Continuous Spaces[J]. Journal of Global Optimization,1997(11):341-359.
[126]刘波,王凌,金以慧.差分进化算法研究进展[J].控制与决策,2007(07):721-729.
[127]崔逊学,林闯.多目标进化算法的研究与进展[J].模式识别与人工智能,2003(03):306-314.
[128]Coello Coello C A, Lamont G B. Applications of Multi-objective Evolutionary Algorithms.2004[M]. World Scientific, Singapore,2004.
[129]Schaffer J D. Multiple Objective Optimization with Vector Evaluated Genetic Algorithms[C]//Proceedings of the Third International Conference on Genetic Algorithms, Pittsburgh,1985:93-100.
[130]Whitley D, Rana S, Dzubera J, et al. Evaluating Evolutionary Algorithms[J]. Artificialintelligence,1996,85(1):245-276.
[131]Deb K. Multi-Objective Genetic Algorithms: Problem Difficulties and Construction of TestProblems[J]. Evolutionary computation,1999,7(3):205-230.
[132]Van Veldhuizen D A, Lamont G B. Evolutionary Computation and Convergence to a Pareto Front,1998:221-228.
[133]Chan T, Man K, Tang K, et al. A Jumping Gene Paradigm for Evolutionary MultiobjectiveOptimization[J]. Evolutionary Computation, IEEE Transactions on,2008,12(2):143-159.
[134]刘立衡.多目标进化算法的研究及其在负荷分配中的应用[D].北京：华北电力大学（北京）博士学位论文,2010:48-49.
[135]董洪波,康永林.有限元模拟技术在板带钢轧制中的应用[J].轧钢,2004(02):44-47.
[136]杨志民,刘广利.不确定性支持向量机——原理及应用[M].科学出版社,2012:54-55.
[137]Vapnik V N, Chervonenkis A Y. On the Uniform Convergence of Relative Frequencies of Eventsto their Probabilities[J]. Theory of Probability&Its Applications,1971,16(2):264-280.
[138]Boser B E, Guyon I M, Vapnik V N. A Training Algorithm for Optimal Margin Classifiers,1992:144-152.
[139]Smola A J, Lkopf B S. A Tutorial On Support Vector Regression[J]. Statistics and Computing,2004,14(3):199-222.
[140]闫国华,朱永生.支持向量机回归的参数选择方法[J].计算机工程,2009,35(14):218-220.
[141]刘胜,李妍妍.自适应GA-SVM参数选择算法研究[J].哈尔滨工程大学学报,2007(04):398-402.
[142]Zhou L C, Yang H Z, Liu C B. QPSO-Based Hyper-Parameters Selection for LS-SVMRegression[C]//Natural Computation,2008. ICNC '08. Fourth International Conference on, Jinan,2008,18-20Oct.:130-133.
[143]Shi Y, Li X, Qi X. Parameter Optimization of Support Vector Machine Based on CombinedAlgorithm of QPSO and SA[C]//Pervasive Computing Signal Processing and Applications(PCSPA),2010First International Conference on, Harbin,2010,17-19Sept.:483-486.
[144]甄立东.西门子WinCC V7基础与应用[M].北京:机械工业出版社,2011:1-9.
[145]何华.深入浅出西门子WinCC V6[M].北京:北京航空航天大学出版社,2004:112-150.
[146]谢维成,苏长明. SQL Server2005实例精讲[M].北京:清华大学出版社,2008:150-154.